![](media/image1.png){width="3.0in" height="0.9791666666666666in"}

***Technical Design Report***

***of the***

***Forward Silicon Vertex Tracker (FVTX)***

***13 November 2023***

![](media/image2.jpeg){width="3.9in" height="2.4895833333333335in"}

**Proposal for a Forward Silicon Vertex Tracker (FVTX) for the PHENIX
Experiment**

R. K. Choudhury, P. Shukla, D. Dutta, A. K. Mohanty

Bhabba Atomic Research Centre, Mumbai, India

R. Pak

Brookhaven National Laboratory, Physics Dept., Upton NY USA

K.A. Drees

Brookhaven National Laboratory, Collider Accelerator Dept., Upton NY USA

H. Pereira

CEA Saclay, Gif-sur-Yvette, France

M. Finger, M. Finger

Charles University, Prague, Czech Republic

J. Klaus

Czech Technical University, Prague, Czech Republic

P. Mikes, J. Popule, L. Tomasek, M. Tomasek, V. Vrba

Institute of Physics, Academy of Sciences, Prague, Czech Republic

B. Cole, E. Mannel, D. Winter, W. Zajc

Columbia University, NewYork, NY

J.C. Hill, J.G. Lajoie, C.A. Ogilvie, A. Lebedev, H. Pei, G.Skank,

A. Semenov, G. Sleege, F. Wei

Iowa State University, Ames, IA 56011, USA

Naohito Saito

High Energy Accelerator Research Organization (KEK), Tsukuba, Japan

T. Murakami, K. Tanida

Kyoto University, Kyoto 606, Japan

J.G. Boissevain, M.L. Brooks, S. Butsyk, C. M. Camacho, G. Grim, H.W.
van Hecke, J. Kapustinsky, A. Klein, G.J. Kunde, D.M. Lee, M.J. Leitch,
M.X. Liu, P.L. McGaughey, A.K. Purwar, W.E. Sondheim

Los Alamos National Laboratory, Los Alamos, NM 87545, USA

Hisham Albataineh, G. Kyle, H. Liu, S. Pate, X.R. Wang

New Mexico State University, Las Cruces, NM, USA

T. Alho, M. Bondila, R. Diaz, D. J. Kim, J. Rak,

University of Jyvaskyla, Finland

B. Bassalleck, D.E. Fields, M. Hoeferkamp, M. Malik, J. Turner

University of New Mexico, Albuquerque, NM, USA

J.H. Kang, Y. Kweon

Yonsei University, Seoul, Korea

**Other Interested Institutions:**

A.D. Frawley

Florida State University, Tallahassee, FL 32306, USA

B. Hong

Korea University, Seoul, Korea

[1 Executive Summary 15](#executive-summary)

[2 Physics Goals of the FVTX Endcap Upgrade
22](#physics-goals-of-the-fvtx-endcap-upgrade)

[2.1 Heavy ion Collisions and the Quark Gluon Plasma
22](#heavy-ion-collisions-and-the-quark-gluon-plasma)

[2.1.1 Energy Loss and Flow of Heavy Quarks
23](#energy-loss-and-flow-of-heavy-quarks)

[2.1.2 Charm and Bottom Measurements with the FVTX
27](#charm-and-bottom-measurements-with-the-fvtx)

[2.1.3 Separating Charm and Bottom 28](#separating-charm-and-bottom)

[2.1.4 Open Charm Enhancement 32](#open-charm-enhancement)

[2.1.5 J/ψ Suppression and Comparisons with Open charm, ψ' and ϒ
34](#jψ-suppression-and-comparisons-with-open-charm-ψ-and-ϒ)

[2.1.6 Reaction Plane and Azimuthal Asymmetries
38](#reaction-plane-and-azimuthal-asymmetries)

[2.2 Proton(Deuteron) + Nucleus Collisions and Nuclear Effects on Quarks
and Gluons
43](#protondeuteron-nucleus-collisions-and-nuclear-effects-on-quarks-and-gluons)

[2.2.1 Heavy-quarks in d-Au Collisions: Charm and Bottom Mesons
43](#heavy-quarks-in-d-au-collisions-charm-and-bottom-mesons)

[2.2.2 Disentangling the Physics of J/ψ and ϒ Production in Nuclei
50](#disentangling-the-physics-of-jψ-and-ϒ-production-in-nuclei)

[2.2.3 Hadrons at Forward and Backward Rapidity
53](#hadrons-at-forward-and-backward-rapidity)

[2.2.4 Drell-Yan Measurements 58](#drell-yan-measurements)

[2.2.5 Summary of Physics Addressed by the FVTX in d(p)+A Collisions
58](#summary-of-physics-addressed-by-the-fvtx-in-dpa-collisions)

[2.3 Polarized Proton Collisions, and the Gluon and Sea Quark Spin
Structure of the Nucleon
59](#polarized-proton-collisions-and-the-gluon-and-sea-quark-spin-structure-of-the-nucleon)

[2.3.1 The Role of the FVTX Detector 61](#the-role-of-the-fvtx-detector)

[2.3.2 Polarized Gluon Distribution and Heavy Quark Production
62](#polarized-gluon-distribution-and-heavy-quark-production)

[2.3.3 Polarized Sea Quark Distributions and *W/Z* Production
69](#polarized-sea-quark-distributions-and-wz-production)

[2.3.4 Physics with Transversely Polarized Beams
76](#physics-with-transversely-polarized-beams)

[2.3.5 Tests of pQCD Model Calculations and Providing a Baseline for pA
and AA Measurements
78](#tests-of-pqcd-model-calculations-and-providing-a-baseline-for-pa-and-aa-measurements)

[2.3.6 Summary of Physics Addressed by the FVTX in Polarized *pp*
Collisions
81](#summary-of-physics-addressed-by-the-fvtx-in-polarized-pp-collisions)

[2.4 Trigger Plans 81](#trigger-plans)

[2.5 Si Endcap Event Rates 82](#si-endcap-event-rates)

[3 FVTX Detector Performance 83](#fvtx-detector-performance)

[3.1 Simulation Code 84](#simulation-code)

[3.2 Distance of Closest Approach Measurement
84](#distance-of-closest-approach-measurement)

[3.3 Determining the Primary Vertex 91](#__RefHeading___Toc170092499)

[3.4 Heavy Quark Measurements with the FVTX Using D, B μ X
92](#heavy-quark-measurements-with-the-fvtx-using-d-b-μ-x)

[3.4.1 Error Bar Improvement on Single Muon Physics Measurements with
the FVTX
94](#error-bar-improvement-on-single-muon-physics-measurements-with-the-fvtx)

[3.5 Occupancy in Central AuAu Events
96](#occupancy-in-central-auau-events)

[3.6 Analogue Information from the FVTX
97](#__RefHeading___Toc170092503)

[3.7 Matching Tracks from the Muon Spectrometers to the FVTX
98](#__RefHeading___Toc170092514)

[4 FVTX Detector system 100](#fvtx-detector-system)

[4.1 Overview 100](#overview)

[4.2 FPHX Chip Development 102](#fphx-chip-development)

[4.3 Silicon Mini-strip Sensors and Wedge Assembly
105](#silicon-mini-strip-sensors-and-wedge-assembly)

[4.4 Electronics Transition Module and FEM
108](#electronics-transition-module-and-fem)

[4.5 Radiation Environment and Component Selection
116](#radiation-environment-and-component-selection)

[4.6 Mechanical Structure and Cooling
119](#mechanical-structure-and-cooling)

[4.6.1 Design Criteria 120](#design-criteria)

[4.6.2 Structural Support 120](#structural-support)

[4.6.3 Endcap Ladder Wedge Structure
122](#endcap-ladder-wedge-structure)

[4.6.4 Analysis of the Full VTX/FVTX Structure
124](#analysis-of-the-full-vtxfvtx-structure)

[4.7 Endcap Analysis Summary 126](#endcap-analysis-summary)

[4.8 Assembly and Integration 126](#assembly-and-integration)

[4.8.1 Assembly 126](#assembly)

[4.8.2 Integration 128](#integration)

[4.9 Q/A procedures 130](#qa-procedures)

[4.9.1 Silicon sensors, design and prototype
130](#silicon-sensors-design-and-prototype)

[4.9.2 FPHX Readout Chips, Design and Prototyping
132](#fphx-readout-chips-design-and-prototyping)

[4.9.3 High Density Interconnect (HDI)
134](#high-density-interconnect-hdi)

[4.9.4 Composite Backplane (Support/Heat Spreader)
134](#composite-backplane-supportheat-spreader)

[4.9.5 Adhesives 134](#adhesives)

[4.9.6 Wedge Assembly 135](#wedge-assembly)

[5 R+D Schedule, Responsibilities and Budget
136](#rd-schedule-responsibilities-and-budget)

[5.1 R+D Areas 136](#rd-areas)

[5.1.1 FPHX 136](#fphx)

[5.1.2 Sensor 136](#sensor)

[5.1.3 Interface 137](#interface)

[5.2 Schedule 137](#schedule)

[5.2.1 Cost 141](#cost)

[5.2.2 Project Management and Responsibilities
142](#project-management-and-responsibilities)

[6 Appendix A -- Contingency Analysis
145](#appendix-a-contingency-analysis)

[6.1 Contingency Analysis 145](#contingency-analysis)

[7 Appendix B -- The FVTX Level-1 Trigger System
149](#appendix-b-the-fvtx-level-1-trigger-system)

[7.1 Introduction 149](#introduction)

[7.2 Required Event Rejection 149](#required-event-rejection)

[7.3 FVTX LL1 Trigger Strategy 150](#fvtx-ll1-trigger-strategy)

[7.3.1 Single Displaced Tracks 151](#single-displaced-tracks)

[7.3.2 Muon Pair Trigger 152](#muon-pair-trigger)

[7.4 Combined Forward Muon Trigger 152](#combined-forward-muon-trigger)

[7.4.1 The PHENIX Muon Trigger Upgrade
152](#the-phenix-muon-trigger-upgrade)

[7.5 Combining the FVTX with the Downstream Muon Trigger
154](#combining-the-fvtx-with-the-downstream-muon-trigger)

[7.5.1 Hardware Integration of FVTX and Muon Trigger Systems
155](#hardware-integration-of-fvtx-and-muon-trigger-systems)

[7.6 Research and Development on FVTX LL1 Trigger Design
156](#research-and-development-on-fvtx-ll1-trigger-design)

[7.7 FVTX LL1 Cost Estimate 159](#fvtx-ll1-cost-estimate)

[8 Appendix C -- Estimates for Rates and Triggers for the PHENIX FVTX
162](#appendix-c-estimates-for-rates-and-triggers-for-the-phenix-fvtx)

[8.1 Cross sections, branching ratios and acceptances:
162](#cross-sections-branching-ratios-and-acceptances)

[8.1.1 D → mu X 162](#d-mu-x)

[8.1.2 B → mu X 162](#b-mu-x)

[8.1.3 B → J/ψ X 164](#b-jψ-x)

[8.2 Luminosities 164](#luminosities)

[8.3 Reality factors 165](#reality-factors)

[8.4 Summary of Changes from Old Numbers
166](#summary-of-changes-from-old-numbers)

[8.5 Rates 166](#rates)

[8.6 Rates for Prompt Vector Mesons: J/ψ, ψ' and ϒ
168](#rates-for-prompt-vector-mesons-jψ-ψ-and-ϒ)

[8.7 Trigger considerations 168](#trigger-considerations)

[8.7.1 Rejection factors 168](#rejection-factors)

[8.7.2 Trigger Rates and Needed Rejection Factors
169](#trigger-rates-and-needed-rejection-factors)

[9 Appendix D -- Synergy with other PHENIX Upgrades
171](#appendix-d-synergy-with-other-phenix-upgrades)

[9.1 Central Barrel Vertex Detector (VTX) Upgrade
171](#central-barrel-vertex-detector-vtx-upgrade)

[9.2 Muon Trigger Upgrade 171](#muon-trigger-upgrade)

[9.3 Nose Cone Calorimeter (NCC) Upgrade
172](#nose-cone-calorimeter-ncc-upgrade)

[9.4 Muon Piston Calorimeter (MPC) 173](#muon-piston-calorimeter-mpc)

**List of Figures**

[Figure 1 Conceptual layout of the PHENIX FVTX showing the four vertical
planes of each endcap in the red circles.
20](#__RefHeading___Toc170092577)

[Figure 2 - Suppression of high-p~T~ hadrons and pions as seen in Au+Au
vs d+Au collisions, measured by PHENIX and publish in PRL.
23](#__RefHeading___Toc170092578)

[Figure 3 -- High-p~T~ suppression of π^0^'s and η's -- indicative of
energy loss in large density matter; compared to no suppression of
direct photons which indicates that the initial-state is not modified.
24](#__RefHeading___Toc170092579)

[Figure 4 -- The large elliptic flow for light hadrons in Au+Au
collisions is near the hydrodynamic limit and scales with the number of
valence quarks (n) in the observed hadron when plotted vs transverse
kinetic energy (KE~T~). 25](#__RefHeading___Toc170092580)

[Figure 5 -- Heavy quark suppression and flow vs p~T~ from PHENIX
measurements using electrons in 200 GeV Au+Au collisions at mid
rapidity. 26](#__RefHeading___Toc170092581)

[Figure 6 Heavy flavor R~AA~ measurement that can be achieved with RHIC
Run 5 p+p statistics, with the FVTX detector (blue error bars) and
without the FVTX detector (red error bars). Theory predictions which
include radiative energy loss (green band), radiative energy loss plus
elastic scattering energy loss (blue band) and radiative energy loss
plus dissociation (yellow band) are shown for comparison.
28](#__RefHeading___Toc170092582)

[Figure 7 -- The DCA for semi-leptonic decays of charm (blue) and bottom
(red), light meson decays (green), and prompt punch-through hadrons
(black). 29](#_Ref36878645)

[Figure 8 -- Transverse momentum spectrum for charm and bottom decays.
The different colored curves correspond to the same primary particles as
in Figure 8 30](#__RefHeading___Toc170092584)

[Figure 9 The p~T~ of the decay muon from D mesons (lower average value)
and from B mesons (larger average value) is shown, properly normalized
by their respective cross section and branching ratios.
31](#__RefHeading___Toc170092585)

[Figure 10 - The reconstructed Z-vertex distribution for J/ψ from B
decays (black line) and for prompt J/ψ (red line). Note that the prompt
J/ψ yield has been scaled down by a factor of 100. The relative yield of
J/ψ from B decays versus prompt J/ψ is estimated to be about 1%.
32](#__RefHeading___Toc170092586)

[Figure 11 - Charm enhancement expected at RHIC from ref. 21. In both
panels, contribution from the initial gluon fusion (solid), pre-thermal
production (dot-dashed), and thermal production (dashed, lowest) are
shown. The left panel is the calculation with energy density of 3.2
GeV/fm^3^, while the right panel shows the case with energy density 4
times higher. The barely visible dotted curve in the left panel figure
is the thermal production assuming an initially fully equilibrated QGP.
In the right panel the curves with stars are the same as the
corresponding curves without stars except that the initial temperature
is reduced to 0.4 GeV (compared to 0.55 GeV).
33](#__RefHeading___Toc170092587)

[Figure 12 - Rapidity distribution from Vogt for charm in pp collisions
at √s = 200 GeV. One third of the total cross section comes from the
region of the FVTX coverage, \|y\|\>1.2
34](#__RefHeading___Toc170092588)

[Figure 13 -- J/ψ results for 200 GeV Au+Au collisions. (a) (top)
Nuclear modification factor for J/ψ at mid (red) and forward (blue)
rapidity, and (b) (bottom) the ratio of these suppressions for
forward/mid rapidity, all vs centrality in terms of the number of
participants (N~part~). 35](#__RefHeading___Toc170092589)

[Figure 14 -- Fraction of dimuon pair background containing decay muons
versus dimuon mass. At the J/ψ mass (3.1 GeV), about 60% of the total
background contains at least one decay muon, which can be rejected using
the FVTX. 36](#__RefHeading___Toc170092590)

[Figure 15 - Simulated dimuon mass spectrum for p+p collisions before
(left) and after (right) FVTX vertex cuts are applied to eliminate the
light meson decay backgrounds. The mass resolution of the J/ψ and ψ' are
improved from 150 MeV to 100 MeV, as shown, by the FVTX. These plots
correspond to a 10 week RHIC-II run and the initial J/ψ signal/noise
(before the FVTX cuts) is set according to that observed in the 2005 p+p
run. There are about 1.5 million J/ψ and 27,000 ψ' entries in the peaks.
37](#__RefHeading___Toc170092591)

[Figure 16 - Simulated dimuon mass spectrum for minimum bias Au+Au
collisions before (left) and after (right) FVTX vertex cuts are applied
to eliminate the light meson decay backgrounds. The mass resolution of
the J/ψ and ψ' are improved from 150 MeV to 100 MeV, as shown, by the
FVTX. These plots correspond to a 10 week RHIC-II run and the initial
J/ψ signal/noise (before the FVTX cuts) is set according to that
observed in the 2004 Au+Au run. There are about 400,000 J/ψ and 7,100 ψ'
entries in the peaks. 37](#__RefHeading___Toc170092592)

[Figure 17 - Azimuthal asymmetry v2 as function of pseudo rapidity for
minimum bias A-A collisions at 200 GeV. The measurement from run 4 with
the MVD pad detectors is colored in magenta; the FVTX will cover the
same range in pseudo rapidity. 39](#__RefHeading___Toc170092593)

[Figure 18 - The two dimensional color representation of the mean
reaction plane resolution as function of the charge particle
multiplicity Nhits and the elliptic flow signal v2 present in the
rapidity interval of the FVTX detector. The total number of charge
tracks expected for a mid central Au+Au collision at 200 GeV is
simulated to be about 800 traversing the FVTX silicon detector, the
previously measured elliptic flow signal v2 is on the order of 0.035,
the resulting expected mean reaction plane resolution is approximately
0.75. 40](#__RefHeading___Toc170092594)

[Figure 19 - Azimuthal asymmetry v2 (elliptic flow) as function of
centrality for A-A collisions at 200 GeV. The measurement was obtained
with the MVD pad detectors which covered in run 4 the same pseudo
rapidity rage as the FVTX will in the future.
41](#__RefHeading___Toc170092595)

[Figure 20 - Three dimensional representation of confidence level (0 to
1 corresponds to 0 to 100 percent) of a given delta phi bin as function
of the mean reaction plane resolution for the FVTX. The reaction plane
resolution of 0.75 estimated in figure 4 would result is a 65 percent
confidence level if binning the reaction plane into 3 bins. Two bins
(delta phi = 90 degrees) will give a confidence level of 85 percent for
the \'true reaction plane\' being in the measured bin.
42](#__RefHeading___Toc170092596)

[Figure 21 - Azimuthal asymmetry v1 (directed flow) as function of
centrality for A-A collisions at 200 GeV. The measurement was obtained
with the MVD pad detectors which covered the same pseudo rapidity rage
as the FVTX will. 43](#__RefHeading___Toc170092597)

[Figure 22 - Gluon shadowing from Eskola as a function of x for
different Q^2^ values: 2.25 GeV^2^ (solid), 5.39 GeV^2^ (dotted), 14.7
GeV^2^ (dashed), 39.9 GeV^2^ (dotted-dashed), 108 GeV^2^ (double-dashed)
and 10000 GeV^2^ (dashed). The regions between the vertical dashed lines
show the dominant values of *x~2~* probed by muon pair production from
charm pairs at SPS, RHIC and LHC energies.
45](#__RefHeading___Toc170092598)

[Figure 23 - Gluon shadowing calculations from Frankfurt and
Strikman^30^ that predicts substantially larger shadowing than that of
EKS^29^. 45](#__RefHeading___Toc170092599)

[Figure 24 - Diagram showing the gluon saturation region at small x and
Q^2^. 46](#__RefHeading___Toc170092600)

[Figure 25 - Gluon shadowing predictions along with PHENIX coverage. The
red bars indicate the additional range provided by the FVTX upgrade,
green bars are for the barrel (VTX) upgrade, while the blue bars cover
the PHENIX baseline. The red and blue curves are the theoretical
predictions for gluon shadowing from EKS^29^ and FGS^30^ for different Q
values. 47](#__RefHeading___Toc170092601)

[Figure 26 - Vitev, et. al.^32^ predictions of coherent power
corrections (left panel) and the sum of the power corrections and
initial state energy loss (right) for the nuclear dependence of D meson
production compared to prompt muon data from PHENIX fromn dAu
collisions. Significant energy loss is predicted.
48](#__RefHeading___Toc170092602)

[Figure 27 - Nuclear modification factor in d+Au collisions, R~dAu~, for
prompt muons in the forward and backward rapdity regions versus p~T~.
The prompt muons are primarily from the decays of charm and bottom
mesons although perhaps 10% are from other processes such as light meson
decays. 49](#__RefHeading___Toc170092603)

[Figure 28 -- Vitev's calculations show that gluon fusion is not the
dominant process in open charm production at RHIC energies. Here he
shows the fraction of the total cross section contributed by each
process vs p~T~ for different rapidity values for the processes (1)
$\text{cg} \rightarrow \text{cg}$, (2) $\text{cq} \rightarrow \text{cq}$
(where *q* is a light quark or anti-quark), (3)
$\text{gg} \rightarrow c\overline{c}$, (4)
$q\overline{q} \rightarrow c\overline{c}$ and (5)
$c\overline{c} \rightarrow c\overline{c}$(intrinsic charm).
50](#__RefHeading___Toc170092604)

[Figure 29 - J/ψ nuclear dependence versus rapidity, compared to
theoretical predictions with two types of gluon shadowing^36^.
51](#__RefHeading___Toc170092605)

[Figure 30 - The dependence of alpha on x~2~ and x~F~ for J/ψ production
shows that the suppression does not scale with x~2~ but does exhibit
approximate scaling with x~F~. Alpha is defined as
$\sigma_{A} = \sigma_{p}A^{\alpha}$, where $\sigma_{p}$($\sigma_{A}$) is
the nucleon (heavy nucleus, A) cross section. Data is from PHENIX (√s =
200 GeV) ^35^, E866/NuSea (√s = 39 GeV) and NA3 (√s = 19 GeV).
52](#__RefHeading___Toc170092606)

[Figure 31 -- PHENIX J/ψ nuclear depedence data for Au+Au and Cu+Cu
collisions versus centrality at forward and mid rapidity. The shaded
areas are EKS shadowing calculations with absorbtion cross sections
between 0 and 3 mb. 53](#__RefHeading___Toc170092607)

[Figure 32 - Nuclear modification factor in d+Au collisions (R~dAu~) for
hadrons decaying into muons in the forward (red) and backward (blue)
rapidity directions (PHENIX Preliminary).
54](#__RefHeading___Toc170092608)

[Figure 33 -- Nuclear modification in d+Au collisions in terms of the
ratio between central and peripheral collision yields, Rcp, for light
hadrons that decay into muons from PHENIX, compared to similar results
from Brahms and to PHENIX data for the J/ψ.
55](#__RefHeading___Toc170092609)

[Figure 34 -- Calculations from Vitev^32^ Top: Suppression of the single
inclusive hadron yields in d+Au collisions versus p~T~ for rapidities
y~1~ = 1.25 and 2.5. Bottom: Impact parameter dependence of the
calculated nuclear modification for central, b=3 fm, minimum bias, 5.6
fm and peripheral, 6.9 fm, collisions. 56](#__RefHeading___Toc170092610)

[Figure 35 -- Calculations from Kopeliovich^28^ Ratio of negative
particle production rates in d+Au and p+p collisions as a function of
p~T~. Data are from Ref. , solid and dashed curves correspond to
calculations with the diquark size 0.3 fm and 0.4 fm, respectively.
57](#__RefHeading___Toc170092611)

[Figure 36 - Dimuon mass spectrum from E866/NuSea, showing the Drell-Yan
mass region used in their analysis, which excluded masses below 4
GeV/c^2^ because of the large backgrounds from open charm decays
(labeled Randoms) in that region. 58](#__RefHeading___Toc170092612)

[Figure 37 - Global polarized quark and gluon distributions from AAC
collaboration. The red line is the result of their fit, and the green
band is the total uncertainty with respect to the red line. The other
colored lines are alternative parameterizations of these distributions.
60](#__RefHeading___Toc170092613)

[Figure 38 - Expected *x*-range for different channels used to extract
the gluon spin structure function. The blue bars indicate PHENIX's
existing capability, green bars are for the Barrel upgrade, while the
red bars indicate the additional coverage provided by the proposed
Endcap vertex upgrade. The curves show various estimates of the expected
gluon polarization. 61](#__RefHeading___Toc170092614)

[Figure 39 - At RHIC-SPIN, quarks and gluons interact directly at
leading order. 62](#__RefHeading___Toc170092615)

[Figure 40 The error bars that would be obtained on an ALL measurement,
assuming 32 pb^-1^ integrated luminosity with (blue) and without (red)
the FVTX detector. 64](#__RefHeading___Toc170092616)

[Figure 41 - Muon *p*~T~ spectra with different origins from Pythia
simulation, as a function of *p*~T~ \[GeV\]. Muons from light charged
hadron decays (black); from open charm (green); from open bottom (red).
65](#__RefHeading___Toc170092617)

[Figure 42 - Partonic origin of charged pions produced within the
acceptance of muon spectrometer in pp collisions at  √s = 200 GeV.
65](#__RefHeading___Toc170092618)

[Figure 43 A~LL~ measurement for hadrons obtained with (blue) and
without (red) the FVTX detector. 66](#__RefHeading___Toc170092619)

[Figure 44 - J/ψ measurement from run5 pp run. The J/ψ peak clearly
stands out from the background. The background fraction is about 25%
under the J/ψ mass peak. 67](#__RefHeading___Toc170092620)

[Figure 45 - The first measurement of double spin asymmetry from
polarized *pp* collisions at RHIC. 67](#__RefHeading___Toc170092621)

[Figure 46 - Expected experimental sensitivities of double spin
asymmetry measurements with prompt J/ψ (not from *B* decay).
68](#__RefHeading___Toc170092622)

[Figure 47 - Left panel: Correlation between gluon x1 and p~Z~ of J/ψ
from B meson decays (PYTHIA simulation.) Right panel: Correlation
between x2 and p~T~. 69](#__RefHeading___Toc170092623)

[Figure 48 -- W production and decay to a muon plus a neutrino.
70](#__RefHeading___Toc170092624)

[Figure 49 The single muons from W decay (red) and the muons from
various p~T~ bins which are mis-reconstructed to higher momentum. As can
be seen, the lowest (true) p~T~ bins make the largest contributions to
the (fake) backgrounds at high p~T~. 71](#__RefHeading___Toc170092625)

[Figure 50 - Expected flavor dependent polarized quark distribution
functions measured by the PHENIX muon spectrometers.
72](#__RefHeading___Toc170092626)

[Figure 51 Schematic of an isolation cut: the number of particles in a
given layer that are within a cone are counted and if the number found
is less than some value the particle is considered to be "isolated" and
if it is larger than that value it is not isolated.
73](#__RefHeading___Toc170092627)

[Figure 52 The number of particles (y axis) that are found in an event
surrounding a muon from minimum bias events (blue) and muons from W
events (red), versus momentum. 73](#__RefHeading___Toc170092628)

[Figure 53 Efficiency for background and and signal tracks in the single
particle spectrum, for each successive cut. Red is the W efficiency with
all cuts, turquoise is the background with muon quality cuts and FVTX
hits ≥3, green adds the MuTr+FVTX χ^2^ cut and black adds the isolation
cut. 75](#__RefHeading___Toc170092629)

[Figure 54 The W signal and background muon contributions before cuts
(black dotted is background and red dotted is W signal) and after track
cuts (black solid is the background and red solid is the W signal)
75](#__RefHeading___Toc170092630)

[Figure 55 - Maximized values of transverse single spin asymmetry A~N~
for the process pp-\>DX as a function of x~F~ at fixed transverse
momentum calculated using saturated Sivers function. The dashed line
corresponding to a maximized quark Sivers function (with the gluon
Sivers function set to zero), while the dotted line corresponding to a
maximized gluon Sivers function (with the quark Sivers function set to
zero). Red marks indicate the x~F~ range that the PHENIX upgrade
detectors can measure. 78](#__RefHeading___Toc170092631)

[Figure 56 -- Predicted double spin asymmetry for charmonium at RHIC.
The asymmetry value depends on the final state charmonium polarization,
which can be tested experimentally. The red circles indicate the
acceptance region for the PHENIX muon arms and FVTX detector.
79](#__RefHeading___Toc170092632)

[Figure 57 Heavy flavor production diagrams from flavor excitation
(left) and gluon fusion (right) 80](#__RefHeading___Toc170092633)

[Figure 58 Back-to-back correlation expected for flavor excitation is
shown in blue and for flavor creation (gluon-gluon fusion) is shown in
red. Note the strong correlation when c-cbar pairs are created in flavor
creation as opposed to the non-existent correlation that would be true
if single charm production were the primary production mechanism.
80](#__RefHeading___Toc170092634)

[Figure 59 - Principle of operation of the FVTX silicon endcap detector
in the r-z plane. A D meson is produced at the collision point. It
travels a distance proportional to its lifetime (purple line), then
decays to a muon (green line). The muon's trajectory is recorded in the
four layers of silicon. The reconstructed muon track (dashed line) has a
small, but finite distance of closest approach (dca) to the collision
point (black line). The primary background is muons from pion and kaon
decays, which have a much larger average DCA.
85](#__RefHeading___Toc170092635)

[Figure 60 - Plot of vertex silicon layers hit as a function of muon
track angle (y-axis) and primary vertex position (x-axis). The magenta
crosshatched area includes tracks that hit all four FVTX layers (labeled
endcap hits), while the red hatched area has three VTX hits. The area
above the dark blue lines (labeled barrel) indicates the number of
barrel pixel layers hit, either one or two. Over much of the FVTX active
area, at least one barrel pixel layer is also hit.
86](#__RefHeading___Toc170092636)

[Figure 61 The DCA resolution in r (left) and phi (right) for just the
FVTX (red) and for the FVTX plus VTX hits (black). Note that the
resolution improvement is primarily in the phi coordinate, which is the
good measurement direction for the VTX.
87](#__RefHeading___Toc170092637)

[Figure 62 - Top panel: The DCA resolution in the r direction, versus
ptotal, for prompt muons and a detector with 75 μm (red) and 50 μm
(black) strip pitch. Bottom panel: the same, except the DCA resolution
is in the phi direction. 88](#__RefHeading___Toc170092638)

[Figure 63 The DCA resolution in r (top) and in phi (bottom) for a
detector which has all strips oriented with zero degrees with respect to
a circular chord and the same for a detector which has two stations with
strips oriented at 11 degrees with respect to the baseline strips.
89](#__RefHeading___Toc170092639)

[Figure 64 The DCA r resolution (top) and phi resolution (bottom) for a
detector which has the sensors at all stations in the same phi
positions, and the same resolutions for a detector which has the sensors
in each station rotated by ¼ of a sensor width with respect to each
other. 90](#__RefHeading___Toc170092640)

[Figure 65 - The p~T~ distribution of negative prompt muons (muons from
heavy quarks), decay muons from π and K and punch-through hadrons at
pseudorapidity (η) = -1.65. The punch-throughs become the dominant
background for p~T~ values above 3 GeV. The curves are simulations,
based on real data extrapolations, while the data are PHENIX
measurements. 92](#__RefHeading___Toc170092641)

[Figure 66 -- Signal to background improvement for Ds (left) and Bs
(right) which decay to μ^+^ for no vertex cut and successive FVTX cuts.
Cuts applied are χ^2^ cut, DCA cut in the phi direction, and DCA cut in
the r direction. 93](#__RefHeading___Toc170092642)

[Figure 67 - Signal to background improvement for Ds (left) and Bs
(right) which decay to μ^-^ for no vertex cut and successive FVTX cuts.
Cuts applied are χ^2^ cut, DCA cut in the phi direction, and DCA cut in
the r direction. 94](#__RefHeading___Toc170092643)

[Figure 68 The fractional reduction in statistical and systematic error
bars that we would obtain for Run 2 pp data cross section measurement if
we had the FVTX included in the analysis. Note that additional
statistical error bar improvements will be obtained just by increasing
the integrated luminosity with respect to Run 2.
95](#__RefHeading___Toc170092644)

[Figure 69 The statistical and systematic error bars from run 2 p+p data
are shown for μ+ (left) and μ- (right) with (blue) and without (red) the
FVTX. 96](#__RefHeading___Toc170092645)

[Figure 70 - Simulated occupancy at the first silicon plane for Au+Au
central collisions using the HIJING model. The color scale is in units
of hits per cm^2^, with a maximum of 7 hits per cm^2^ at the inner
radius. The other silicon planes have lower occupancies.
97](#__RefHeading___Toc170092646)

[Figure 71 - Matching of 3 GeV muon tracking tracks with FVTX silicon
tracks in central Au+Au collisions. The red historgram shows the Kalman
filter χ^2^ for the correctly matches tracks while the black histogram
shows that for the soft pion background tracks. The correct FVTX track
is matched 75% of the time. 99](#__RefHeading___Toc170092649)

[Figure 72 - Matching of 9 GeV muon tracking tracks with FVTX silicon
tracks in central Au+Au collisions. The red histogram shows the Kalman
filter χ^2^ for the correctly matches tracks while the black histogram
shows that for the soft pion background tracks. The correct FVTX track
is matched 93% of the time 99](#__RefHeading___Toc170092650)

[Figure 73 - 3-D model of the full vertex detector showing the barrel
portion and the endcaps on left and on the right. The Readout Out Cards
are at either end of the detector at a larger radius and visible in the
exploded view on the left. 100](#__RefHeading___Toc170092651)

[Figure 74 A block diagram of the readout system required for the FVTX.
The red block (ROC) and blue block (FEM) are boards which will reside
between the FPHX readout chip and the DCM and are currently under
development. 101](#__RefHeading___Toc170092652)

[Figure 75 The FPHX amplifier front end.
103](#__RefHeading___Toc170092653)

[**Figure 76 Pulse Shape before and after shaper**.
104](#__RefHeading___Toc170092654)

[**Figure 77 Noise vs. Capacitance**. 104](#__RefHeading___Toc170092655)

[Figure 78 The large wedge assembly on the left showing the location of
the sensor and chips and blow up the bottom of the wedge n more detail
on the right. 107](#__RefHeading___Toc170092656)

[Figure 79 The HDI and wedge stack up. The radiation length of the wedge
is 1.2%. 107](#__RefHeading___Toc170092657)

[Figure 80 The noise canceling strategy for the HDI.
108](#__RefHeading___Toc170092658)

[Figure 81 The silicon tracker region, indicating at the far right the
location of the ROCs for the FVTX. 110](#__RefHeading___Toc170092659)

[**Figure 82 Block diagram of the ROC which will take data from 56
chips, derserialize and strip off the sync words, serialze the data and
send it out on fiber**. 111](#__RefHeading___Toc170092660)

[Figure 83 Layout of a ROC board which would span 30° and service 4
layers\*4 sensor wedges. Shown are the connectors would would receive
signals from and route signals to the FPHX chips, the FPGAs which would
compress the data, serdes which serialize the data and fiber drivers
which sned the combined data to the FEMs and Lvl-1 boards. Voltage
regulators and LVDS repeaters are also included above.
112](#__RefHeading___Toc170092661)

[Figure 84 -- Block diagram of the data buffering for the FEM.
114](#__RefHeading___Toc170092662)

[Figure 85 Block diagram of the FVTX readout electronics components.
115](#__RefHeading___Toc170092663)

[Figure 86 Design concepts studied for the vertex detector support
structures. The center most concept with the constant outer diameter
shell had the highest fundamental frequency.
121](#__RefHeading___Toc170092664)

[Figure 87 First mode shape that dominated the dynamic structural
stiffness analysis 121](#__RefHeading___Toc170092665)

[Figure 88 Displacement and principle stress from a 1.0g gravity load on
a full mass loaded structure 122](#__RefHeading___Toc170092666)

[Figure 89 The forward region disk assembly is shown on the left and a
close up of the detail showing the individual wedges is at right.
122](#__RefHeading___Toc170092667)

[Figure 90 Thermal analysis of the wedge assembly. The temperature
gradient from top to bottom is 2.5 deg C.
123](#__RefHeading___Toc170092668)

[Figure 91 The FVTX modal analysis. The first modal frequency is 83.9 Hz
is seen as a pivoting about the attachment points.
124](#__RefHeading___Toc170092669)

[Figure 92 FEA model of the combined VTX and FVTX. The first modal
frequency is 38.5 Hz 125](#__RefHeading___Toc170092670)

[Figure 93 Full system FEA. The first frequency mode is 24 Hz.
125](#__RefHeading___Toc170092671)

[Figure 94 Assembly jigs for Backplane to HDI in the left panel and the
sensor to HDI in the right panel. 127](#__RefHeading___Toc170092672)

[Figure 95 Exploded view of the disk showing the series of alignment
pins on the outer and inner radius. The alignment pins accurately locate
the wedges on the disk. 127](#__RefHeading___Toc170092673)

[Figure 96 Closeup view of the outer boundary of the disk assembly
showing the tab for attachment to the FVTX cage. Located at three points
on the circumference, the disk is pinned accurately to the cage and then
fastened with a screw. 128](#__RefHeading___Toc170092674)

[Figure 97 -- PHENIX Forward Silicon Vertex (FVTX) project timeline.
141](#__RefHeading___Toc170092675)

[Figure 98 - Organizational Chart for the FVTX project.
143](#__RefHeading___Toc170092676)

[Figure 99 - A schematic representation a displaced vertex cut in the
FVTX Level-1 as a function of momentum. The upper limit is designed to
reject muons from pion and kaon decays, while the lower cut defines a
minimum distance from the event vertex. To avoid potential bias against
high momentum decays and still achieve a reasonable rejection factor, it
will be necessary to change the upper cut as a function of momentum.
151](#__RefHeading___Toc170092677)

[Figure 100 - The PHENIX Muon Trigger Upgrade is designed to provide an
effective trigger on muons from the decay of polarized W bosons in
polarized p+p collisions at 500GeV. Such muons dominate the inclusive
muon production above a momentum of \~20GeV/c. The location of the
additional RPC chambers that will be added to the PHENIX muon arm are
shown at right. 153](#__RefHeading___Toc170092678)

[Figure 101 - Block diagram showing the communication between the FVTX
and combined MuID and MuRPC triggers with the Combined Trigger
Processor. Each LL1 system will have the ability to send trigger data to
Global Level-1 (GL1) for independent triggering, or the primitives can
be combined in the Combined Trigger Processor (as described in the text)
to generate trigger primitives based on information from both systems.
154](#__RefHeading___Toc170092679)

[Figure 102 - Block diagram of the FVTX LL1 trigger algorithm, as
implemented by Northern Microdesign for STTR Phase-1 feasibility
testing. 159](#__RefHeading___Toc170092680)

[Figure 103 - Cross section calculations for bottom with FONNL for
various parameters from Ramona Vogt. 163](#__RefHeading___Toc170092681)

**List of Tables**

[Table 1 -- Level-1 Rejection factors needed beyond those available from
the present muon triggers. 81](#__RefHeading___Toc170092682)

[Table 2 -- Triggered rates for RHIC-II p+p and Au+Au in one week of
running. Integrated luminosities are 33 pb^-1^ for p+p and 2.5 nb^-1^
for Au+Au. The semi-leptonic decay rates are before application of a
vertex cut. 83](#__RefHeading___Toc170092683)

[Table 3 - Determination of primary vertex using prompt pions, shown
versus collision species. 91](#__RefHeading___Toc170092684)

[Table 4 - Summary of the parameters of the FVTX disks.
101](#__RefHeading___Toc170092685)

[Table 5 Power consumption calculations for the FVTX ROC card
components. 113](#__RefHeading___Toc170092686)

[Table 6 - Buffer requirements for the transition module for most
challenging case of AuAu events, various options of readout lines/chip,
different levels of chip "ganging", and a extremely conservative noise
estimate. In addition the time to readout an event is given for the same
conditions. 115](#__RefHeading___Toc170092687)

[Table 7 FVTX distortions from gravity and temperature gradients.
124](#__RefHeading___Toc170092688)

[Table 8 -- Cost estimate for the FVTX endcaps with contingency. The
methodology used for contingency is in Appendix A (Section 6).
142](#__RefHeading___Toc170092689)

[Table 9 - Technical, cost and schedule risk factors.
148](#__RefHeading___Toc170092690)

[Table 10 - Technical, cost, schedule and design weighting factors.
148](#__RefHeading___Toc170092691)

[Table 11 - Event rejection required beyond the MuID LL1 for RHIC-I
(2008) and RHIC-II running for single muon triggers.
149](#__RefHeading___Toc170092692)

[Table 12 - Event rejection required beyond the MuID LL1 for RHIC-I
(2008) and RHIC-II running for di-muon triggers.
150](#__RefHeading___Toc170092693)

[Table 13 - Physics signals and potential FVTX and muon trigger
primitive combinations that could be used to generate Level-1 triggers.
155](#__RefHeading___Toc170092694)

[Table 14 - Time budget for the STTR Phase-I FVTX algorithm as described
in the text. Notes that the time required for the line finding algorithm
could be reduced with added parallelization.
158](#__RefHeading___Toc170092695)

[Table 15 - Cost estimate breakdown for the FVTX LL1 trigger. The
estimate is based on the conceptual design as outlined in the proposal
and assumes that the prototype board design is completed as part of the
Northern Microdesign Phase-II STTR. The Combined Trigger Processor is
assumed to be a GenLL1 Rev2 board, as used in the Muon RPC trigger, so
the costs shown are for materials and additional programming.
160](#__RefHeading___Toc170092696)

[Table 16 - Luminosity estimates for RHIC-II from Thomas Roser.
164](#OLE_LINK20)

[Table 17 - Summary of luminosities used in these rate calculations for
RHIC-II and RHIC-I (2008). 165](#__RefHeading___Toc170092698)

[Table 18 - Comparison of new and old values for various parameters used
in these rate calculations. 166](#__RefHeading___Toc170092699)

[Table 19 Estimated rates per week for p+p collisions
166](#__RefHeading___Toc170092700)

[Table 20 -- p+p rates vs p~T~ for same estimates as in Table 19.
167](#__RefHeading___Toc170092701)

[Table 21 Estimated rates per week for d+Au collisions.
167](#__RefHeading___Toc170092702)

[Table 22 d+Au rates vs p~T~ for same estimates as inTable 21.
167](#__RefHeading___Toc170092703)

[Table 23 Estimated rates per week for Au+Au collisions.
167](#__RefHeading___Toc170092704)

[Table 24 Au+Au rates vs p~T~ for same estimates as in Table 23.
168](#__RefHeading___Toc170092705)

[Table 25 - Counts for prompt vector mesons per week into both muon arms
at RHIC-II luminosity. 168](#__RefHeading___Toc170092706)

[Table 26 - Level-1 muon trigger rejection factors for pp and AuAu based
on previous data and simulations of the level -1 triggers.
169](#__RefHeading___Toc170092707)

[Table 27 -- Estimated trigger rates and addition rejection factors
needed for p+p and Au+Au collisions in PHENIX.
170](#__RefHeading___Toc170092708)

#   {#section .unnumbered}

# Executive Summary

The main goal of the RHIC heavy ion program is the identification and
study of the hot, high-energy-density matter created in heavy ion
collisions, the Quark Gluon Plasma (QGP). Measurements to date support
the formation of the QGP at RHIC[^1]^,^[^2]^,^[^3]^,^[^4], but the
detailed properties of the plasma are only poorly determined. It is
widely recognized in the RHIC community that the direct detection of
heavy quarks, such as charm and beauty, provides one of the most
powerful probes of the plasma and is the next frontier of RHIC physics.
We propose the construction of two Forward Silicon Vertex Trackers
(FVTX) for the PHENIX experiment that will directly identify and
distinguish charm and beauty decays within the acceptance of the muon
spectrometers. The FVTX will provide this essential coverage over a
range of forward and backward rapidities (1.2 \< \|y\| \< 2.4) -- a
rapidity range coverage which not only brings significantly larger
acceptance to PHENIX but which is critical for separating cold nuclear
matter effects from QGP effects and is critical for measuring the proton
spin contributions over a significant fraction of the kinematic range of
interest. In addition, the FVTX will provide greatly reduced background
and improved mass resolution for dimuon events, culminating in the first
measurements of the ψ\' and Drell-Yan at RHIC. These same heavy flavor
and dimuon measurements in p+p collisions will allow us to place
significant constraints on the gluon and sea quark contributions to the
proton's spin and to make fundamentally new tests of the Sivers function
universality.

From measurements that have been made at RHIC to date, the energy loss
of quarks or gluons traversing this dense matter is apparently very
large, leading to the observed large suppression of high transverse
momentum light-quark mesons. However, the surprising results that there
is comparable suppression of heavy-quark mesons, and comparable flow at
low to intermediate p~T~, has raised many questions about our
understanding of the interaction of the quarks in the medium formed: Are
there more mechanisms than radiative energy loss that are contributing
to the large suppression of light-quark and heavy quark mesons? Is the
heavy-quark radiative energy loss much larger than predicted or are
there additional suppression mechanisms which affect heavy quarks more
than light quarks? Could solving the uncertainties in the radiative
energy loss and the uncertainties in cold nuclear matter effects lead to
different extraction of the medium's properties? With the baseline
PHENIX detector, these questions cannot be addressed because the heavy
flavor measurements have very large systematic error bars due to large
backgrounds and there is no capability for separating charm and bottom;
therefore, the various model predictions cannot be separated from each
other.

To address these questions, and many more that we will outline, we
propose the construction of two Forward Silicon Vertex Trackers (FVTX)
for the PHENIX experiment at RHIC, these trackers will allow for
precision measurements of heavy quark production and the separation of
the charm and bottom components. These detectors will extend the vertex
capabilities of the PHENIX Silicon Vertex Tracker (VTX) to cover a much
larger rapidity interval, including forward and backward rapidities, and
allow displaced track and secondary vertex measurements in conjunction
with the PHENIX muon arms. The heavy flavor measurements provided by
these detectors will move us from making qualitative statements that
heavy flavor is suppressed in heavy ion collisions to being able to
distinguish among models which include radiative energy loss,
collisional energy loss, and/or collisional dissociation for light and
heavy quarks---a distinction which is not possible without the addition
of a vertex detector, and without which there remains large uncertainty
in what the various suppression mechanisms are for light and heavy
quarks and what the extracted properties of the medium should be. By
adding vertexing capability covering the muon arms we not only increase
the acceptance for physics observables by a factor of 3-10 but also
allow coverage in the forward rapidity regions -- coverage which is
critical to separate cold nuclear matter effects from QGP effects, and
critical for understanding the geometric extent of the medium.

J/ψ vector mesons are also considered to be a very sensitive probe of
the dense matter created in heavy ion collisions and have been shown to
be highly suppressed at RHIC\], as they were at SPS. At SPS the
suppression of J/ψ production was one of the measurements given to
support the statement that a new state of matter (the QGP) was
forme^\[^\]. The baseline PHENIX detector was designed to provide good
measurements of J/ψ production. However, to understand the modification
of J/ψ production in the medium, these measurements must be coupled with
precise open heavy flavor measurements that can constrain recombination
models. The FVTX will provide the needed precision open heavy flavor
measurements to allow for a much better understanding of J/ψ
suppression. Together with this, we need to measure production of other
vector mesons such as ψ' and χ~c~ to understand Debye screening
contributions. With the addition of the FVTX detector, we will be able
to separate the ψ' and J/ψ production through improved mass resolution
and enhanced background rejection. These new measurements, coupled with
the J/ψ measurements should significantly advance our understanding of
J/ψ suppression in heavy ion collisions.

The RHIC spin program was developed to determine the gluon and sea quark
contributions to the proton's spin and (possibly) put constraints on the
angular momentum contributions to the spin. With the addition of the
FVTX detectors, we will significantly extend the x coverage for gluon
spin measurements in PHENIX by adding precision heavy flavor asymmetry
measurements at forward and backward rapidities which are sensitive to
the gluon spin distribution. These measurements cannot be made with the
baseline detector alone. Measuring the gluon spin distributions over a
large x coverage is critical for extracting ∆G = ∫∆G(x)dx. The FVTX
detector will provide precise Drell-Yan measurements (in conjunction
with the muon arms), which will allow measurements of sea quark
contributions to the proton's spin because the Drell-Yan production
asymmetry is sensitive to the ubar polarization. This provides us a
unique opportunity to produce a sea quark measurement which is
complimentary to the W measurements that are proposed. The FVTX will
also provide unique track reconstruction constraints which will help
reject hadronic backgrounds which contribute to the single muon spectra.
The single muon spectra will be used to measure sea quark contributions
to the proton spin by extracting the WμX single spin asymmetry at high
p~T~ so background rejection at high p~T~ is essential to making a
precision measurement.

The Drell-Yan measurements with polarized proton beams will also allow
for a new fundamental test of QCD theory. Sivers-type single-spin
asymmetry has been observed in semi-inclusive DIS at HERMES and COMPASS
very recently[^5]^,^[^6]. A fundamental prediction of QCD is that such
effects will give an opposite sign in the transverse single spin
asymmetry in DY production in p+p collisions[^7]. Its verification (or
not) will be an important milestone in our study of the strong
interaction, as it tests all concepts for analyzing hard-scattering
reactions that we know of today.

With the present PHENIX detector, heavy-quark production in the forward
and backward directions has been measured indirectly via the observation
of single muons. The current measurements are inherently limited in
accuracy by systematic uncertainties resulting from the large
contributions to the single muon spectra from prompt pion and kaon
semi-leptonic decays and from pion and kaons which punch through the
entire muon system and are mistakenly tagged as muons. In addition, the
analysis does not allow for a model-independent separation of the charm
and bottom contributions. The FVTX detector will provide vertex tracking
with a distance of closest approach (DCA) resolution in r-z that is
better than 100 μm over a large coverage in rapidity (1.2 \< \|η\| \<
2.2) and with full azimuthal coverage. This will allow for vertex cuts
which separate prompt particles from decay particles and short-lived
heavy quark mesons from long-lived light mesons (pions and kaons). In
addition, bottom measurements can be made directly via B → J/ψ+X by
looking for a displaced J/ψ vertex, and this will allow charm and bottom
contributions to be separated in semi-inclusive single lepton
measurements. Therefore, with this device fundamentally new measurements
can be made and current muon measurements will be significantly
enhanced.

The precision of the J/ψ and other dimuon measurements in AuAu
collisions is currently limited by the large amount of combinatorial
background that must be subtracted from the opposite sign dimuon signal
obtained with the muon tracker and by the inherent mass resolution. With
added rejection power for pion and kaon decays, the significance of all
dimuon measurements will be greatly improved. Further improvement in
these measurements results from the improved mass resolution, which will
be attained because of the more accurate determination of the opening
angles of the dimuons. All together, this will result in improved dimuon
data as well as provide access to several new measurements: separation
of ψ' from J/ψ, extraction of a Drell-Yan signal from the dimuon
continuum, extraction of B→J/ψ and measurement of upsilons at central
rapidity.

The FVTX adds several additional enhancements to PHENIX:

-   Enhances tracking resolution for tracks passing through the muon
    system by adding measurement points close to the vertex

-   Provides a fast data path for a Level-1 FVTX trigger

-   Helps with electron/photon separation for the Nose Cone Calorimeter

-   Improves event vertex location determination for triggering and
    offline analyses

-   Gives an event topology cut capability for heavy quarks

-   Provides unique track cuts which allow rejection of hadronic
    backgrounds in the single muon spectra

-   Provides reaction plane measurement.

As a result of this proposed upgrade, numerous areas of physics
exploration will become accessible, as summarized here in three broad
classes associated with the type of collision:

-   A+A collisions and the Quark Gluon Plasma:

    -   Study of energy loss and flow of heavy quarks into very forward
        and backward rapidity regions using robust charm and bottom
        measurements over a broader x range than available with the
        barrel VTX detector alone and with greater precision than is
        possible with the muon detectors alone. This allows the
        extension of studies of the geometrical and dynamical effects of
        the hot-dense matter created in high-energy heavy ion collisions
        into the forward and backward rapidity regions and will allow
        for the first time separate measurements for charm and bottom.

    -   Precise open charm and bottom measurements will provide a solid
        \"denominator\" for comparison with production of bound states
        of heavy quarks (J/ψ and ϒ). These comparisons will allow for
        the isolation of common physics, e.g., initial-state effects
        such as those on the gluon structure function and physics that
        only affects the bound states, e.g., final-state absorption.
        These measurements will also provide strong constraints on
        production of J/ψs from recombination by determining a precise
        open-charm cross section over a broad rapidity range.

    -   Direct measurement of ϒs at mid-rapidity will be possible by
        eliminating the large random backgrounds from light-meson
        decays. Will also improve the mass resolution and
        signal/background for J/ψ production and enable improved
        separation of the J/ψ from the ψ'.

    -   Unambiguous measurement of the Drell-Yan and heavy-flavor dimuon
        continuum by separating background muons from light meson
        decays, muons from heavy flavor decay and prompt muons.

    -   An accurate reaction plane measurement will be provided by the
        FVTX.

    -   Flow in the forward and backward regions will be able to be
        measured.

-   p(d)+A collisions and small-x or gluon saturation physics:

    -   The study of the gluon structure function modification in nuclei
        at small (and large) *x* values, where gluon saturation or
        shadowing (anti-shadowing) is thought to be important will be
        possible, by adding precision open charm and bottom measurements
        at forward rapidity.

    -   Determine the initial state for AA collisions and provide a
        robust baseline for cold-nuclear matter effects in studies of
        hot-dense matter in heavy ion collisions, again by adding
        precision heavy flavor measurements at forward rapidity.

    -   Help untangle the intricate physics of J/ψ and ϒ production in
        cold nuclear matter by providing robust measurements of
        open-heavy quark production that can, by contrast, separate
        initial and final-state physics for these resonances.

    -   Allow for a clean measurement of Drell-Yan which can further
        help untangle production issues for the J/ψ.

```{=html}
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```
-   Polarized p+p collisions, and the contributions to the spin of the
    nucleon:

    -   Provide an increased x range (up to x ≈ 0.2 and down to 10^-3^)
        over which the mostly unknown gluon polarization (*∆G/G*) can be
        determined through open heavy flavor measurements. Without the
        FVTX the range covered is likely to be insufficient to study the
        shape of any polarization or to determine its peak value.

    -   Allow for a direct measurement of the spin asymmetry in bottom
        production, which is expected to be different from open charm
        and light hadrons, thus providing much-needed cross checks.

    -   Add background rejection capabilities for W and Z bosons
        measurements (which give information about the sea-quark
        contributions to the spin) by rejecting muons from light and
        heavy hadron decays which contribute to the high p~T~ muon
        spectra and by adding the possibility of event topology cuts.

    -   Enable Drell-Yan asymmetry measurements, which can give
        information about the sea quark polarization distributions.

The FVTX will be composed of two endcaps, with four silicon mini-strip
planes each, covering angles (1.2 \< \|η\| \< 2.2) that match the two
muon arms. Each silicon plane consists of wedges of mini-strips with 75
μm pitch in the radial direction and 3.75° wide strips in phi, which
translates to lengths in the phi direction varying from 2.8 mm at small
angles to 12.1 mm at 35 degrees. An r-z DCA resolution of 100 μm can be
achieved with a maximum occupancy per strip in central Au+Au collisions
of less than 2.8%. A picture of the detector is shown in Figure 1. The
four stations of the North and South FVTX arms are circled in red, the
central support structure for the VTX system can be seen between the
two, and the large gray planes surrounding the FVTX sensors are the
planes that will hold the readout electronics for the VTX and FVTX
systems.

![](media/image11.jpeg){width="6.134027777777778in"
height="4.598611111111111in"}

[]{#__RefHeading___Toc170092577 .anchor}Figure 1 Conceptual layout of
the PHENIX FVTX showing the four vertical planes of each endcap in the
red circles.

The FVTX will consist of approximately 1.1 million mini-strips that will
be read out with an IC chip (FPHX) to be designed by Fermilab, which is
wire-bonded directly to the mini-strips. This chip will provide analog
and digital processing with zero-suppression and produces a digital
output which is \"data-pushed\" at 200 Mbps to intelligent readout
boards containing FPGAs. The data are then transformed into the standard
PHENIX format and transmitted to the PHENIX DAQ system via fiber optics.
In parallel, a fast \"level-1\" trigger algorithm can be run on the data
to select interesting heavy-quark events.

The FPHX is a custom IC being designed by engineers in the Fermi
National Accelerator Laboratory Particle Physics Division. The chip
design borrows heavily from previously successful IC designs, FPIX2,
FSSR, SVX4, etc. Standard p-on-n silicon strip technology, which has
been the baseline detector technology for dozens of silicon trackers in
Nuclear and High Energy physics experiments, will be used for the FVTX
mini-strips sensors.

A collaboration of 16 institutions with approximately 60 physicists and
engineers has been formed to carry out this project. The collaboration
brings expertise in silicon vertex detectors from the FNAL E866, SSC,
L3, Atlas and BTeV experiments together with general experience on
construction and operation of large detector subsystems such as the
PHENIX muon arms. Members of the collaboration come with extensive
experience in heavy-quark and J/ψ physics, small-x nuclear effects,
gluon structure functions and polarization, various other physics
projects with muons, and expertise in simulations and analysis to
support those measurements.

With the help of an LDRD Exploratory Research (ER) grant from LANL
during FY02-FY04 we were able to develop a conceptual design of the FVTX
and to settle many of the R&D issues necessary to advance to a full
proposal. A new LDRD Directed Research (DR) project at LANL (FY06-FY08)
will produce a small prototype detector covering approximately 1/8 of
one muon arm, to be installed in the RHIC beam at the same time as the
barrel pixel detector. As part of this effort we will advance the R&D
for the FVTX by fully designing the interface electronics that connects
the FPHX read-out chip to the PHENIX Data Collection Modules (DCMs) so
that it will seamlessly provide data to the existing PHENIX DAQ. In
addition, the LDRD DR project will support part of the design of the
cooling system and support structure. Other experience relevant to the
full detector will be obtained, such as measurements of single muon
rates and noise. We will not describe further details of this effort
here, but they are available on our LDRD-DR part of the FVTX web
page[^8] and in the proposal listed there.

We request that the full project be funded by the DOE Office of Nuclear
Physics at a total cost of \$4.59M (\$3.67M + 25% contingency in FY07
dollars). Construction of the full FVTX detector should proceed starting
in early FY08 on a time scale that will allow it to be completed and
begin commissioning by the end of FY10.

A preliminary management plan of the FVTX detector project, which also
discusses the roles and expected responsibilities of the participating
institutions, is included in this document.

The proposal has the following structure:

-   The physics motivation for the upgrade and the simulated physics
    performance is given in Section 2

-   The general detector simulations and its performance is documented
    in Section 3.

-   Section 4 gives a detailed description of the forward vertex tracker
    and the technical aspects of the proposed project.

-   Section 5 discusses our R&D plan.

-   A draft of our management plan, section 6, specifies deliverables
    and institutional responsibilities.

-   Section 7 lays out the budget request and the proposed schedule.

# Physics Goals of the FVTX Endcap Upgrade

In this section we outline the physics goals of the FVTX detector and
present the physics performance of the trackers related to these goals.

The PHENIX Forward Vertex Detector (FVTX) endcaps complement the barrel
vertex detector (VTX) already being built for PHENIX by providing
increased coverage in rapidity (two additional units of rapidity
compared to about one), extending the sensitivity to gluon momentum
fraction (x) up to x\~0.2 and down to x\~10^-3^, providing a broad reach
in transverse momentum, and allowing a larger portion of the dynamical
geometry of the hot dense matter created in heavy ion collisions to be
explored. Heavy-quark mesons and bound states of heavy-quarks
(quarkonia) coming from bottom meson decay can be identified with the
FVTX by their short detached vertices. The light-meson yields that
ordinarily comprise most of the backgrounds to these measurements can be
largely eliminated because of their large detached vertices. Prompt
muons and kaons which punch through the muon system can be eliminated by
their lack of a displaced vertex. Dimuon measurements of open charm,
quarkonia and Drell-Yan signals can be improved by rejecting light meson
decay particles which contribute to the background and by improving the
opening angle resolution, and thus mass resolution of dimuons.

We will now discuss the main physics goals by starting with those that
are important in heavy ion collisions, then those of interest in proton
or deuteron nucleus collisions, and finally those that are probed in
polarized proton collisions.

## Heavy ion Collisions and the Quark Gluon Plasma

The main goal of the RHIC heavy ion program is the identification and
study of the hot high-density matter created in heavy ion collisions,
i.e. the Quark Gluon Plasma (QGP). The energy loss of fast quarks or
gluons traversing this dense matter is very large, leading to the
observed suppression of high transverse momentum light hadrons and
nearly comparable suppression of electrons arising from non-photonic
decays, presumably from heavy mesons. This, along with large elliptic
flow, suppression of J/ψ, and other signatures observed by the RHIC
experiments point to rapid thermalization, extremely high energy
density, and partonic rather than hadronic interactions. The dense
matter formed at RHIC apparently has the properties of a perfect liquid,
rather than an ideal gas. However, the composition of this high-density
matter, whether or not it is truly deconfined, and what the degrees of
freedom are, are still unknown. Addressing these questions requires
measurements over a larger kinematic reach, along with additional
observables. The FVTX detector coupled with the muon detector systems
will allow for precision measurements of open charm and bottom versus
rapidity, p~T~ and reaction plane, much improved measurements of vector
mesons (J/ψ, ψ', ϒ) as well as first measurements of dimuons from the
Drell-Yan process in heavy ion collisions. It is hoped that these
precision measurements will allow one to understand heavy quark energy
loss and flow in heavy ion collisions, understand how prompt production
and quark recombination contribute to charmonium production, how
initial-state and final-state interactions modify charmonium production,
and provide important reference measurements by studying the Drell-Yan
process.

### Energy Loss and Flow of Heavy Quarks

One of the most significant physics results produced in the first
several years of RHIC operations was the measurement of strong
suppression of high-p~T~ light particle production in Au+Au collisions.
This is illustrated by measurements with the PHENIX detector, shown in
Figure 2 and Figure 3. Figure 2 shows the suppression factor for charged
and neutral pion production in Au+Au and d+Au collisions, with respect
to p+p collisions. The suppression factor for d+Au is typically greater
than 1 while the suppression for Au+Au collisions is approximately 0.2,
indicating that the large suppression seen in Au+Au collisions comes
from final state interactions with the produced medium and is not due to
initial state interactions or interactions within the Au nuclei. This
statement is further supported by the data shown in Figure 3 where the
light meson suppression factor for Au+Au collisions is shown compared to
a direct photon measurement. The direct photons, which do not interact
with the medium, show no suppression with respect to p+p collisions. The
strong suppression observed for the light mesons is interpreted as
energy loss of the outgoing particles or ts ^\[^[^9][^10]^,^[^11]\] in
dense matter with densities up to 15 times normal nuclear matter
inferred. This energy loss shifts the produced particle spectra to lower
energy, effectively suppressing the production at a given p~T~. These
densities are much larger than what is needed to dissociate the nuclear
matter into quarks and gluon.

![](media/image12.png){width="3.123611111111111in"
height="2.1333333333333333in"}

[]{#__RefHeading___Toc170092578 .anchor}Figure 2 - Suppression of
high-p~T~ hadrons and pions as seen in Au+Au vs d+Au collisions,
measured by PHENIX and publish in PRL.

![](media/image13.png){width="4.4625in" height="3.620833333333333in"}

[]{#__RefHeading___Toc170092579 .anchor}Figure 3 -- High-p~T~
suppression of π^0^'s and η's -- indicative of energy loss in large
density matter; compared to no suppression of direct photons which
indicates that the initial-state is not modified.

A large elliptical flow (momentum asymmetry with respect to the reaction
plane) is also seen for the light hadrons as shown in Figure 4 and a
universal behavior is seen when v~2~ of the flow per valence quark in
the hadron that is observed is plotted versus transverse kinetic energy.
The large flow indicates a strongly interacting medium is produced and
thermalization is achieved relatively quickly. The scaling of the flow
with the valence quarks indicates the flow is a reflection of partonic
matter flow as opposed to hadronic flow.

![](media/image14.png){width="5.503472222222222in"
height="3.2243055555555555in"}

[]{#__RefHeading___Toc170092580 .anchor}Figure 4 -- The large elliptic
flow for light hadrons in Au+Au collisions is near the hydrodynamic
limit[^12] and scales with the number of valence quarks (n) in the
observed hadron when plotted vs transverse kinetic energy (KE~T~).

More recent measurements of heavy flavor measured via single leptons at
central rapidity\] indicate that heavy quarks (charm and bottom) also
suffer substantial suppression (see top half of Figure 5 where a PHENIX
measurement of the heavy flavor suppression factor is shown for Au+Au
collisions). In the most recent measurements, they even appear to flow,
though the flow measurements at high p~T~ are rather imprecise (see
bottom half of Figure 5). In all of these measurements large backgrounds
coupled with the necessity to calculate non-heavy-quark contributions to
the single lepton spectra and then statistically subtract these to
isolate the heavy-quark component result in large systematic errors,
severely limiting the accuracy of these measurements. In addition, once
the heavy quark component is identified, there is still no clean way to
separate the charm and bottom components of the resulting subtracted
spectra. The FVTX detector will address both of these issues. Because of
their higher mass, b quarks are expected to have substantially smaller
energy loss and be much more difficult to thermalize and flow along with
the medium. Consequently the large suppression of the electrons,
especially at high p~T~ where bottom contributions are expected to
dominate, is quite mysterious. The expected reduction in flow appears
consistent with the data, but the error bars at high p~T~ are too large
to make any definitive statements about comparisons to models. What is
really needed are much more precise measurements which include
separation of D and B decay sources of single leptons.

![](media/image15.png){width="4.625694444444444in"
height="4.486111111111111in"}

[]{#__RefHeading___Toc170092581 .anchor}Figure 5 -- Heavy quark
suppression and flow vs p~T~ from PHENIX measurements using electrons in
200 GeV Au+Au collisions at mid rapidity[^13].

The measurement of large suppression of heavy flavor production came as
a surprise because a few years ago theoreticians predicted that heavy
quarks would not lose much energy in the hot-dense matter due to the
\"dead-cone\" effect[^14] \-- seemingly inconsistent with the recent
results. This dead-cone effect refers to the reduction in phase space
that is available for radiated gluons as you move to higher quark mass,
thus resulting in less predicted radiative energy loss for heavy quarks
than for light quarks. A number of different theoretical models now
attempt to explain the unexpected large suppression of heavy quarks:

-   Some studies suggest that the magnitude of the
    dead-cone[^15]^,^[^16]^,^[^17] may be similar between heavy quarks
    and light quarks, unlike the predictions in reference Error:
    Reference source not found, which would lead to an energy-loss for
    heavy quarks closer to that for light quarks..

-   M. Djordjevic^11^ suggests that collisional energy loss accounts for
    the extra suppression that is seen in the measurements. In this
    model, the charm suppression reaches approximately the levels of the
    measured inclusive heavy quark suppression and the bottom
    suppression would be much less than the charm suppression.

-   A. Adil, I. Vitev [^18] takes into account the formation time which
    is long for light quark mesons (relative to the lifetime of the
    medium) but short for heavy quark mesons. Because of the short
    lifetime, dissociation of the heavy quark mesons inside the medium
    is calculated to contribute to suppression of heavy meson production
    in addition to the heavy quark energy loss. In this model, the
    bottom component suffers less suppression than the charm component
    at low p~T~, but the two become comparable at as low as 10 GeV.

-   Cold nuclear matter (CNM) effects will provide additional
    suppression of heavy flavor production, especially at forward
    rapidity. A rapidity dependence measurement helps allow separation
    of CNM effects and dense medium effects since CNM.

The various suppression models also give different predictions for flow
of heavy flavor mesons, as indicated in Figure 5. In general, models
which predict larger suppression will also tend to predict larger flow
because the suppression is larger perpendicular to the reaction plane
(where it passes through more medium) than in the reaction plane (where
less medium is traversed). This leads to an asymmetry in production
which is reflected in a v~2~ measurement. The combination of precision
flow and R~AA~ measurements, along with separation of charm and bottom
components, should allow us to clearly determine which among the
different suppression mechanisms that have been proposed is correct.

The predictions of these models for charm plus bottom production,
relative to p+p production, are indicated in Figure 6 and will be
described in the next section. To distinguish among these various models
higher precision measurements of heavy quark production are required to
compare quantitatively the amount of suppression seen in Au+Au
collisions compared to p+p collisions, separation of charm and bottom
will allow the collisional energy loss and formation time models to be
clearly distinguished, and a measurement across a large rapidity range
further distinguishes the models and helps understand the cold nuclear
matter effects. We will now show the heavy flavor measurement precision
that we expect to obtain with the FVTX detector.

### Charm and Bottom Measurements with the FVTX

The signal to background improvements in charm and bottom that are
obtained with the FVTX and discussed in Section 3.4 can be used to
determine the precision of an R~AA~ measurement of open charm and bottom
using the FVTX detector. The resulting predicted measurement
capabilities are shown in Figure 6. The red error bars indicate the
measurement precision that can be obtained without the FVTX detector,
using RHIC Run 5 p+p statistics and the blue error bars indicate the
precision that can be obtained with the same integrated luminosity run
but using the FVTX in the analysis. Also shown are theory predictions
which include radiative energy loss (green band), radiative energy loss
plus elastic scattering energy loss (blue band) and radiative energy
loss plus dissociation (yellow band).

![](media/image16.png){width="4.179861111111111in"
height="4.011805555555555in"}

[]{#__RefHeading___Toc170092582 .anchor}Figure 6 Heavy flavor R~AA~
measurement that can be achieved with RHIC Run 5 p+p statistics, with
the FVTX detector (blue error bars) and without the FVTX detector (red
error bars). Theory predictions which include radiative energy loss
(green band), radiative energy loss plus elastic scattering energy loss
(blue band) and radiative energy loss plus dissociation (yellow band)
are shown for comparison.

### Separating Charm and Bottom

There are a few possible methods for separating charm and bottom
production using the FVTX system:

-   Since bottom mesons have a larger lifetime than charm mesons
    (especially the D^0^), and the decay muons are typically produced at
    a larger angle with respect to the parent meson, it is possible to
    separate the charm and bottom in single muons from semi-leptonic
    decays by placing a p~T~ dependent cut on the DCA of the tracks.

-   The topology of B events is somewhat different from D events, and
    will be shown in section 3 later. Both the multiplicity and physical
    size of a heavy quark jet is different for B and D events. Selective
    kinematic cuts may greatly enhance the B signal from muons with
    respect to the D signal from muons (or vice versa).

-   The decay channel *B*  J/ψ+X produces J/ψs that are displaced from
    the collision point by about one mm in Z. The FVTX can separate
    these from the prompt J/ψ and thus provide a direct B measurement
    channel..

-   When the dimuons are tagged to come from a displaced vertex, bottom
    dominates the like-sign dimuon production.

#### Separating Charm and Bottom by Distance of Closest Approach (DCA) and p~T~

B heavy quara from the light quark muons.

![](media/image18.png){width="4.776388888888889in"
height="2.8020833333333335in"}![](media/image18.png){width="4.776388888888889in"
height="2.8020833333333335in"} []{#_Ref36878645 .anchor}

Figure 7 -- The DCA for semi-leptonic decays of charm (blue) and bottom
(red), light meson decays (green), and prompt punch-through hadrons
(black).

Figure 8 shows the p~T~ spectra for muons from D decays (black) and
muons from B decays (red), produced by PYTHIA and accepted into the muon
arms. Although there is currently uncertainty in the relative cross
sections of charm and bottom at RHIC energies, you can see that at low
enough momentum the D decay muons will dominate and at high enough
momentum the B decays will dominate. This can be used as a crude tool to
separate Ds and Bs and/or as a way to check whether cuts are correctly
separating the two contributions. See section 3.4 for more on this
possibility.

![](media/image20.png){width="3.0569444444444445in"
height="2.3020833333333335in"}

[]{#__RefHeading___Toc170092584 .anchor}Figure 8 -- Transverse momentum
spectrum for charm and bottom decays. The different colored curves
correspond to the same primary particles as in Figure 8

#### Separating Charm and Bottom by Event Topology Cuts

Because of the larger mass of the B mesons with respect to the D mesons,
the decay muon that comes from a B typically has a larger p~T~ with
respect to the original meson than the decay muon that comes from the
original D meson. This is illustrated in Figure 9 where the p~T~
spectrum of the decay muon with respect to the parent meson is shown for
B muons and D muons. The two spectra have been normalized to each other
to take into account the cross sections and branching ratios for each
process. If we can effectively measure the momentum vector of the jets,
by measuring the average vector of all the charged particles from the
jet in the FVTX detector, we can then measure the decay muon with
respect to the meson and we may be able to place a cut on the muon that
would enhance the B signal in single muons relative to the D signal, or
vice versa.

![](media/image21.png){width="4.878472222222222in"
height="3.479861111111111in"}

[]{#__RefHeading___Toc170092585 .anchor}Figure 9 The p~T~ of the decay
muon from D mesons (lower average value) and from B mesons (larger
average value) is shown, properly normalized by their respective cross
section and branching ratios.

#### Displaced Vertex for B Meson Decays: $B \rightarrow \frac{J}{\psi} \rightarrow \mu^{+}\mu^{-}$, $B \rightarrow \mu X$

Bottom measurements can be made directly by reconstructing
BJ/ψμ^+^μ^-^. With the FVTX detector, J/ψs from B decay can be tagged
by measuring the displaced vertex.

We simulated our performance for this direct bottom measurement by using
PYTHIA to simulate B decays and tracking the decay muons through the
silicon and muon spectrometers using PISA. The BJ/ψ decay muons have an
impact resolution with respect to the displaced vertex of \~55 μm,
better than single muons from D decays, due to their larger average
momentum. The muon pair z-vertex resolution of the prompt J/ψ is \~133
μm, while the mean decay length is \~1.1mm, and this is indicated in
Figure 10 where the reconstructed Z-vertex distribution for the J/ψ from
B decays and prompt J/ψ (scaled down by a factor of 100) are shown. With
a downstream pair z-vertex cut of 1 mm, we found 39% of the B decays are
retained, while the prompt J/ψ are attenuated by a factor of 2x10^-4^,
leaving a sample which is dominated by BJ/ψ.

![](media/image22.jpeg){width="3.5145833333333334in"
height="3.3930555555555557in"}

[]{#__RefHeading___Toc170092586 .anchor}Figure 10 - The reconstructed
Z-vertex distribution for J/ψ from B decays (black line) and for prompt
J/ψ (red line). Note that the prompt J/ψ yield has been scaled down by a
factor of 100. The relative yield of J/ψ from B decays versus prompt
J/ψ is estimated to be about 1%.

The rates of bottom from single muons and of BJ/ψ events have been
calculated using the following assumptions. We have assumed a total
$b\overline{b}$cross-section of 2 μb and 4 μb for J/ψ production. The
branching ratio (BR) of 1.09% for B→J/ψ+X has been previously measured.
The total acceptance for these events into one Si Endcap is \~ 4.6%.
Assuming an integrated RHIC-II p-p luminosity per week of 33 pb^-1^,
about 650 B→J/ψ+X events would be reconstructed after the application of
a 1 mm vertex cut. For $B \rightarrow \mu X$, the acceptance is \~4.5%.
The corresponding yield is \~880,000 reconstructed events over the
acceptance of the muon and FVTX arms.. See rate details in Appendix C
(Section 8). Thus, an excellent *B* measurement is possible.

### Open Charm Enhancement

It has been predicted that open charm production could be enhanced in
high-energy nucleus-nucleus collisions relative to the expectation from
elementary collisions[^19]^,^[^20]^,^[^21]. Heavy quarks are produced in
different stages of a heavy ion reaction. In the early stage charm and
bottom are formed in collisions of the incoming partons. The yield of
this component is proportional to the product of the parton density
distributions in the incoming nuclei (thus giving binary scaling). If
the gluon density is high enough, a considerable amount of charm can be
produced via fusion of energetic gluons in the pre-equilibrium stage
before they are thermalized. Finally, if the initial temperature is
above 500 MeV, thermal production of charm can be significant. The last
two mechanisms (pre-equilibrium and thermal production) can enhance
charm production relative to binary scaling of the initial parton+parton
collisions. These are the same mechanisms originally proposed for
strangeness enhancement, but in the case of charm may reveal more about
the critical, early partonic-matter stage of the reaction since the rate
of heavy-quark production is expected to be negligible later when the
energy density has decreased. In comparison, strangeness production is
expected to continue even in the final hadronic stages of the reaction.

![](media/image23.jpeg){width="2.7222222222222223in"
height="3.0375in"}![](media/image24.jpeg){width="2.428472222222222in"
height="2.9763888888888888in"}

Figure 11 - Charm enhancement expected at RHIC from ref. Error:
Reference source not found. In both panels, contribution from the
initial gluon fusion (solid), pre-thermal production (dot-dashed), and
thermal production (dashed, lowest) are shown. The left panel is the
calculation with energy density of 3.2 GeV/fm^3^, while the right panel
shows the case with energy density 4 times higher. The barely visible
dotted curve in the left panel figure is the thermal production assuming
an initially fully equilibrated QGP. In the right panel the curves with
stars are the same as the corresponding curves without stars except that
the initial temperature is reduced to 0.4 GeV (compared to 0.55 GeV).

At RHIC energies the anticipated enhancement is a small effectError:
Reference source not found^,Error:\ Reference\ source\ not\ found^. The
contributions to charm production from various stages of a Au+Au
collision are shown in Figure 11Figure 12 (taken from reference Error:
Reference source not found). From the left panel of the figure it is
evident that for an initial energy density of 3.2 GeV/fm^3^ the
pre-thermal or pre-equilibrium production contributes about 10% of total
charm production, while the thermal contribution is negligible. However,
the yield is very sensitive to the initial density, and with 4 times the
energy density the pre-equilibrium contribution can be as large as the
initial fusion. This is illustrated in the right panel of the figure.
Present single electron measurements of PHENIX indicate that within
\~25% systematic uncertainty charm production approximately scales with
the number of binary collisions. Thus, charm enhancement, if it exists,
cannot be a large effect. A measurement of the charm yield with
substantially higher accusion is therefore required to establish a
potential charm enhancement.

The FVTX combined with the muon spectrometers will allow measurements of
charm and bottom over a broader range in *p*~T~. This will extend the
single muon measurement to the *p*~T~ region near 0.5 GeV/c. Since more
than half of the yield from charm decays is in this *p*~T~ region, this
is essential for an accurate determination of the *p*~T~ integrated
charm yield at forward and backward rapidities. Approximately one third
of the total charm cross section is expected to come from the rapidity
range measured by the FVTX, as shown in Figure 13. Combined with the
central rapidity (\|y\|\<1.2) measurement from the VTX detector, this
will allow an accurate measurement of the total charm cross section
which then allows us to see a potential charm (or bottom) enhancement.

![](media/image25.jpeg){width="4.376388888888889in"
height="3.3583333333333334in"}

[]{#__RefHeading___Toc170092588 .anchor}Figure 13 - Rapidity
distribution from Vogt[^22] for charm in pp collisions at √s = 200 GeV.
One third of the total cross section comes from the region of the FVTX
coverage, \|y\|\>1.2

### J/ψ Suppression and Comparisons with Open charm, ψ' and ϒ

J/ψ production in heavy ion collisions has long been considered a very
sensitive probe of the quark gluon plasma. Its formation is expected to
be suppressed because the c and cbar pair are screened from each other
by the high density of quarks and gluons in the plasma and cannot form a
bound state. However, the J/ψ production is a complicated process that
is potentially modified at several stages of the collision process. J/ψ
production can be modified in Au+Au collisions with respect to p+p
collisions by changes in the gluon distribution functions in a nucleus
compared to a nucleon (gluon-gluon fusion is a primary production
mechanism for J/ψs so modified gluon distribution functions mean
modified J/ψ production), energy loss of the composite charm quarks in
the medium will modify the distribution of J/ψs that are produced,
having additional contributions to the production from recombination (if
the charm density is high enough) can *enhance* production, and one can
have suppression due to the Debye screening mentioned above.

The most recent J/ψ measurements from PHENIX are shown in Figure 14,
where one can see a large suppression at central rapidity (red points)
and a substantial difference in suppression between mid and forward
rapidity for the mid-central collisions. The suppression measured at
central rapidity is similar to the amount of suppression measured at
lower energies at the SPS, though many predictions expected the
suppression to be larger at RHIC because of the higher density state
that is achieved at RHIC energies. Recombination of c and cbar pairs
would enhance production and may account for less suppression than
expected at RHIC. This can, in principle, be checked by measuring p~T~
and rapidity distributions which are different for J/ψ from
recombination than from prompt production, and by having precise open
charm measurements so that we can estimate the contributions from
recombination. The difference in suppression at forward rapidity
compared to central rapidity may come from cold nuclear matter effects,
which tend to give larger suppression at forward rapidity, but cannot be
precisely checked currently because of the poor precision of d+Au
collision data. The Debye screening effects can be checked by looking at
other vector mesons like ψ' because the different sizes of the different
vector mesons lead to different suppressions within the plasma.

![](media/image26.png){width="4.8180555555555555in"
height="4.403472222222222in"}

[]{#__RefHeading___Toc170092589 .anchor}Figure 14 -- J/ψ results for 200
GeV Au+Au collisions[^23]. (a) (top) Nuclear modification factor for J/ψ
at mid (red) and forward (blue) rapidity, and (b) (bottom) the ratio of
these suppressions for forward/mid rapidity, all vs centrality in terms
of the number of participants (N~part~).

The FVTX detector can help untangle the mechanisms that modify J/ψ
production in heavy-ion collisions by, (1) allowing for precision open
charm measurements which helps in the understanding of the initial c and
cbar production, (2) improving the J/ψ measurements by reducing the
background dimuons from π and K decay and improving the J/ψ mass
resolution, which will allow more precise measurements to be made for a
given integrated luminosity, and (3) allowing additional vector meson
measurements like ψ' , and ϒ at mid-rapidity using the muon arms to be
added to the suite of PHENIX measurements. The open charm measurements
have already been covered, so we show here the improvement to the vector
meson measurements.

Figure 15 shows the estimated composition of the background in the J/ψ
mass region. The vertical axis is the ratio of background events
containing a decay muon to the total background. Based on this plot, the
FVTX detector can eliminate about 60% of the total background at the J/ψ
peak, by rejecting the dimuons which contain a decay muon. The
punch-through hadrons cannot be eliminated by a vertex cut, since they
are prompt, as is the signal.

![](media/image27.png){width="4.36875in" height="2.7368055555555557in"}

[]{#__RefHeading___Toc170092590 .anchor}Figure 15 -- Fraction of dimuon
pair background containing decay muons versus dimuon mass. At the J/ψ
mass (3.1 GeV), about 60% of the total background contains at least one
decay muon, which can be rejected using the FVTX.

The mass resolution of the J/ψ measured by the muon arms is currently
determined primarily by the uncertainty in energy loss in the absorber
material that is in front of the muon arms and the uncertainty in the
opening angle of the dimuon due to the multiple scattering in the
absorber material. The latter can be removed from the resolution
contributions by accurately measuring the opening angle with the FVTX.
This results in a reduction in the J/ψ mass resolution from \~150 MeV to
\~100 MeV.

Simulations of the improvement of the dimuon mass spectrum, when the
light meson decay muons are rejected and with the expected mass
resolution improvement, are shown in Figure 16 for p+p collisions and in
Figure 17 for minimum-bias Au+Au collisions. For the p+p spectrum the
signal-to-background for the J/ψ is already quite good, so the
improvement of the J/ψ is not as dramatic, but the improvement of the
separation of the J/ψ and ψ' is. For the Au+Au collisions, especially
those for central Au+Au, the J/ψ peak is very hard to see until the FVTX
eliminates the light hadron decays and the improvement is quite
dramatic. The ψ' is not quite as dramatic because the backgrouds have
not been subtracted, but even in these plots the improvement is quite
clear. The yields are representative of those expected for RHIC-II
luminosities and the starting signal-to-background ratios are taken from
recent runs for Au+Au. We also expect that with more sophisticated cuts
in the future, we will be able to eliminate some of the punch-throughs
and further improve the signal-to-backgrounds shown here.

![](media/image28.png){width="5.747222222222222in"
height="2.723611111111111in"}

[]{#__RefHeading___Toc170092591 .anchor}Figure 16 - Simulated dimuon
mass spectrum for p+p collisions before (left) and after (right) FVTX
vertex cuts are applied to eliminate the light meson decay backgrounds.
The mass resolution of the J/ψ and ψ' are improved from 150 MeV to 100
MeV, as shown, by the FVTX. These plots correspond to a 10 week RHIC-II
run and the initial J/ψ signal/noise (before the FVTX cuts) is set
according to that observed in the 2005 p+p run. There are about 1.5
million J/ψ and 27,000 ψ' entries in the peaks.

![](media/image29.png){width="5.747222222222222in"
height="2.723611111111111in"}

[]{#__RefHeading___Toc170092592 .anchor}Figure 17 - Simulated dimuon
mass spectrum for minimum bias Au+Au collisions before (left) and after
(right) FVTX vertex cuts are applied to eliminate the light meson decay
backgrounds. The mass resolution of the J/ψ and ψ' are improved from 150
MeV to 100 MeV, as shown, by the FVTX. These plots correspond to a 10
week RHIC-II run and the initial J/ψ signal/noise (before the FVTX cuts)
is set according to that observed in the 2004 Au+Au run. There are about
400,000 J/ψ and 7,100 ψ' entries in the peaks.

For the ϒ family resonances, since the mass resolution is dominated by
the momentum resolution obtained by the muon tracker, this resolution is
not expected to improve much from the FVTX tracker. On the other hand,
the backgounds from decays of light mesons will be decreased in the same
way as they are for J/ψ. The rejection of backgrounds will be especially
important if we try to measure ϒ at mid-rapidity through detection of
one muon in each muon arm. Here, the backgrounds are larger (because of
the smaller momentum needed to make high mass) and must be reduced if we
are to extract the upsilon signal.

Another dimuon measurement that becomes possible with the addition of
the FVTX is measurement of Drell-Yan. The dimuon continuum between the
vector meson resonance peaks is comprised of Drell-Yan, dimuons from
(correlated and uncorrelated) open heavy flavor, and combinatorial
background from decay muons from pions and kaons and punch-through
hadrons. With the FVTX detector prompt dimuons from Drell-Yan can be
separated from dimuons which contain a decay muon from heavy flavor or
light mesons, leaving a much cleaner Drell-Yan signal. Since Drell-Yan
dimuons are produced in the initial hard-scattering, the production of
the muons does not suffer from any interactions with the medium, making
Drell-Yan a good measurement for helping to separate final state
interactions with the medium from initial-state interactions.

### Reaction Plane and Azimuthal Asymmetries

The large increase in the overall solid angle for observing charged
particles provided by the FVTX and the more optimal rapidity coverage
will result in a substantial improvement in the reaction plane
resolution, compared with the baseline PHENIX measurements, which will
aid in the study of many signals in PHENIX versus reaction plane. Many
physics measurements made by PHENIX with respect to the reaction plane
are more limited by the reaction plane resolution than by other
systematic or statistical errors, so it is critical to maintain this
capability to the PHENIX physics program.

#### Reaction Plane

The determination of the reaction plane for heavy ion collisions from
charged particle asymmetries is very important for it allows the
measurement of observables (e.g. charm R~AA~) as a function of path
length in the medium. It is generally agreed that in mid-central
collisions, the path length in plane is much smaller than out of plane
due to the almond shaped overlap zone. A binning of the reaction plane
orientation into e.g. 3 bins would therefore allow for path length
dependency study of various physics signals with a 60 degree separation
of in and out of plane bins (±30 degrees).

In order to avoid auto correlations, the reaction plane has to be
determined in a region that does not overlap with the actual
measurement, e.g. current central rapidity measurements with respect to
the reaction plane use the BBC information at much higher rapidity to
determine the reaction plane. Figure 18 shows a measurement with the MVD
pad detectors for minimum bias Au+Au collisions from run4, and
demonstrates that the elliptic flow at the shaded rapidity region for
the former MVD pad detectors and the currently proposed FVTX exhibits a
stronger v2 signal than at BBC rapidity and should therefore provide a
reaction plane measurement with better resolution.

![](media/image30.png){width="5.008333333333334in"
height="3.529166666666667in"}

[]{#__RefHeading___Toc170092593 .anchor}Figure 18 - Azimuthal asymmetry
v2 as function of pseudo rapidity for minimum bias A-A collisions at 200
GeV. The measurement from run 4 with the MVD pad detectors is colored in
magenta; the FVTX will cover the same range in pseudo rapidity.

A simulation has been performed to study the reaction plane resolution
and confidence levels for providing \'reaction plane bins\'. The typical
way to measure or report a reaction plane resolution is quoting the
square root of two times the mean cosine of the difference between
reaction planes obtained from two subsets of tracks, in this case the
north and south tracks. As this is a rather complex variable, we choose
to first represent it in Figure 19 and then translate it into a more
intuitive variable in Figure 20, namely a confidence level of having
made the right determination.

![](media/image31.jpeg){width="5.995138888888889in"
height="4.063888888888889in"}

[]{#__RefHeading___Toc170092594 .anchor}Figure 19 - The two dimensional
color representation of the mean reaction plane resolution as function
of the charge particle multiplicity Nhits and the elliptic flow signal
v2 present in the rapidity interval of the FVTX detector. The total
number of charge tracks expected for a mid central Au+Au collision at
200 GeV is simulated to be about 800 traversing the FVTX silicon
detector, the previously measured elliptic flow signal v2 is on the
order of 0.035, the resulting expected mean reaction plane resolution is
approximately 0.75.

Figure 19 shows in color the square root of the mean cosine of the
reaction plane difference between north and south FVTX detector as
function of the track multiplicity (here called Nhits), i.e. the
reaction plane resolution on the ordinate. The flow signal v2 present in
the given rapidity interval of the detector is shown on the abscissa.
The general trend visible is that the reaction plane resolution is
increasing (improving) with the number of charged tracks and increasing
with the strength of the elliptic flow signal v2. The red colored top
right corner marks the area which yields the best resolution. (Note that
since this is cosine of the difference, a value of 1.0 indicates the
reaction plane difference is zero and a value of 0.0 indicates they are
90 degrees apart, i.e. a larger number means a smaller resolution)

Studies from HIJING have shown that the mean number of charged tracks to
be expected for the FVTX is on the order of 400 tracks per endcap, i.e.
about 800 charged tracks total.

![](media/image32.png){width="4.78125in" height="3.3673611111111112in"}

[]{#__RefHeading___Toc170092595 .anchor}Figure 20 - Azimuthal asymmetry
v2 (elliptic flow) as function of centrality for A-A collisions at 200
GeV. The measurement was obtained with the MVD pad detectors which
covered in run 4 the same pseudo rapidity rage as the FVTX will in the
future.

The elliptic flow measurement v2, shown in Figure 20 as a function of
centrality for Au+Au collisions at 200 GeV, indicates that the expected
value v2 is about 0.035 for mid central collisions. The expected
reaction plane resolution we obtain via Figure 19 is therefore about
0.75.

Figure 21 shows in color the expected confidence levels as function of
the reaction plane bin size. For a given reaction plane bin size in
delta phi one can see that the confidence level that the actual reaction
plane lies in the measured reaction plane bin increases with the
reaction plane resolution. It also shows that a 2 sigma confidence level
can only be reached in the limit of two broad bins in and out of plane
with a nearly perfect detector.

If we interpret Figure 21 with the number for the reaction plane
resolution obtained above (0.75) and assume that we want to have 3 bins
in reaction plane as mentioned earlier (i.e. ±30 degrees around the
major axis plus a 60 degree gap), then we obtain a confidence level of
about 65 percent; two broad bins in vs. out will have a confidence level
of 85 percent, a very good measurement.

![](media/image33.png){width="4.685416666666667in"
height="3.0965277777777778in"}

[]{#__RefHeading___Toc170092596 .anchor}Figure 21 - Three dimensional
representation of confidence level (0 to 1 corresponds to 0 to 100
percent) of a given delta phi bin as function of the mean reaction plane
resolution for the FVTX. The reaction plane resolution of 0.75 estimated
in figure 4 would result is a 65 percent confidence level if binning the
reaction plane into 3 bins. Two bins (delta phi = 90 degrees) will give
a confidence level of 85 percent for the \'true reaction plane\' being
in the measured bin.

#### Flow Measurements

In addition to providing a reaction plane for the central detector
measurements, the FVTX can obviously measure the actual elliptic and
directed flow signal. In the following we discuss the measurements
obtained with the MVD pad detectors in run 4 which covered about the
same rapidity range and were already shown above in the context of the
reaction plane measurements.

Figure 18 shows the measurements of the azimuthal asymmetry v2 as
function of the pseudo rapidity with three sets of PHENIX detectors. The
measurement obtained with the MVD is colored in magenta, it shows a
sizeable v2 which translates into a good reaction plane measurement. The
FVTX has an improved granularity and the same rapidity coverage as the
former MVD pad detectors. In addition the measurement of asymmetries and
reaction plane will be improved by using tracklets in the four FVTX
planes rather than just hits as was done in the MVD analysis.

Figure 20 and Figure 22 show elliptic and directed flow measurements
with the MVD pad detectors as function of centrality for Au+Au
collisions. The proposed FVTX will provide for the same measurements,
but with better statistical and systematic error bars.

![](media/image35.png){width="4.122222222222222in"
height="2.904861111111111in"}

[]{#__RefHeading___Toc170092597 .anchor}Figure 22 - Azimuthal asymmetry
v1 (directed flow) as function of centrality for A-A collisions at 200
GeV. The measurement was obtained with the MVD pad detectors which
covered the same pseudo rapidity rage as the FVTX will.

## Proton(Deuteron) + Nucleus Collisions and Nuclear Effects on Quarks and Gluons 

Proton-nucleus collisions not only provide important baseline
information for the study of QCD at high temperatures, they also address
fundamental issues of the parton structure in nuclei. Since the
discovery of the EMC effect in the 1980s, it is clear that the
parton-level processes and the structure of a nucleon are modified when
embedded in nuclear matter[^24]. These changes reflect fundamental
issues in the QCD description of parton distributions, their
modifications by the crowded nuclear environment of nucleons, gluons and
quarks, and the effect of these constituents of the nucleus on the
propagation and reactions of energetic partons that pass through them.

There are many ways that cold nuclear matter can effect particle
production and propagation. Initial state effects, which occur before
the incoming parton undergoes a hard scattering, include parton
shadowing, energy loss and multiple scattering. These generally conserve
the incident parton flux, but change their kinematics. Final state
effects, which take place after the hard scatter occurs, include energy
loss, multiple scattering and dissociation of bound states. For some
processes the hard scattering part may not factorize from the soft
collisions, resulting in additional process-dependent effects. These are
usually minimized by choosing reactions with sufficiently large Q^2^.

### Heavy-quarks in d-Au Collisions: Charm and Bottom Mesons

The most compelling physics issues that can be studied using single
heavy quarks include:

-   Gluon shadowing or saturation effects for single heavy quarks. To be
    contrasted with similar studies of quarkonia.

-   Energy loss and multiple scattering of heavy versus light quarks in
    cold nuclear matter.

-   Accurate heavy quark cross section measurements over large rapidity
    and p~T~ ranges in order to constrain recombination models for
    quarkonia ($c\overline{c}$or $b\overline{b}$ bound states).

#### Shadowing or Gluon Saturation via Heavy-quarks Measurements

A cold nuclear matter effect that is of particular interest is the
apparent depletion of low momentum partons (gluons or quarks) in nuclei,
called shadowing, which can result from the large density of low
momentum partons. For gluons with very low momentum fraction, *x* \<
10^-2^, one can assign, following the uncertainty principle, a large
distance scale. These gluons will then interact strongly with many of
their neighbors and by gluon recombination or fusion are thought to
promote themselves to larger momentum fraction, thus depleting the small
*x* region. In most models the overall momentum is conserved in this
process, so that the small *x* gluon region is depleted while the
moderate *x* region is enhanced. This shift of the gluon distribution
function translates into a shift in particle production. Production via
low-x gluons gets reduced and production via high-x gluons gets
enhanced. The kinematic acceptance of the PHENIX detector is such that
the low-x particle production has good acceptance in one muon arm (in
the direction of the deuteron beam in a d+Au collision) and high-x
production has good acceptance in the other muon arm (i.e. the direction
of the Au beam in a d+Au collision). Therefore, particle production
measurements in the muon arms potentially provide measurements of gluon
shadowing.

However, modification of the gluon distribution function is not the only
way that particle production can be modified to give less particle
production at small x. In recent years a model for gluon saturation at
small *x* has been developed by McLerran and collaborators[^25]. Gluon
saturation affects both the asymptotic behavior of the nucleon's gluon
distribution as *x* approaches zero and causes shadowing.

It should also be noted that a model from Qui and Vitev[^26] involving
higher-twist (power corrections) effects predicts a similar suppression
of the cross sections at forward rapidity. These effects arise from
coherent multiple scattering of the final state parton, in contrast to
shadowing, which occurs in the initial state. If the energy loss of the
outgoing partons is added to the model, even larger suppression is seen
at forward rapidity.

Kopeliovich has argued that suppression at large rapidity may be caused
by Sudakov suppression[^27]. In this case, energy conservation results
in particle production in p+A collisions going to zero as x~F~1.

![](media/image36.png){width="4.079861111111111in"
height="2.6381944444444443in"}

[]{#__RefHeading___Toc170092598 .anchor}Figure 23 - Gluon shadowing from
Eskola[^28] as a function of x for different Q^2^ values: 2.25 GeV^2^
(solid), 5.39 GeV^2^ (dotted), 14.7 GeV^2^ (dashed), 39.9 GeV^2^
(dotted-dashed), 108 GeV^2^ (double-dashed) and 10000 GeV^2^ (dashed).
The regions between the vertical dashed lines show the dominant values
of *x~2~* probed by muon pair production from charm pairs at SPS, RHIC
and LHC energies.

![](media/image37.jpeg){width="4.372916666666667in"
height="3.1534722222222222in"}

[]{#__RefHeading___Toc170092599 .anchor}Figure 24 - Gluon shadowing
calculations from Frankfurt and Strikman\] that predicts substantially
larger shadowing than that of
EK^Error:\ Reference\ source\ not\ found^\].

At RHIC energies many of the observables are affected by gluon
distributions at small *x* where nuclear shadowing is thought to be
quite strong. However, theoretical predictions of the amount of
shadowing differ by factors as large as three. For example, in the
production of J/ψ in the large rapidity region covered by the PHENIX
muon arms, models from Eskola et al (EKS) (Figure 23) predict only a 30%
reduction due to gluon shadowing, while those of Frankfurt &
Strikman[^29] (Figure 24) or Kopeliovich[^30] predict up to a factor of
three reduction.

Figure 25 shows the different regions of evolution in Q^2^ and x,
highlighting the region at small x and Q^2^ where the non-linear
processes described by the Color Glass Condensate (CGC) model become
important and reduce the gluon density. Since these effects are
amplified in a nucleus (a factor of \~5 in a Gold nucleus), they also
produce a shadowing effect where the gluon density per nucleon is
reduced at small x.

![](media/image38.png){width="5.070138888888889in"
height="3.9916666666666667in"}

[]{#__RefHeading___Toc170092600 .anchor}Figure 25 - Diagram showing the
gluon saturation region at small x and Q^2^.

The coverage in *x* for the FVTX is indicated in Figure 26, superimposed
on calculations of the ratio of nuclear to nucleon gluon structure
functions. The red bars indicate the additional coverage provided by the
FVTX upgrade compared to the baseline of the PHENIX detector. The FVTX
extends the *x*-range from the anti-shadowing region into the shadowing
domain, which means we will be able to establish the shape of the gluon
structure function in nuclei. The shadowing region (x \< 10^-2^) is not
accessible at the central rapidits covered by the VTX barrel. J/ψ and
open charm production in the forward direction covered by the FVTX would
be affected by shadowing. For the J/ψ, final state effects such as
absorption complicate the connection to the gluon structure function,
while for open charm and bottom there is some uncertainty about whether
the dominant production mechanism is gluon fusion or flavor excitation.
Therefore, comprehensive measurements of both open and closed heavy
flavor are necessary to obtain a reliable measure of the modification of
the gluons. Given sufficient RHIC luminosity, it would also be quite
instructive to measure for bottom the same observables as for charm,
since open-bottom production should be largely unaffected by shadowing.

The additional coverage in the anti-shadowing region (x \~ 0.1) is also
important. Many models of shadowing predict that the momentum of the
shadowed partons collects in this region. Anti-shadowing has only been
observed for quarks, not for gluons, so a good measurement would have a
strong impact on theory. The suppression of quarks at large x in nuclei
(EMC effect) is well characterized, but the situation for gluons is
unclear.

![](media/image39.jpeg){width="5.504166666666666in"
height="4.261805555555555in"}

[]{#__RefHeading___Toc170092601 .anchor}Figure 26 - Gluon shadowing
predictions along with PHENIX coverage. The red bars indicate the
additional range provided by the FVTX upgrade, green bars are for the
barrel (VTX) upgrade, while the blue bars cover the PHENIX baseline. The
red and blue curves are the theoretical predictions for gluon shadowing
from EKS\] and FG^Error:\ Reference\ source\ not\ found^\] for different
Q values.

#### Energy Loss and Multiple Scattering of Quarks and Gluons in Nuclei.

As discussed above, measurements of single heavy quarks (charm and
bottom) are sensitive to the gluon distributions and their modification
(shadowing) in nuclei. They provide a complementary view to that
provided by studies of quarkonia as they involve the same initial-state
gluon distributions but have quite different, and probably simpler,
final-state effects than those of the J/ψ. For example both quarkonia
and single heavy quarks can experience energy loss and multiple
scattering in the final state, while quarkonia also have potentially
large effects from absorption (i.e. disassociation of the two heavy
quarks that would otherwise form the heavy quark-antiquark bound state).

Energy loss of partons in the initial state was thought to have a small
effect at RHIC, since the energy loss per unit length in many models is
thought to be approximately constant and small compared to the
initial-state parton momenta at RHIC, but no definitive data were
available to confirm these models or energy loss values. Recently, Vitev
et. al.[^31] have shown that *significant* energy loss in the initial
state is consistent with the nuclear dependence seen for prompt muons
from PHENIX as shown in Figure 27 where the production suppression
factor is shown for dAu collisions versus p~T~. These issues are very
important in the high-density regions created in heavy ion collisions,
but we also need a baseline for normal nuclear densities from
proton-nucleus collisions.

![](media/image40.jpeg){width="5.592361111111111in"
height="3.365972222222222in"}

[]{#__RefHeading___Toc170092602 .anchor}Figure 27 - Vitev, et. al.Error:
Reference source not found predictions of coherent power corrections
(left panel) and the sum of the power corrections and initial state
energy loss (right) for the nuclear dependence of D meson production
compared to prompt muon data from PHENIX fromn dAu collisions.
Significant energy loss is predicted.

Another general feature of most produced particles comes from the
multiple scattering of initial-state partons, which causes a broadening
of the transverse momentum (Cronin effect) of the produced particles.
Final-state multiple scattering can further broadenthe transverse
momenta.

A recent result for the p~T~ dependence of the nuclear modification
factor for prompt muons is shown in Figure 28 from PHENIX[^32]. Data for
prompt muons from d+Au collisions show a supression at forward rapidits
(small *x* values) in Au where one would expect shadowing effects. At
backward rapidits an enhancement that increases with p~T~ is observed
which could be due to initial-state multiple scattering effects, but
this data is in the anti-shadowing region where an enhancement that
balances the depletion of the gluons at smaller x could also occur.

![](media/image41.png){width="4.819444444444445in" height="4.30625in"}

[]{#__RefHeading___Toc170092603 .anchor}Figure 28 - Nuclear modification
factor in d+Au collisions, R~dAu~, for prompt muons in the forward and
backward rapdity regions versus p~T~. The prompt muons are primarily
from the decays of charm and bottom mesons although perhaps 10% are from
other processes such as light meson decays.

These results were obtained through a statistical method where the
vertex distribution is used to determine and subtract the single muon
component which comes from light meson decays. The punch-through hadrons
were also removed through a statistical method by studying how many
particles reach each layer of the muon identifier system. These
statistical methods suffer from substantial systematic effects that are
probably more than 20-30%. With the FVTX upgrade these events can be
identified on an event-by-event basis and a much more robust and
accurate heavy-quark semi-leptonic decay spectrum can be obtained. This
will also allow measurements at p~T~ values down to 0.5 GeV by
substantially reducing the low-mass meson decay backgrounds

#### Heavy Quark Cross Sections

Many models assume that heavy quarks are formed in pairs from a
combination of gluon fusion and quark anti-quark annihilation.
Next-to-leading-order calculations are performed using the appropriate
parton distribution functions. In contrast to this conventional
expectation, Vitev et al. have shown in their theoretical approach\]
that gluon fusion is not the dominant process for production of open
charm. In their model "flavor excitation" diagrams,
$\text{cg} \rightarrow \text{cg}$ and $\text{cq} \rightarrow \text{cq}$,
dominate the production, rather than gluon fusion,
$\text{gg} \rightarrow c\overline{c}$. Note that this mechanism produces
single charm quarks, not pairs. The relative contribution of these
different processes versus transverse momentum at several different
rapidities is shown in Figure 29.

![](media/image42.png){width="5.9944444444444445in"
height="4.170138888888889in"}

[]{#__RefHeading___Toc170092604 .anchor}Figure 29 -- Vitev's
calculations[^33] show that gluon fusion is not the dominant process in
open charm production at RHIC energies. Here he shows the fraction of
the total cross section contributed by each process vs p~T~ for
different rapidity values for the processes (1)
$\text{cg} \rightarrow \text{cg}$, (2) $\text{cq} \rightarrow \text{cq}$
(where *q* is a light quark or anti-quark), (3)
$\text{gg} \rightarrow c\overline{c}$, (4)
$q\overline{q} \rightarrow c\overline{c}$ and (5)
$c\overline{c} \rightarrow c\overline{c}$(intrinsic charm).

If correct, this model implies that the initial state already contains
the heavy quark, which complicates the interpretation of any nuclear
effects. An accurate measurement of the heavy quark cross section is
needed to determine the production mechanism for heavy quarks ranges and
to constrain recombination models for quarkonia as discussed below.

### Disentangling the Physics of J/ψ and ϒ Production in Nuclei

Recent measurements by PHENIX of the J/ψ nuclear dependence for d+Au
collisions[^34] are shown in Figure 30. The large rapidity region
corresponds to small x in Au, the region where shadowing is thought to
be important. Extraction of gluon densities from these measurements is
not only hampered by the poor statistical precision of the present d+Au
data, but also by theoretical issues including the possibility that much
of the suppression at large rapidity might come from coherent multiple
scattering as calculated i^Error:\ Reference\ source\ not\ found^\],
initial-state energy loss of the incident gluon[^35] or from Sudakov
suppression of the
final-state$c\overline{c}$^\[Error:\ Reference\ source\ not\ found\]^.
Increased statistics together with definitive measurements of open charm
and bottom will help constrain the underlying theoretical QCD processes,
though additional measurements will likely be needed to unambiguously
determine what cold nuclear matter effects are contributing to particle
production rates.

Different d+Au runs at different energies and rapidities will help since
the relative contributions of energy loss and shadowing changes versus
x~F~. Adding Drell-Yan measurements to the mix will also help as
Drell-Yan does not suffer from final-state effects. With the FVTX a
Drell-Yan measurement becomes possible as we can reject the other dimuon
backgrounds which contribute at the same mass as Drell-Yan (open heavy
flavor and decay muons from pi and kaon decays). The potential additon
of ψ' measurements (because background rejection and mass resolution
improvement make the measurement possible) and upsilons at forward and
mid-rapidity will further help to constrain models since ψ' does not
suffer from feed-down and upsilons probe a different x-region.

![](media/image43.jpeg){width="4.853472222222222in"
height="4.997916666666667in"}

[]{#__RefHeading___Toc170092605 .anchor}Figure 30 - J/ψ nuclear
dependence versus rapidity, compared to theoretical predictions with two
types of gluon shadowing^\]^.

![](media/image44.jpeg){width="5.376388888888889in"
height="3.8256944444444443in"}

[]{#__RefHeading___Toc170092606 .anchor}Figure 31 - The dependence of
alpha on x~2~ and x~F~ for J/ψ production shows that the suppression
does not scale with x~2~ but does exhibit approximate scaling with x~F~.
Alpha is defined as $\sigma_{A} = \sigma_{p}A^{\alpha}$, where
$\sigma_{p}$($\sigma_{A}$) is the nucleon (heavy nucleus, A) cross
section. Data is from PHENIX (√s = 200 GeV) \], E866/NuSea (√s = 39
GeV)[^36] and NA3 (√s = 19 GeV)[^37].

Data from lower-energy fixed-target p+A measurements by E866 and NA3
have already provided some x~F~ dependent measurements and these are
shown in Figure 31, compared to data from PHENIX. The experiments E866
and NA3 report stronger suppression at large x~F~ (or small x~2~), where
x~2~ is the momentum fraction of the gluon in the nucleus and x~F~ =
x~1~ - x~2~ (x~1~ being the momentum fraction in the proton). A stronger
absorption at mid-rapidity is also observed by the lower energy
experiments. This lack of scaling versus x~2~ for the three experiments
indicates that the observed suppression is not dominated by shadowing,
and suggests that energy loss or other nuclear effects are playing
important roles in J/ψ production, at least at lower energies. Clearly,
a larger x~F~ coverage by PHENIX is highly desired.

.

![](media/image45.png){width="5.999305555555556in"
height="4.777777777777778in"}

[]{#__RefHeading___Toc170092607 .anchor}Figure 32 -- PHENIX J/ψ nuclear
depedence data for Au+Au and Cu+Cu collisions versus centrality at
forward and mid rapidity. The shaded areas are EKS shadowing
calculations with absorbtion cross sections between 0 and 3 mb.

Figure 32 demonstrates the uncertainty in the cold nuclear matter
effects when extrapolated from d+Au collisions to Au+Au collisions. As
seen by the large blue band, most of the suppression of J/ψ in Au+Au
could be due to cold matter effects, with a factor of about two
uncertainty. Although higher statistics data will help, one of the
largest uncertainties comes from the subtraction of the combinatoric
background due to random combinations of muons from light hadron decays.
The FVTX will eliminate most of the hadron decays using the large DCAs
of their decays to muons (see section 2.1.5), resulting in a statistics
limited measurement rather than a systematics limited measurement.

### Hadrons at Forward and Backward Rapidity

Light hadrons, π and K, can also be measured at forward and backward
angles by the PHENIX muon arms using their decays into muons or by
identifying those hadrons that "punch through" all layers of a muon
identifier. These punch-through hadrons are identified by measuring
particles which stop in the middle of the muon identifier planes and
requiring that the momentum measured in the tracker is greater than the
momentum of a muon that would stop in the same plane. The decay muons
from pion and kaon decays are measured by fitting the single particle
spectra versus the z position of the event vertex. Since decay muons
will contribute more for vertices far from the absorber than vertices
close to the absorber, the decay component can be inferred from this
fit.

Nuclear modification factors for light mesons (via their decay to muons)
for dAu collisions from PHENIX are shown for positive and negative
rapidity in Figure 33. Similar to the prompt muon results shown earlier,
these particles also exhibit suppression at forward rapidits and
enhancement at backward rapidits. Hadron production at forward rapidity
is sensitive to the gluon structure function and its modification in
nuclei, e.g. shadowing. However, whether these hadron measurements
actually probe small momentum fractions that lie within the shadowing
region is unclear, as some theoretical calculations indicate that unless
one measures two hadrons in the forward direction one does not actually
sample small enough x values.^32^

![](media/image46.png){width="5.747222222222222in" height="3.90625in"}

[]{#__RefHeading___Toc170092608 .anchor}Figure 33 - Nuclear modification
factor in d+Au collisions (R~dAu~) for hadrons decaying into muons in
the forward (red) and backward (blue) rapidity directions (PHENIX
Preliminary).

Like the prompt muons discussed earlier, this method of measuring
hadrons suffers from large systematic errors due to the statistical
method used to separate prompt particles from light hadron decays. With
the FVTX we will be able to cleanly separate the prompt component from
that due to the decaying hadrons by measuring the displacement of tracks
from the primary vertex. This will allow direct identification of the
light hadrons, especially at larger p~T~ where the heavy-quark decays
would normally start to dominate, and produce a cleaner result with much
smaller systematics. In addition, the FVTX can provide an independent
sample of punch-through hadrons that can also be used to measure the
forward and backward hadron spectra.

The ratio of yields for all particles measured in the muon arms in
central divided by peripheral d+Au collisions is shown versus rapidity
in Figure 34. Data for light hadrons and for the J/ψ show a surprisingly
similar trend: suppression at forward rapidity and enhancement at
backward rapidity. This has been interpreted as the consequences of
nuclear shadowing. The FVTX will provide reduced systematic errors for
all of the measurements at \|y\|\>0 (include estimates or reference).
Figure 33 clearly points to the importance of a broad rapidity coverage
that can be provided by the FVTX.

![](media/image47.jpeg){width="5.5in" height="4.715277777777778in"}

[]{#__RefHeading___Toc170092609 .anchor}Figure 34 -- Nuclear
modification in d+Au collisions in terms of the ratio between central
and peripheral collision yields, Rcp, for light hadrons that decay into
muons from PHENIX, compared to similar results from Brahms and to PHENIX
data for the J/ψ.

A different interpretation is provided by Vitev et al., where the most
important effect in the increasing suppression at large rapidity comes
from energy loss in the initial state. In their calculations, shown in
Figure 35, coherent multiple scattering plus a rapidity shift of
$\Delta y = 0\text{.}\text{25}$ providing a phenomenological energy loss
gives suppressions very similar to both the hadron and charm data. The
calculations do not include initial-state p~T~ broadening (Cronin
effect) which could slightly alter the comparison of the calculation to
the data.

![](media/image48.png){width="5.999305555555556in"
height="5.852777777777778in"}

[]{#__RefHeading___Toc170092610 .anchor}Figure 35 -- Calculations from
Vitev\] top: Suppression of the single inclusive hadron yields in d+Au
collisions versus p~T~ for rapidities y~1~ = 1.25 and 2.5. Bottom:
Impact parameter dependence of the calculated nuclear modification for
central, b=3 fm, minimum bias, 5.6 fm and peripheral, 6.9 fm,
collisions.

One should also note that the model of Kopeliovich\] which includes
Sudakovnsuppression, provides a somewhat universal explanation for
increasing suppressions at forward rapidity as well. As an example we
show these calculations compared to the Brahms forward π^-^ suppression
ratios in Figure 36.

![](media/image49.png){width="5.035416666666666in"
height="5.123611111111111in"}

[]{#__RefHeading___Toc170092611 .anchor}Figure 36 -- Calculations from
Kopeliovich\] Ratio of negative particle production rates in d+Au and
p+p collisions as a function of p~T~. Data are from Ref. [^38], solid
and dashed curves correspond to calculations with the diquark size 0.3
fm and 0.4 fm, respectively.

It is also important to study the modification of jets in the forward
and backward directions from d+Au, both to understand the fragmentation
and how it is modified in cold nuclear matter. Jet data will also
provide a baseline for similar studies in nucleus-nucleus collisions
where jets are one of our most important tools for studying the
properties of the hot-dense matter (QGP) created in those collisions.
The FVTX will detect all charged particles in the jet, rather than just
the leading particle.

### Drell-Yan Measurements

Drell-Yan events, which provide a direct measure of the anti-quark
distributions in nucleons or nuclei, have always been limited in the
past in their reach to low *x* by the inability to separate the
Drell-Yan muon pairs below the J/ψ mass from copious pairs due to
open-charm decays. For example, as shown in Figure 37, the FNAL E866
Drell-Yan data was limited to masses above 4 GeV, due to a significant
contribution of randoms (charm decays) at lower masses. At RHIC
energies, the backgrounds from charm decays are much worse.

![](media/image50.png){width="4.843055555555556in"
height="2.3361111111111112in"}

[]{#__RefHeading___Toc170092612 .anchor}Figure 37 - Dimuon mass spectrum
from E866/NuSea, showing the Drell-Yan mass region used in their
analysis, which excluded masses below 4 GeV/c^2^ because of the large
backgrounds from open charm decays (labeled Randoms) in that region.

On the other hand, PHENIX, with the addition of the FVTX, should be able
to identify and quantify the portion of the low mass dimuon continuum
from charm decays and also remove the large numbers of random pairs from
light hadron decays by measuring the displacement of the tracks from the
primary vertex. This should allow Drell-Yan measurements over a broad
mass range including values below the J/ψ, therefore spanning a large
range of x with values well into the shadowing region. Since the
relative Drell-Yan rates at RHIC are small, such measurements will still
be a challenge, but with RHIC-II luminosities such measurements have the
potential to provide information on the anti-quark distributions in
nuclei at much smaller values of *x* than are currently accessible. At
the same time, one would also learn more about charm production and the
correlation of the charm pairs through the decay pairs found in the
continuum.

### Summary of Physics Addressed by the FVTX in d(p)+A Collisions

The FVTX addresses the following physics in d+A reactions:

-   Probing the small-x shadowing region in nuclei through the
    production of single heavy quarks (c and b) and of bound states of
    heavy quarks (J/ψ, ψ' and ϒ).

-   Comparison of light and heavy-quark *p*~T~ distributions to
    determine differences in energy loss and Cronin effects.

-   Measurements of light hadrons to contrast with heavy quarks in the
    same kinematical regions.

-   Bottom cross sections as a constraint on the contributions of
    $B \rightarrow \frac{J}{\psi}$to J/ψ production.

-   Measurements of the energy loss and multiple scattering of heavy
    quarks in cold nuclear.

-   Disentangling various nuclear effects on J/ψ production by
    contrasting it with open charm production at large positive and
    negative rapidity.

-   Separation of the ψ' from the J/ψ, leading to the first ψ' nuclear
    dependence data from RHIC.

-   Drell-Yan measurements of anti-quark shadowing at small *x* values.

-   ϒ and Drell-Yan nuclear dependence measurements at mid-rapidity
    where x is large.

## Polarized Proton Collisions, and the Gluon and Sea Quark Spin Structure of the Nucleon

Understanding the substructure of the nucleon is of fundamental interest
in nuclear and particle physics. The strong nuclear interaction observed
between nucleons inside a nucleus is a residual "van-der-Waals" force
arising from a more fundamental interaction, Quantum Chromodynamics,
between the nucleon\'s partonic constituents, namely the quarks and
gluons. Studying the partonic distributions inside the nucleon can shed
light on why and how quarks and gluons are confined inside hadrons.

The striking results, first from the EMC experiment at CERN and then
from subsequent experiments at SLAC, DESY, and Jefferson Lab, showed
that the total spin of the quarks does not account for the total spin of
the proton. These deep-inelastic scattering (DIS) experiments have
established that only 10-30% of the proton spin is carried by the quarks
and anti-quarks. The rest of the spin must come from the gluon spin and
the parton orbital angular momentum. Figure 38 shows the AAC
collaboration analysis of the polarized parton distributions for quarks
and gluons. SU(3) flavor symmetry is assumed in the analysis, and for
sea quarks it is assumed that
$\Delta\overline{u} = \Delta\overline{d} = \Delta\overline{s}$. The sea
quark polarization is poorly constrained (lower right panel) and gluon
polarization is virtually unknown(upper right panel), with the present
set of data.

![](media/image51.png){width="4.041666666666667in"
height="3.6770833333333335in"}

[]{#__RefHeading___Toc170092613 .anchor}Figure 38 - Global polarized
quark and gluon distributions from AAC collaboration. The red line is
the result of their fit, and the green band is the total uncertainty
with respect to the red line. The other colored lines are alternative
parameterizations of these distributions.

The PHENIX spin program seeks to measure the gluon spin structure
function in the proton. Shown in Figure 39 are the different channels
that can be used for the extraction of the gluon spin structure
function. The existing PHENIX capability is shown in the blue bars.
However, precision measurements for heavy quarks with the separation of
charm and bottom are only possible with the addition of a precision
vertex tracking detector. The green bars display the additional
capability supplied by the barrel VTX detector. However, there are
significant gaps in this *x*-range that will make it difficult to fully
address the spin issue. The FVTX proposed here extends the coverage (red
bars) to the lowest and highest *x*-values, 0.001 \< *x* \< 0.3, as well
as providing significant regions where multiple channels overlap. These
overlaps will provide vital cross-checks that will improve the
reliability of global fits to the spin structure functions.

![](media/image52.jpeg){width="5.497916666666667in"
height="4.240972222222222in"}

[]{#__RefHeading___Toc170092614 .anchor}Figure 39 - Expected *x*-range
for different channels used to extract the gluon spin structure
function. The blue bars indicate PHENIX's existing capability, green
bars are for the Barrel upgrade, while the red bars indicate the
additional coverage provided by the proposed Endcap vertex upgrade. The
curves show various estimates of the expected gluon polarization[^39].

### The Role of the FVTX Detector

The Endcap Vertex Detector provides significant improvements in
*x*-range coverage over a Barrel-only detector, as shown in Figure 39.
It also provides a model independent clean separation of light hadron,
charm and bottom production. The following list of measurements that are
possible with the FVTX detector has been studied by simulating *p+p*
collisions with PYTHIA and requiring sufficient counts in each exit
channel to be able to make a reasonable measurement:

-   $c\overline{c}$production via gluon fusion, measuring DμX. The
    *x*-range is extended considerably down to *x* = 0.001 and up to
    x\~0.3, using$D \rightarrow \mu X$, with a displaced muon from charm
    decay.

-   $b\overline{b}$production via gluon fusion. With the upgrade we can
    identify displaced *J*/ψ from $B \rightarrow \frac{J}{y}$ decay.
    This provides coverage for 0.005 \<  *x* \< 0.3. The selection of
    semi-leptonic decays BμX at high momentum is improved using
    displaced vertices. This extends the *x*~gluon~ coverage for these
    semi-leptonic decays to 0.01−0.3.

-   π, K measurements via decay muons or direct measurement of
    punch-throughs

-   Drell-Yanμ^+^μ^-^

-   Background suppression for *W* physics events. The main background
    for a *W* measurement with single muons is muons from heavy flavor
    decay and light hadron decay and/or punch-through. The heavy flavor
    background can be identified and rejected based on displaced
    vertices. The light hadron background can be suppressed with an
    isolation cut, DCA cuts, and χ^2^ cuts on the MuTr+FVTX track fit
    and on the dE/dx measurement in the FVTX. This could also extend *W*
    physics to a broader kinematic coverage by measuring low *p*~T~
    muons from *W* decays.

### Polarized Gluon Distribution and Heavy Quark Production

The RHIC-SPIN program provides a new tool to directly collide polarized
protons at high energy (shown at leading order in Figure 40) and as such
PHENIX has a major goal of measuring the gluon spin-structure function
of the proton. At RHIC energy, heavy flavor production is dominated by
gluon-gluon interactions as is also shown in Figure 40, and is therefore
sensitive to the polarized gluon distribution in polarized p+p
collisions.

![](media/image53.png){width="4.385416666666667in"
height="2.6041666666666665in"}

[]{#__RefHeading___Toc170092615 .anchor}Figure 40 - At RHIC-SPIN, quarks
and gluons interact directly at leading order.

Experimentally we measure the double spin asymmetry;

$A_{\text{LL}}^{Q\overline{Q}} = \frac{\sigma^{\text{++}} - \sigma^{+ -}}{\sigma^{\text{++}} + \sigma^{+ -}}\text{\textasciitilde}\frac{\Delta G(x_{1})}{G(x_{1})} \otimes \frac{\Delta G(x_{2})}{G(x_{2})}a_{\text{LL}}(x_{1} + x_{2} \rightarrow Q\overline{Q} + X)$

The partonic asymmetry $a_{\text{LL}}(x_{1} + x_{2} \rightarrow H + X)$
is normally calculated within the framework of pQCD. In the PHENIX
experiment, we will measure the polarized gluon distribution
$\frac{\Delta G(x)}{G(x)}$ using many different processes as indicated
in Error: Reference source not found. However, in reality, one always
faces various backgrounds in the measurement, so the measured signal
asymmetry is diluted,

$\begin{array}{r}
A_{\text{LL}}^{Q\overline{Q}} = \frac{A_{\text{LL}}^{\text{incl}} - r \cdot A_{\text{LL}}^{\text{BG}}}{1 - r} \\
{dA}_{\text{LL}}^{Q\overline{Q}} = \frac{\sqrt{({dA}_{\text{LL}}^{\text{incl}})^{2} + r^{2} \cdot ({dA}_{\text{LL}}^{\text{BG}})^{2}}}{1 - r}
\end{array}$

where $r = \frac{N^{\text{BG}}}{N^{Q\overline{Q}} + N^{\text{BG}}}$ is
the background fraction, $A_{\text{LL}}^{\text{incl}}$ and
$A_{\text{LL}}^{\text{BG}}$ are the asymmetries of the inclusive signal
and background, respectively. Normally, the background asymmetry itself
is not well known, so it is very important to minimize the background
fraction. The proposed Forward Silicon Vertex detector will
significantly improve the purity of the signals both for the light
hadron and heavy quark measurements by permitting an additional cut on
displaced vertex information.

####  Measurements of Open Heavy Quark Production

In section 3.1.2 a general discussion of the need to remove light hadron
decays and punch through hadrons to get a clean measurement of charm and
bottom decays was given. Those cuts presented in that section are
relevant here and have been studied in p+p measurements for charm and
bottom. Methods for separating charm from bottom as defined in section
3.2 will also be applied to the p+p data.

We have simulated the improvement in determining the double asymmetry
measurement A~LL~ for charm and bottom. Figure 41 shows projected
experimental sensitivities of double spin asymmetry measurements with
(blue) and without (red) the FVTX detector if we can identify prompt
muons from open charm and open bottom decay. Also shown in the figure
are theoretical predictions for the charm, bottom,and the sum, asymmetry
using gluon spin distributions from the world's data fit. The error bars
are derived in a similar manner as done in section 3.1.3. A very precise
asymmetry measurement is possible over a large p~T~ range, allowing us
to distinguish between zero asymmetries and asymmetries predicted for
nominal gluon polarization, even without separating the charm and bottom
components. In addition, if we can separate charm and bottom
measurements, as was discussed in section 2.1.3, we will provide more
sensitive asymmetry measurements as the charm and bottom asymmetries
partly cancel over much of the p~T~ range. Therefore the individual
asymmetries are expected to be much larger than the sum of the two. Note
that the flavor excitation mechanism can contribute to open charm
production, but has not been included in the theoretical asymmetries
shown in Figure 41.

![](media/image54.wmf){width="4.627083333333333in"
height="3.3159722222222223in"}

[]{#__RefHeading___Toc170092616 .anchor}Figure 41 The error bars that
would be obtained on an ALL measurement, assuming 32 pb^-1^ integrated
luminosity with (blue) and without (red) the FVTX detector.

#### Measurement of Light Hadron Production with the Muon Spectrometers

There is copious production of light hadrons at RHIC. Figure 42 shows
the muon *p*~T~ spectra from different sources in 200 GeV *p+p*
collisions, where the muons from light charged hadron decays dominate at
low *p*~T~ (\< 3 GeV.) Using recently developed analysis techniques, we
can measure inclusive light hadron production with the muon
spectrometer, using event vertex and muon penetration depth analysis to
statistically establish the hadron and muon event rates. This method was
used in the dAu analysis and is being used now for the 2005 *pp* data
analysis of spin asymmetries. The proposed forward silicon vertex
detector will enable us to identify muons from light hadron decay on an
event-by-event basis, as they tend to have large vertex separations of
order of few mm or greater. Furthermore, these light hadrons are
dominantly produced through *gg* and *gq* scattering at low *p*~T~, see
Figure 43. Such samples can be used to explore gluon polarization since
they have good statistics and also cover a wide range of momentum
fraction *x*.

![](media/image55.png){width="4.245138888888889in"
height="3.3541666666666665in"}

[]{#__RefHeading___Toc170092617 .anchor}Figure 42 - Muon *p*~T~ spectra
with different origins from Pythia simulation, as a function of *p*~T~
\[GeV\]. Muons from light charged hadron decays (black); from open charm
(green); from open bottom (red).

![](media/image56.png){width="3.3333333333333335in" height="2.46875in"}

[]{#__RefHeading___Toc170092618 .anchor}Figure 43 - Partonic origin of
charged pions produced within the acceptance of muon spectrometer in pp
collisions at  √s = 200 GeV.

The improvement in an A~LL~ measurement for hadrons, that can be
obtained with the FVTX detector compared to without the FVTX detector is
shown in Figure 44 along with theoretical predictions of the asymmetries
for different gluon spin assumptions. With the FVTX we enter the realm
of being able to distinguish among different gluon polarization
predictions, whereas without the FVTX no discrimination can be made.

![](media/image57.wmf){width="4.999305555555556in"
height="3.5881944444444445in"}

[]{#__RefHeading___Toc170092619 .anchor}Figure 44 A~LL~ measurement for
hadrons obtained with (blue) and without (red) the FVTX detector.

#### Measurements of Heavy Quarkonium Production 

Presently the most accurate way to measure the polarized gluon
distribution in the nucleon is to study those processes which can be
calculated in the framework of perturbative QCD, i.e., those for which
the involved production cross section and subprocess asymmetry can be
predicted. Heavy quarkonium has been a useful laboratory for
quantitative tests of QCD and, in particular, of the interplay of
perturbative and non-perturbative phenomena, as the heavy quark pair
production processes can be controlled perturbatively, due to the large
mass of heavy quarks. The factorization formalism of non-relativistic
QCD provides a rigorous theoretical framework for the description of
heavy quarkonium production and decay. It successfully describes the
inclusive cross section of charmonium production at the Tevatron and
RHIC. In *pp* collisions, heavy quark pairs are mainly produced in gluon
fusion processes, and therefore, asymmetries are expected to be
sensitive to the polarized gluon distribution function in the proton.
Another advantage of heavy quarkonium is that it provides a very good
event-by-event measurement of gluon "*x*" values since we can almost
fully reconstruct the parton collision kinematics. Production of the
ground state quarkonia from decays of the higher levels is significant
and needs to be taken into account.

During the RHIC run in 2005, PHENIX accumulated 3.8 pb^-1^ of integrated
luminosity with an average beam polarization of 47%. This provides the
first opportunity to explore the gluon polarization with heavy quarks at
RHIC. Figure 45 shows the opposite charge dimuon pair mass spectrum from
run5 *pp* data. The J/ψ signal clearly stands out from the background.
There were about 7300 J/ψ candidates from which the double spin
asymmetry was measured, see Figure 46.

![](media/image58.png){width="3.6493055555555554in"
height="2.497916666666667in"}

[]{#__RefHeading___Toc170092620 .anchor}Figure 45 - J/ψ measurement from
run5 pp run. The J/ψ peak clearly stands out from the background. The
background fraction is about 25% under the J/ψ mass peak.

![](media/image59.png){width="3.875in" height="2.7291666666666665in"}

[]{#__RefHeading___Toc170092621 .anchor}Figure 46 - The first
measurement of double spin asymmetry from polarized *pp* collisions at
RHIC.

The majority of the background under the J/ψ mass peak is from muons
produced by open charm and light hadron decay. As in the case of single
muons, at high *p*~T~ it is expected that the J/ψ sample will be also
contaminated by J/ψ's from *B* decay. The proposed forward silicon
vertex detector will help us to improve the prompt J/ψ signal purity by
rejecting background muon pairs through a cut on displaced vertices
since muons from prompt J/ψ decay point back to the original collision
vertex and by improving the mass resolution which will also result in
fewer background dimuons below the J/ψ peak. Figure 47 shows the
expected asymmetry measurements for prompt J/ψ (not from *B* decay) with
projected luminosities at RHIC, without the FVTX detector. With the FVTX
detector, the error bars will be improved because of the reduced
systematic errors which come from smaller backgrounds below the J/ψ
peak.

![](media/image60.png){width="4.322916666666667in" height="3.3125in"}

[]{#__RefHeading___Toc170092622 .anchor}Figure 47 - Expected
experimental sensitivities of double spin asymmetry measurements with
prompt J/ψ (not from *B* decay).

J/ψ from bottom decay can also be measured using the FVTX, as was
indicated in section 2.1.3.3

![](media/image61.jpeg){width="2.875in" height="2.207638888888889in"}

[]{#__RefHeading___Toc170092623 .anchor}Figure 48 - Left panel:
Correlation between gluon x1 and p~Z~ of J/ψ from B meson decays (PYTHIA
simulation.) Right panel: Correlation between x2 and p~T~.

### Polarized Sea Quark Distributions and *W/Z* Production

*W* production at PHENIX presents a unique opportunity to study the
flavor dependence of (polarized) quark and anti-quark distributions
inside the proton. The *W*^+^ is produced by collisions of up and
anti-down quarks and identified experimentally through a decay muon
(Figure 49):

$u + \overline{d} \rightarrow W^{+} \rightarrow \mu^{+} + \nu$

Similarly, for *W*^−^, the process is:

$d + \overline{u} \rightarrow W^{-} \rightarrow \mu^{-} + \overline{\nu}$

![](media/image63.png){width="3.3875in" height="3.453472222222222in"}

[]{#__RefHeading___Toc170092624 .anchor}Figure 49 -- W production and
decay to a muon plus a neutrino.

A measurement of the single spin asymmetry of muons from W+ (W-)
production yields a measure of the anti-d and u (anti-u and d)
polarization. In order to make a sensitive measurement of these quark
and anti-quark distributions, the lepton-ν decay channel should be
clearly separated from other W decay channels and the muons in this
decay channel should be clearly separated from other sources of muons.
We can discriminate among the different decay channels using the FVTX
detector by making an isolation cut (the μν channel will not have
neighboring tracks from the W event but the other decay channels will)
and a DCA cut (muons from hadron or τ decay will show a displaced DCA).

The main backgrounds for a *W* measurement are muons from heavy flavor
decay, punch-through hadrons and low energy hadrons which decay within
the tracker volume and are mis-reconstructed into a high-p~T~ muon.. The
decay-in-tracker-volume component is shown in Figure 51, along with the
muons from W decay. As seen in the figure, the lowest p~T~ bins (true
momentum) make the largest contributions to the fake high p~T~
background for W measurements.

![](media/image65.png){width="4.75in" height="3.1743055555555557in"}

[]{#__RefHeading___Toc170092625 .anchor}Figure 51 The single muons from
W decay (red) and the muons from various p~T~ bins which are
mis-reconstructed to higher momentum. As can be seen, the lowest (true)
p~T~ bins make the largest contributions to the (fake) backgrounds at
high p~T~.

The background from heavy flavor decaysFigure 50 can be identified and
rejected based on a displaced secondary vertex; for light hadrons, an
isolation cut can be used to suppress the background: in general, a muon
from *W* decay has no accompanying jet, while a light hadron normally
has associated jet particles around it, and for hadrons which decay in
the tracker volume an isolation cut can also be used to reduce the
background. Additional discrimination against in-tracker decays comes
from a χ^2^ cut on a full FVTX+Muon tracker fit). Reduction of these
backgrounds could also allow us to extend the *W* physics to a broader
kinematic coverage by lowering the minimum *p*~T~ requirement for muons
from *W* decays. Figure 52 shows the expected sensitivity and *x*-range
for the flavor dependent polarized quark distribution functions measured
by the PHENIX muon spectrometers at √s = 500 GeV if we have a clean W
measurement. In the next section we describe the performance for
rejecting the background muons.

![](media/image66.png){width="3.90625in" height="4.583333333333333in"}

[]{#__RefHeading___Toc170092626 .anchor}Figure 52 - Expected flavor
dependent polarized quark distribution functions measured by the PHENIX
muon spectrometers.

#### W Measurements via Single Muons

As indicated in Section 2.3.3 polarized sea quark distributions can be
extracted from W measurements via single muons if the background muons
are sufficiently low and the μν decay channel can be selected. The
background from decay muons from light mesons can be reduced using the
FVTX detector just as they are to be reduced for open heavy flavor
measurements via a DCA cut on the muon. Pions and kaons which
punch-through the muon system, and pions and kaons which decay within
the tracker volume can not be removed via a DCA cut since they come from
the same primary vertex as the W particles. However, they can be removed
to some extent if an isolation cut is placed on the muon since the W
decay muon typically has very few particles surrounding it in an event
but the hadrons are typically produced within a jet of particles. An
isolation cut is illustrated in Figure 53 where a primary particle and
secondary particles within a given cone are shown.

[]{#__RefHeading___Toc170092627 .anchor}Figure 53 Schematic of an
isolation cut: the number of particles in a given layer that are within
a cone are counted and if the number found is less than some value the
particle is considered to be "isolated" and if it is larger than that
value it is not isolated.

The number of particle tracks that are found close to a muon are shown
for all muons from minimum bias events (blue) and for muons from W decay
(red) in Figure 54 versus momentum. As seen, the momentum of muons from
W decay is typically much higher than the muons created in a minimum
bias event and the number of tracks found surrounding the muon from W
decay is typically zero while there are typically several other tracks
found surrounding a background muon track. A combined cut on momentum
and number of surrounding tracks will provide isolated high momentum
tracks which are predominantly from W decay.

![](media/image67.png){width="6.1375in" height="3.5909722222222222in"}

[]{#__RefHeading___Toc170092628 .anchor}Figure 54 The number of
particles (y axis) that are found in an event surrounding a muon from
minimum bias events (blue) and muons from W events (red), versus
momentum.

To understand the various contributions to the single muon spectrum,
relative to the signal from W decays, 5 million minimum bias events and
several hundred thousand W events were thrown using the PYTHIA event
generator, run through our full simulation, and the number of tracks
reconstructed versus p~T~ was counted. Additionally, 1.9 billion single
π and 1.9 billion single K particles were simulated to look at the
contributions from mis-reconstructed particles which decayed in the muon
tracker volume. These single particles were normalized based on
PYTHIA-generated and UA1-generated events, and the contributions were
shown in Figure 51. We then apply the various cuts that have been
described above on all reconstructed tracks:

-   ≥3 hits in the FVTX (to allow a track to be reconstructed)

-   Muon Tracker quality cuts (track reaches last plane of MuID,
    χ^2^\<20, DG0\<15, DDG0\<10, DS3\<50, DS0\<200, DS3ctpc\<30,
    mutr_nhits\>=12)

-   

-   Muon Tracker plus FVTX track fit χ^2^\<3

-   Hits in a cone of 0.3 rad \<2 (isolation cut)

The background and signal efficiency that is achieved for each of these
cuts is shown in Figure 57. The red line gives the efficiency for muons
from W, and the other lines show the efficiency when successive cuts are
applied to the background. Turquoise is with the FVTX acceptance cut of
≥3 hits, green adds MuTr+FVTX χ^2^ cut and black adds the isolation cut.
As seen, a large overall rejection factor is achieved for the
background. The efficiency for the W is about 40%, with much of the loss
coming from requiring ≥3 hits in the FVTX system. If we add the use of
barrel silicon hits, we expect to regain some of this efficiency loss.
Some caveats to note on the background rejection are:d the track fitting
uses perfect pattern recognition (we pick the Monte Carlo hits which are
known to go with a particular track). We expect some reduction in the
background rejection when these reality factors are added to the
simulation. However, the rejection factor is already quite large (as
high as 1^4^ -1^66^ at high p~T~) so we still expect to retain
significant rejection of the backgrounds, allowing a very significant W
measurement even if backgrounds are increased. Additionally, statistics
were poor for the background simulations in the highest p~T~ bins, so
extrapolations of our rejection factors were compared to the absolute
calculations and the extrapolations were then used to calculate the
final rejection factors. Some of the high pT bin background rejection
may be over-estimated based on this method. We are in the process of
running larger statistics simulations to address this short-coming.

![](media/image68.png){width="4.129166666666666in"
height="2.9743055555555555in"}

[]{#__RefHeading___Toc170092629 .anchor}Figure 55 Efficiency for
background and and signal tracks in the single particle spectrum, for
each successive cut. Red is the W efficiency with all cuts, turquoise is
the background with muon quality cuts and FVTX hits ≥3, green adds the
MuTr+FVTX χ^2^ cut and black adds the isolation cut.

Figure 56 shows the signal to:background which we achieve with the cuts
applied, and the background tracks appropriately normalized to the W
signal. The background (black dotted lines) and W signal (red dotted
lines) are shown before any track cuts are placed and after the cuts are
placed (black solid is the background and red solid is the signal). As
seen, the current simulations give signal to:background \>1 above around
15 GeV p~T~.

![](media/image69.png){width="4.144444444444445in"
height="2.4930555555555554in"}

[]{#__RefHeading___Toc170092630 .anchor}Figure 56 The W signal and
background muon contributions before cuts (black dotted is background
and red dotted is W signal) and after track cuts (black solid is the
background and red solid is the W signal)

### Physics with Transversely Polarized Beams

The aim of this section on transverse spin is to elucidate another
unique measurement that the FVTX upgrade makes possible, namely the
measurement of the Sivers gluon distribution
in$p^{­}p \rightarrow \text{DX}$**.** To make this understandable,
however, it is necessary to briefly introduce the phenomenology of
transverse spin and transversity.

#### Introduction to Transverse Spin Phenomenology

In addition to the familiar unpolarized quark parton distribution
function *q*(*x*) measured in *ep* and *pp* scattering, and the
polarized (helicity) distribution function $Dq(x)$ measured in
$\overrightarrow{e}\overrightarrow{p}$ and
$\overrightarrow{p}\overrightarrow{p}$ scattering, there is a third
equally fundamental distribution function associated with the transverse
polarization of the quarks, called the transversity distribution
function $dq(x)$. In a basis of helicity spin states, the transversity
distribution $dq(x)$ represents a spin-flip amplitude between two
helicity states. However, in a basis of transverse spin states the
transversity distribution $dq(x)$ has a probabilistic interpretation
similar to that of $Dq(x)$ in a helicity basis. For this reason, a
measurement program involving transversely polarized protons has been
developed at RHIC to measure$dq(x)$.

Transverse single spin asymmetries (SSAs) can be produced in a number of
ways[^40]. The simplest mechanism is to observe the asymmetry
proportional to the triple product of spin *S*, beam momentum *P*, and
observed transverse momentum$p_{T}$ , $A_{N}µS \cdot (P´p_{T})$, in
inclusive hadron production $p^{­} + p \rightarrow h(p_{t}) + X$.
However[^41] this asymmetry is suppressed by a factor
$\alpha_{s}m_{q}/p_{T}$ and so this mechanism is not useful for the
exploration of the transversity distribution function$dq(x)$.

Other mechanisms for SSAs arise when one (necessarily) takes into
account the effect of initial-state parton transverse momentum$k_{T}$.
Sivers showed[^42] that a $k_{T}$-dependent quark distribution for a
transversely polarized nucleon, anti-symmetric with respect to nucleon
spin-flip, can be a source of SSAs. This distribution (now called the
Sivers distribution) describes an initial-state correlation between the
transverse spin of the nucleon *S* and the parton transverse
momentum$k_{T}$, and thus contains a tremendous amount of information
about the structure of the nucleon. The asymmetry it produces is
proportional to $A_{N}µS \cdot (P´k_{T})$.

Another mechanism involving parton transverse momentum $k_{T}$ is the
Collins-Heppelmann effect[^43] whereby the final-state jet momentum
$P_{\text{jet}}$is correlated to the spin and initial state $k_{T}$ and
produces an asymmetry$A_{N}µS \cdot (P_{\text{jet}}´k_{T})$.

The three mechanisms described so far all involve the transversity
distribution $dq(x)$ through the transverse spin *S*. There is another
mechanism to produce a transverse SSA, noted by Brodsky, Hwang and
Schmidt[^44]. Final state interactions between the struck quark and the
spectator system can produce such asymmetries. We will not concern
ourselves here with this mechanism, because the asymmetry we are most
interested to discuss does not require this mechanism. However, such
final state interactions could *modify* the asymmetry of interest.

The Sivers idea can be invoked to define a Sivers gluon function[^45],
and that is the topic of most interest to us here.

#### Measurement of the Sivers Gluon Distribution in $p^{­}p \rightarrow \text{DX}$

Recently[^46] a new window into the gluon structure of the nucleon was
opened by realizing that a measurement of the transverse single spin
asymmetry in $p^{­}p \rightarrow \text{DX}$ is uniquely sensitive to the
Sivers gluon distribution function, see Figure 57. There are two
channels that dominate open charm pair production; *s*-channel quark
annihilation $q\overline{q} \rightarrow c\overline{c}$, and the gluon
fusion process $\text{gg} \rightarrow c\overline{c}$. Note that the
possible production of charm due to flavor excitation has not yet been
included. Gluons do not carry transverse spin, therefore for **both** of
these channels there cannot be any polarization of the final state charm
quarks if the initial state protons are only transversely polarized. The
lack of final state quark polarization rules out any Collins effect,
leaving the Sivers distribution as the only source of a single spin
asymmetry.

The FVTX upgrade can make such a unique measurement idea into a reality.
As already discussed in other sections of this proposal, *D* production
can be tagged on an event-by-event basis, therefore a very clean sample
of $p^{­}p \rightarrow \text{DX}$ events can be produced for subsequent
SSA analysis. This same physics will also be accessible in the central
arms, using the VTX upgrade, but this was not known at the time of the
VTX proposal because the Anselmino et al. paper was not published.

![](media/image70.jpeg){width="4.502083333333333in"
height="3.498611111111111in"}

[]{#__RefHeading___Toc170092631 .anchor}Figure 57 - Maximized values of
transverse single spin asymmetry A~N~ for the process pp-\>DX as a
function of x~F~ at fixed transverse momentum calculated using saturated
Sivers function. The dashed line corresponding to a maximized quark
Sivers function (with the gluon Sivers function set to zero), while the
dotted line corresponding to a maximized gluon Sivers function (with the
quark Sivers function set to zero). Red marks indicate the x~F~ range
that the PHENIX upgrade detectors can measure.

### Tests of pQCD Model Calculations and Providing a Baseline for pA and AA Measurements

Spin plays a key role in fundamental interactions. The experimental
study of spin observables (polarization, spin correlations and
asymmetries) provides information on the most important dynamical
properties of particle interactions. Moreover, the spin studies give us
more complete information than the measurements of spin-averaged
quantities and allow us to make a detailed comparison of various
theoretical model calculations with experiment. The fact that the
nucleon spin composition can be measured directly by experiments has
created an important frontier in hadron structure physics, has had a
crucial impact on our basic knowledge of the internal structure of the
nucleon, and will eventually lead us to a better understanding of strong
interaction phenomena. As an example of how current theory can help us
to understand spin dependent QCD dynamics, Figure 58 shows an NRQCD
prediction for the double spin asymmetry of the J/ψ in two different
helicity states. Experimentally we can identify the helicity state by
examining the dimuon angular distribution from the J/ψ decay.

Before using charm and bottom for spin and heavy ion physics, we need to
test the next-to-leading-order (NLO) pQCD calculations for heavy-quark
production. Qualitatively, low-*p*~T~ charm and bottom production are
dominated by gluon-fusion, while production at high-*p*~T~ is expected
to be dominated by the hard-scattered gluon splitting into a *QQ*
pair[^47]. Present data on charm and bottom production is scarce and of
limited statistics. Data from polarized *pp* collisions at RHIC will
provide critical information on heavy quark production mechanisms.

![](media/image71.png){width="4.719444444444444in"
height="3.839583333333333in"}

[]{#__RefHeading___Toc170092632 .anchor}Figure 58 -- Predicted double
spin asymmetry for charmonium at RHIC[^48]. The asymmetry value depends
on the final state charmonium polarization, which can be tested
experimentally. The red circles indicate the acceptance region for the
PHENIX muon arms and FVTX detector.

There is also significant uncertainty in the primary particle production
mechanism for charm. Leading-order calculations typically calculate the
production from gluon-gluon fusion (indicated in Figure 59, left) but
flavor excitation (shown in Figure 59, right) is predicte\] to give
comparable or even larger contributions to the open heavy-flavor
production.

![](media/image72.png){width="1.8472222222222223in" height="2.375in"}
![](media/image73.png){width="1.7916666666666667in"
height="2.3333333333333335in"}

[]{#__RefHeading___Toc170092633 .anchor}Figure 59 Heavy flavor
production diagrams from flavor excitation (left) and gluon fusion
(right)

In the first case, the correlated c-cbar production should give a strong
back-to-back correlation in two-particle correlation measurements, and
in the second case, there will be no correlation since the D mesons
would come primarily from single charm production. The difference
between these two correlation measurements is shown Figure 60 in where
the gluon splitting (flavor excitation) shows no backward peak in a df
spectrum, but the flavor creation process shows a strong backward peak
in the df distribution. With the FVTX, we can measure the two particle
correlations of c-cbar produced in each event and should be able to
determine what the dominant production mechanism is.

![](media/image74.png){width="5.277083333333334in"
height="2.8604166666666666in"}

[]{#__RefHeading___Toc170092634 .anchor}Figure 60 Back-to-back
correlation expected for flavor excitation is shown in blue and for
flavor creation (gluon-gluon fusion) is shown in red. Note the strong
correlation when c-cbar pairs are created in flavor creation as opposed
to the non-existent correlation that would be true if single charm
production were the primary production mechanism.

###  Summary of Physics Addressed by the FVTX in Polarized *pp* Collisions

In summary, the FVTX detector will significantly improve on the
following physics in polarized *pp* collisions:

-   Probing the polarized gluon distributions via muons from light
    hadron, open charm and bottom decay.

-   Measurement of flavor dependent polarized quark distributions via
    muons from *W* production and providing the first experimental test
    of SU(2) flavor symmetry for polarized sea quarks.

-   Providing a vital cross check of pQCD calculations for light and
    heavy hadron production in polarized pp collisions.

## Trigger Plans

An increasingly important issue as RHIC luminosities rise is to be able
to capture all (or a sufficient) amount of the physics signals through
the DAQ onto archival storage. The first line of attack on this issue is
to use fast Level-1 triggers to identify interesting physics events and
make sure as many of them as possible are read out, and are not
prescaled away. Estimates of the needed rejection factors beyond those
from the present muon identifier based level-1 triggers are estimated in
Appendix C (Section 8). They are listed in Table 1.

[]{#__RefHeading___Toc170092682 .anchor}Table 1 -- Level-1 Rejection
factors needed beyond those available from the present muon triggers.

  -------------- -------------- -------------- -------------- --------------
                 Single muons                  Di-muons       

                 p+p            Au+Au          p+p            Au+Au

  2008 RHIC-I    \~1/20                        1              \~1/5

  RHIC-II        \~1/100                       \~1/1.4        \~1/40
  -------------- -------------- -------------- -------------- --------------

Triggers involving new upgrade systems would probably be formed by first
finding tracks in various subsystem independently (muon identifier, muon
trigger upgrade, FVTX, etc.), then combining these in the final stages
to allow matching of tracks and use of information such as a rough
momentum determination from one subsystem in the final cut decisions
applied to integrated tracks from both (all) subsystems. This would be
implemented on high-speed level-1 trigger boards containing
state-of-the-art FPGA's.

Physics triggers that are needed include:

-   B → J/ψ+X where the existing muon trigger would identify a muon
    pair, the muon trigger upgrade would assure these tracks came from
    the primary vertex using its RPC pad pointing and time-of-flight
    information; and then this combined road would be matched to a FVTX
    pair which would be required to have a detached vertex (∆Z~vertex~
    \> 0.1 cm).

-   Other pair triggers (e.g. prompt J/ψ, ψ' and ϒ) could be formed by
    requiring a prompt rather than downstream vertex.

-   Single muon D and B decays using single-track combined roads
    matching FVTX tracks that have detached vertices. In this case a
    vertex cut of 400μm \< ∆Zvertex \< 1 cm could be made, and for the
    lower momentum tracks (as identified by the muon trigger momentum
    measurement) where the rejection might not be sufficient a
    momentum-dependent prescale could be applied. While at higher
    momentum all detached vertex tracks could be kept.

-   It might also be advantageous to use the FVTX for a more efficient
    minimum-bias (vertex) trigger in p+p collisions, because the present
    BBC-based trigger only achieves an efficiency of \~55% because of
    the low multiplicity of tracks in to the BBC in p+p collisions. The
    much larger acceptance of the FVTX should allow it to provide a much
    more efficient trigger..

More details on the developing trigger plans are discussed in Appendix B
(Section 7), and further discussion of the synergy of the different
subsystems and upgrades is discussed in Appendix D (Section 9).

The Iowa State University group is actively developing the trigger plans
and associated hardware with the help of a STTR grant along with
Northern Micro Design Inc.

After events are selected and passed on by the level-1 triggers, they
can then be examined further by level-2 triggers implemented in a large
array of parallel processors as has been done already at PHENIX. These
processors can do fast reconstruction of the events including full
combinations of the different subsystem information and could then make
more refined cuts including mass cuts for pair triggers, or selecting
high momentum tracks using the higher resolution information from the
muon tracks which would only be available at level-2 and above (not in
level-1). This resulting information could then be used to cut the data
rate down further, or just to allow creation of filtered event streams
enriched for the most important physics topics that would enable fast
offline analysis for timely physics results.

## Si Endcap Event Rates

The event yields in the previous sections are summarized below in Table
2. They assume an integrated p+p luminosity of 33 pb^-1^ and Au+Au
luminosity of 2.5 nb^-1^. The FVTX yields for semi-leptonic heavy quark
decays are about an order of magnitude larger than for the VTX silicon
barrel, due to the larger acceptance of the silicon endcap. The *B*
decay rates would benefit most from the increased luminosity at RHIC II
. Details of the rate estimates and additional count estimates for d+Au
collisions and for p~T~ bins can be found in Section 8.5.

[]{#__RefHeading___Toc170092683 .anchor}Table 2 -- Triggered rates for
RHIC-II p+p and Au+Au in one week of running. Integrated luminosities
are 33 pb^-1^ for p+p and 2.5 nb^-1^ for Au+Au. The semi-leptonic decay
rates are before application of a vertex cut.

  -------------------------- ---------------------- ---------------------
  Observable                 Counts per RHIC-II p+p Counts per RHIC-II
                             week                   Au+Au week

  D → μX                     \~ 71M                 \~180M

  B → μX                     \~880k                 \~2.3M

  B → J/ψ X → μμ             \~650                  \~1.7k
  -------------------------- ---------------------- ---------------------

# FVTX Detector Performance

In this section we will discuss the general performance of the FVTX and
its simulation.

The physics-driven requirements for the FVTX silicon endcap detector
design includes:

-   Sufficient position accuracy so that the displacement resolution of
    a track with respect to the collision point is less than the
    displacement produced by the cτ of charm and bottom decays

-   Excellent accuracy for the primary vertex (\<200 μm in z) using all
    tracks seen in the FVTX as well as those from the VTX (central
    rapidity barrel) vertex detector; with high efficiency (\> 90%) even
    for p+p collisions.

-   Low enough occupancy to allow accurate track finding in Au+Au
    central collisions. Occupancy levels of \<2.8% are achieved.

-   Ability to match tracks from the muon arm (muon tracker and muon
    identifier) to those in the FVTX silicon mini-strips, even in Au+Au
    central collisions..

In addition to these detector requirements, the FVTX detector provides a
number of additional features which allow it to contribute to particle
identification and identification of specific physics decay channels.
These include:

-   Full azimuthal and large rapidity coverage allow one to test whether
    a given particle was produced in isolation within the event or
    within a jet of other particles

-   3-bit ADC( or more) information is available from each hit strip,
    allowing the possibility of having energy loss information for a
    track

-   Additional measurement points on the track trajectory provides
    improved dimuon mass resolution.

-   χ^2^ values for tracks passing through the silicon will be large if
    the momentum is small and has been mis-reconstructed to a large
    value. Therefore, cutting on the χ^2^ should discriminate against
    mis-reconstructed tracks.

The discussion of the above requirements and the simulations that
establish the FVTX performance to satisfy these requirements follows.

## Simulation Code

The FVTX detector sensitive and non-sensitive volumes have been
simulated in the PHENIX GEANT framework, PISA. The simulation includes
the beam pipe, the central silicon barrels, support structures, and the
forward silicon tracker. The radiation length per station in the forward
region is \~1.8-2.4% . This 1.8-2.4% includes sensor, readout chips,
readout bus, and support panels and varies from the inside radius to the
outside radius. This radiation length is achievable because we are
implementing a design that has minimized the readout bus and the
mechanical structure, and we are able to thin the chips. We are still
striving to minimize this thickness, in particular for the critical
first disk. The output of the PISA simulation includes a description of
the materials and detector volumes in the GEANT simulation (to be used
by the offline code) and the x, y and z positions of tracks that hit
sensitive silicon volumes.

The detector volume description and the x,y,z positions are fed into the
offline code (Fun4All) where the detector response is simulated and
track reconstruction takes place. The simulation includes a full
digitization of the PISA hits into hit silicon strips, cluster finding
of strips which belong to one hit is performed, and a centroid fit is
applied to each cluster. The centroid positions of the clusters
belonging to a given track are then used in a Kalman Filter track fit.
The parameters from the track fit are used to project the track to the
event vertex and extract the distance of closest approach (DCA) of the
track to the primary vertex. This DCA value is then used to discriminate
among tracks which originate from the primary vertex and tracks which
come from a displaced secondary vertex. In the simulations that include
the muon spectrometers, tracks are found in the muon system and matched
with tracks in the FVTX and a complete Kalman Filter track fit is
applied to get the correct track in the FVTX. Missing in this full track
reconstruction is a track finding algorithm for the FVTX tracks. While
this algorithm will most likely be patterned after the MuTR track
finding algorithm, we have not implemented this yet primarily because
the occupancy in the FVTX is much less than that in the MuTR so FVTX
track finding should be much easier. At this point, we use Monte Carlo
information to combine hits together into tracks. See section 3.5 for a
discussion of the occupancy.

## Distance of Closest Approach Measurement

Figure 61 shows the basic principle of using the FVTX endcap silicon
detector to detect secondary tracks which have been produced at a
displaced vertex. A D meson is created at the primary vertet where the
two beams collide. It travels a distance proportional to its lifetime
and then decays semi-leptonically into a muon. The muon travels off at a
different angle (due to the decay process), passing through four silicon
planes with 75μm radial pitch. The reconstructed muon track has a small
but non-zero *distance of closest approach* (DCA) to the primary vertex
-- typically 200-300μm - unlike particles from pion and kaon decays,
which have a much larger average DCA and prompt particles which have a
DCA that is nominally zero.

![](media/image76.png){width="4.125694444444444in"
height="2.7555555555555555in"}

[]{#__RefHeading___Toc170092635 .anchor}Figure 61 - Principle of
operation of the FVTX silicon endcap detector in the r-z plane. A D
meson is produced at the collision point. It travels a distance
proportional to its lifetime (purple line), then decays to a muon (green
line). The muon's trajectory is recorded in the four layers of silicon.
The reconstructed muon track (dashed line) has a small, but finite
distance of closest approach (dca) to the collision point (black line).
The primary background is muons from pion and kaon decays, which have a
much larger average DCA.

Figure 62 shows the number of layers of active silicon in the VTX and
FVTX detectors traversed by muons as a function of the track angle
(y-axis) and primary vertex position (x-axis). The crosshatched magenta
region corresponds to tracks that hit all four of the FVTX silicon
layers and the crosshatched red region corresponds to tracks that hit 3
layers, indicating that we have met our goal of 3 or more FVTX hits over
much of the muon arm acceptance (10° \< θ \< 34°). Most of the tracks
also first traverse one or both of the central barrel silicon pixel
layers (areas above the two blue tbarrel' lines). These additional hits
will provide useful track confirmation for the pattern recognition,
improve the DCA measurement, plus provide a precise measure of the
azimuthal angle of the track, which the FVTX would otherwise only
roughly reconstruct.

![](media/image77.png){width="4.7965277777777775in"
height="4.594444444444444in"}

[]{#__RefHeading___Toc170092636 .anchor}Figure 62 - Plot of vertex
silicon layers hit as a function of muon track angle (y-axis) and
primary vertex position (x-axis). The magenta crosshatched area includes
tracks that hit all four FVTX layers (labeled endcap hits), while the
red hatched area has three VTX hits. The area above the dark blue lines
(labeled barrel) indicates the number of barrel pixel layers hit, either
one or two. Over much of the FVTX active area, at least one barrel pixel
layer is also hit.

The measured DCA distributions have been produced for prompt, single
muons of various momenta using our simulation code, to establish the DCA
resolution of the detector. In Figure 63 the sigma of the DCA
distributions in r (resolution which is approximately perpendicular to
the strips and gives the best measurement) and phi (resolution which is
approximately parallel to the strips) are shown for the FVTX tracker
alone (red) and the FVTX plus VTX trackers (black). The improvement in
the DCA resolution for the combined system compared to the FVTX system
alone comes because the first pixel layer in the VTX detector is
typically much closer to the vertex point than the first FVTX layer, and
this layer provides the first hit on a track for many tracks which pass
through the FVTX system, as seen above. The resolution improvement is
primarily in the phi direction, which is the good measurement direction
for the VTX detector, and a small improvement is obtained in the r
direction, which is the good measurement direction for the FVTX
detector. All subsequent simulation results will be for the combined VTX
plus FVTX systems.

![](media/image79.png){width="2.9590277777777776in"
height="2.595833333333333in"}![](media/image80.png){width="2.8784722222222223in"
height="2.592361111111111in"}

[]{#__RefHeading___Toc170092637 .anchor}Figure 63 The DCA resolution in
r (left) and phi (right) for just the FVTX (red) and for the FVTX plus
VTX hits (black). Note that the resolution improvement is primarily in
the phi coordinate, which is the good measurement direction for the VTX.

The DCA as a function of momentum and strip width, is shown in Figure
64. The resolution obtained in r is approximately 100 μm at high momenta
and the resolution obtained in phi is approximately 500-600 μm.

![](media/image81.png){width="2.816666666666667in"
height="2.513888888888889in"}

![](media/image82.png){width="2.8715277777777777in"
height="2.5659722222222223in"}

[]{#__RefHeading___Toc170092638 .anchor}Figure 64 - Top panel: The DCA
resolution in the r direction, versus ptotal, for prompt muons and a
detector with 75 μm (red) and 50 μm (black) strip pitch. Bottom panel:
the same, except the DCA resolution is in the phi direction.

The radial resolution is almost completely independent of the
strip-width in this strip-width regime, indicating that the resolution
is entirely dominated by the multiple scattering in the material. Since
we get similar DCA resolutions for 50, 75 or 100 μm strips, we have
chosen a strip pitch of 75 μm for our detectors primarily to minimize
the number of channels required while keeping the occupancy in Au+Au
events to a tolerable level. An additional factor that was considered
was the implication on the physical size of the FPHX chip for different
strip pitches. A 100 μm pitch would have given a chip that was \> 1.2
cm, felt to be a little to long or would have required a pitch adaptor.
Both are undesirable.

We are in the process of studying whether the strips in each station
should be tilted with respect to each other to improve the phi
resolution, and thus allow a tighter three-dimensional cut on the DCA of
tracks. If the strips are tilted at 11° with respect to each other in
two out of the four stations, then the phi resolution shown in Figure 65
is obtained. As can be seen from the figure, the r resolution is
maintained and the phi resolution is improved by approximately a factor
of two.

![](media/image83.png){width="3.928472222222222in"
height="3.5055555555555555in"}![](media/image84.png){width="4.055555555555555in"
height="3.6319444444444446in"}

[]{#__RefHeading___Toc170092639 .anchor}Figure 65 The DCA resolution in
r (top) and in phi (bottom) for a detector which has all strips oriented
with zero degrees with respect to a circular chord and the same for a
detector which has two stations with strips oriented at 11 degrees with
respect to the baseline strips. .

![](media/image85.png){width="3.94375in" height="3.533333333333333in"}

![](media/image86.png){width="3.7888888888888888in"
height="3.390972222222222in"}

[]{#__RefHeading___Toc170092640 .anchor}Figure 66 The DCA r resolution
(top) and phi resolution (bottom) for a detector which has the sensors
at all stations in the same phi positions, and the same resolutions for
a detector which has the sensors in each station rotated by ¼ of a
sensor width with respect to each other.

The DCA phi resolution can also be improved if the silicon sensors in
each station are rotated by a fraction of the width of the sensor with
respect to each other. Figure 66 shows the resolutions obtained if each
station is rotated by ¼ of the width of a sensor. Again, the resolution
is maintained and the phi resolution is improved by about a factor of 2.

Since the phi staggering involves changing only the position of each
station, but no change to the sensor, we adopt phi staggering as a
baseline and will continue to investigate the cost implications for
adding stereo angles. It should also be noted though that having both
stereo angles and phi staggering does not additively improve the phi
resolution, but just improves the resolution of one of them alone by a
small amount.

Based on the above plots, we are currently maintaining the following
baseline detector configuration:

-   75 μm silicon strip pitch, in r

-   3.75° sensor wedges determining the strip width in phi

-   The VTX points are included in track reconstruction whenever a hit
    is produced

-   No stereo angles

-   Phi staggering is included

-   Two dimensional DCA cuts are used to discriminate between different
    decay particles, with one cut value used in the r direction and a
    larger cut value used in the phi direction.

## Determining the Primary Vertex

Displaced vertices are measured with respect to the primary vertex in
the event, so the primary vertex must be found with sufficient accuracy
if the DCA resolution is to be maintained. This is true for both the
offline event reconstruction of the FVTX as well as any level 1 trigger
algorithm that attempts to identify tracks from heavy quark decays. We
have studied the primary vertex resolution in p+p, p+Au and Au+Au
central collisions, using HIJET together with PISA. For each beam
species, the average number of particles traversing the FVTX was
determined. These particles are typically soft pions with a mean
momentum of about 1.4 GeV/c and most probable momentum of about 600
MeV/c. Each of these pions typically provides an impact parameter
measurement with an accuracy of \~250 μm. Assuming that the accuracy of
the vertex determination scales inversely as the square root of the
number of measured tracks the primary vertex accuracies shown in Table 3
below are obtained.

[]{#__RefHeading___Toc170092684 .anchor}Table 3 - Determination of
primary vertex using prompt pions, shown versus collision species.

  ------------- --------------- ----------------- ------------ -------------
  Collision     Number of pions Accuracy of       Additional   Primary
  Species at    detected in     primary vertex    pions in VTX vertex
  √s= 200 GeV   FVTX            determination                  accuracy with
                                from FVTX alone                FVTX + VTX

  p-p min bias  5.8             104 μm            \~3          79 μm

  p-Au min bias 11.2            75 μm             \~6          56 μm

  Au+Au central 1730            6 μm              \~900        5 μm
  ------------- --------------- ----------------- ------------ -------------

Since these tracks are all in the FVTX, they are available to a level 1
trigger. Also shown in the table are the additional pions detected in
the VTX, which can be used to improve the vertex determination offline.
The VTX single-track vertex resolution provided by each of these is
about 210 μm.

## Heavy Quark Measurements with the FVTX Using D, B μ X

Charm and bottom measurements can be made with the FVTX and muon arms
using the semi-leptonic decay channels DμX, BμX. Figure 67 shows the
contributions from charm+bottom decays (called "Prompt" in the figure),
light meson decays, and punch through hadrons to the single muon
spectrum (based on real Run 2 p+p data). The light meson decays dominate
the spectrum below p~T~ of 2 GeV/c and the punch-throughs become
comparable to the heavy quark meson decays at about 3 GeV/c. These light
meson contributions to the single muon spectrum must be rejected if a
precision charm or bottom measurement is to be made. A DCA cut requiring
DCA\<DCAmax will reduce the muons from light meson decays, making a
charm measurement possible at low *p*~T~ (see later). A DCA cut
requiring DCA\>DCAmin will reduce the punch-throughs since the
punch-throughs come from the primary vertex, allowing a heavy flavor
measurement at moderate to high p~T~.

![](media/image88.png){width="4.498611111111111in"
height="3.0680555555555555in"}

[]{#__RefHeading___Toc170092641 .anchor}Figure 67 - The p~T~
distribution of negative prompt muons (muons from heavy quarks), decay
muons from π and K and punch-through hadrons at pseudorapidity (η) =
-1.65. The punch-throughs become the dominant background for p~T~ values
above 3 GeV. The curves are simulations, based on real data
extrapolations, while the data are PHENIX measurements.

We have looked at the signal to background improvement for D and B
measurements by running full D, B and minimum bias PYTHIA events through
our simulation and seeing what fraction of each particle type survives
DCA cuts. Figure 68 and Figure 69 show how the signaert :background for
charm (D) and bottom (B) measurements improves when DCAmin\<DCA\<DCAmax
cuts are applied. Figure 68 shows the signvero :background improvement
for particles decaying to μ^+^ and Figure 69 shows the improvement for
particles decaying to μ^-^. There are more background muons for μ^+^
signals than for μ^-^ signals. For both charm and bottom, an improvement
in the sigoveto :background of about a factor of 10 is attained over
most of the p~T~ range accessible by the FVTX and muon systems when DCA
cuts are employed. These figures will enable us to determine which pt
ranges we can use to enhance either B or D. Generally, D's dominate
below 2 GeV and B's dominate above 3 GeV.

![](media/image89.png){width="6.138888888888889in"
height="3.095833333333333in"}

[]{#__RefHeading___Toc170092642 .anchor}Figure 68 -- Signal to
background improvement for Ds (left) and Bs (right) which decay to μ^+^
for no vertex cut and successive FVTX cuts. Cuts applied are χ^2^ cut,
DCA cut in the phi direction, and DCA cut in the r direction.

![](media/image92.png){width="6.133333333333334in"
height="3.089583333333333in"}

[]{#__RefHeading___Toc170092643 .anchor}Figure 69 - Signal to background
improvement for Ds (left) and Bs (right) which decay to μ^-^ for no
vertex cut and successive FVTX cuts. Cuts applied are χ^2^ cut, DCA cut
in the phi direction, and DCA cut in the r direction.

### Error Bar Improvement on Single Muon Physics Measurements with the FVTX

The heavy flavor measurement improvement that we achieve with the FVTX
comes about because the error bars on an open heavy flavor measurement
get reduced when the signal to background improves. The statistical
error will improve because less background needs to be subtracted to
obtain the signal. This is indicated in the following equations where
the error in the signal (S) is given with respect to the fraction (f) of
the total counts which are background (B) counts.

$\begin{array}{r}
S = N - B; \\
\delta S = \sqrt{\delta^{2}N + \delta^{2}B} = \sqrt{\delta^{2}N + f^{2}\delta^{2}N}; \\
\text{here},\delta N = \sqrt{N}; \\
N = S + B = S + \text{fN} \Rightarrow N = \frac{S}{1 - f}; \\
\delta S = \sqrt{\frac{S}{1 - f}(1 + f^{2})} = \sqrt{S}\sqrt{\frac{1 + f^{2}}{1 - f}}
\end{array}$

As seen, the statistical error will become smaller as the fraction (f),
that is background, is reduced.

The systematic errors also improve because the uncertainty in the
background normalization contributes less to the systematic error as the
background gets reduced. This is indicated in the following equations
where the systematic error is given as a function of the uncertainty of
the fraction (f) of the counts which are background. As f becomes
smaller, the contribution of δf/f to the systematic error also becomes
smaller.

$\begin{array}{r}
{dS}_{\text{sys}} = {dB}_{\text{sys}} = \sqrt{N^{2}d^{2}f} = Ndf \\
\frac{s}{1 - f}df = s(\frac{1}{1 - f})df = s(\frac{f}{1 - f})(\frac{df}{f});
\end{array}$

If the improved signal to background ratio shown in Figure 68 and Figure
69 are used to calculate the statistical and systematic errors for an
open heavy flavor cross section measurement, we obtain the reductions
shown in Figure 70, where we have appldif the improvemeed to a Run 2
single muon measurement.

![](media/image93.wmf)

[]{#__RefHeading___Toc170092644 .anchor}Figure 70 The fractional
reduction in statistical and systematic error bars that we would obtain
for Run 2 pp data cross section measurement if we had the FVTX included
in the analysis. Note that additional statistical error bar improvements
will be obtained just by increasing the integrated luminosity with
respect to Run 2.

The systematic error gets reduced by a factor of approximately 2.5-10,
depending on p~T~, and the statistical error gets reduced by a factor
that is somewhat smaller than 2 at all values of p~T~. Note that any
current or future measurement that has a larger integrated luminosity
than Run 2 will have further improvement in the statistical error bar so
the systematic error bar improvement is the most critical.

If these fractional improvements in statistical and systematic error
bars are applied to the Run 2 published measurement, we get the reduced
error bars indicated in Figure 71 where the Run 2 error bars without the
FVTX are shown in red and the reduced statistical and systematic error
bars that we would obtain with the FVTX detector are shown in blue. Note
that the improvement is more dramatic for μ^+^ than for μ^-^ because
there are more μ^+^ background particles than μ^-^. The physics analyses
that can be made with these improved heavy flavor measurements will be
shown in the physics sections that follow.

![](media/image94.png){width="5.873611111111111in"
height="2.892361111111111in"}

[]{#__RefHeading___Toc170092645 .anchor}Figure 71 The statistical and
systematic error bars from run 2 p+p data are shown for μ+ (left) and μ-
(right) with (blue) and without (red) the FVTX.

## Occupancy in Central AuAu Events

The endcap mini-strips have a radial pitch of 75μm and widths in φ (or
mini-strip lengths) that are 3.75° wide and that therefore vary between
2.8 and 11.2 mm as the radius increases. The simulated hit density at
the first silicon layer for central AuAu collisions, simulated by PISA,
is shown in Figure 72. For 75μ×2.8mm strips at the smallest radii, a
density of 7cm^2^ translates into an occupancy = 1.5%. Accounting for
charge sharing and the total yield of soft charged particles, the
maximum occupancy is expected to be \~2.8% for Au+Au central collisions.
We expect this occupancy to be low enough to allow accurate track
finding even in the central-most AuAu collisions.

![](media/image96.png){width="4.000694444444444in"
height="3.4145833333333333in"}

[]{#__RefHeading___Toc170092646 .anchor}Figure 72 - Simulated occupancy
at the first silicon plane for Au+Au central collisions using the HIJING
model. The color scale is in units of hits per cm^2^, with a maximum of
7 hits per cm^2^ at the inner radius. The other silicon planes have
lower occupancies.

## Analogue Information from the FVTX

The FPHX chip provides analog information in the form of a 3 (or more)
bit ADC. We have begun a study of the use of this information in either
triggering or in offline analysis. In the energy region of the particles
of interest to PHENIX, we are sensitive to the relativistic rise of the
energy loss with momentum. The relativistic rise is governed by the

restricted Bethe-Block formula which predicts a rise for pions (muons)
between 1 and 18 GeV of about 7%. Because of this relativistic rise, we
can use the energy loss as a coarse measure of the momentum of the track
in the FVTX that can then be matched to the muon spectrometer measured
track. An analysis of the backgrounds in the measurement of muons from W
decay has shown that a substantial portion of the backgrounds comes from
low energy kaon decays in the muon spectrometer that mimic high energy
muons. It may be possible to provide some discrimination of these low
energy kaons by looking at the energy loss in the FVTX planes. We are
currently validating the GEANT code to insure that the energy loss is
calculated correctly and will then do a full simulation of the combined
muon system and FVTX to determine at what level we can reduce the
backgrounds for the W physics measurement.

[]{#__RefHeading___Toc170092514 .anchor}Matching Tracks from the Muon
Spectrometers to the FVTX

Track matching between the Si Endcaps and the Muon Spectrometers was
studied by using HIJING Au+Au central collisions in a PISA simulation,
followed by full offline reconstruction. Au+Au central collisions
produce nearly two thousand tracks in the FVTX. Since only a few of
these particles manage to penetrate deep into the muon identifiers, it
is important be able to correctly match the tracks found in the muon
system to those found in the FVTX. We have performed a matching
simulation by looking at matching in stages as follows: First, tracks
are found in the muon spectrometers, seeded by roads in the muon
identifiers, as done in all existing PHENIX muon analyses. Second,
tracks from the FVTX are projected into the muon tracker station one
where a momentum-dependent window is computed, based upon the expected
amount of multiple scattering. The background FVTX tracks are found
within that window. Finally, each of those tracks are joined to the muon
track and fitted using a Kalman filter fit. The combined track with the
best fit is retained.

PISA was used to simulate the projection accuracy for a 5.5 GeV muon
from the FVTX into station one of the muon tracker. The window radius in
station one for 99% efficiency of retaining the muon was 1.8 cm. The
number of background pions within this window is 2.7. One can use a χ^2^
cut on the track fit in the FVTX to remove some of the background pions
but one is still left with one pion for every muon. A more efficient
method for removing the background pions is to fit the muon track in the
spectrometer with each of the tracks in the FVTX with the use of a
Kalman filter.

With the Kalman filter it is possible to cut on the combined χ^2^ of the
fully fitted track. This χ^2^ includes contributions from multiple
scattering in the FVTX, as well as the track position and angle matches
between the FVTX and muon tracker. It also takes the momentum dependence
of these into account. Results for the χ^2^ of the Kalman filter track
in central Au+Au occupancy are shown for tracks which are incorrectly
matched to background tracklets (black histogram) in the FVTX and for
correct matches (red histogram) at 3 GeV (Figure 75) and 9 GeV momentum
(Figure 76). A clear distinction in χ^2^ is seen between the muon
tracking matches with the background tracklets in the silicon or the
correct muon tracklet. If one simply picks the best χ^2^ track for the
match in each case one gets an efficiency for picking the correct
tracklet of 93% (9 GeV muon), 83% (6 GeV muon) and 75% (3 GeV muon).

![](media/image99.png){width="3.9972222222222222in"
height="3.3069444444444445in"}

[]{#__RefHeading___Toc170092649 .anchor}Figure 75 - Matching of 3 GeV
muon tracking tracks with FVTX silicon tracks in central Au+Au
collisions. The red historgram shows the Kalman filter χ^2^ for the
correctly matches tracks while the black histogram shows that for the
soft pion background tracks. The correct FVTX track is matched 75% of
the time.

![](media/image100.png){width="4.126388888888889in"
height="3.4138888888888888in"}

[]{#__RefHeading___Toc170092650 .anchor}Figure 76 - Matching of 9 GeV
muon tracking tracks with FVTX silicon tracks in central Au+Au
collisions. The red histogram shows the Kalman filter χ^2^ for the
correctly matches tracks while the black histogram shows that for the
soft pion background tracks. The correct FVTX track is matched 93% of
the time

# FVTX Detector system

## Overview

The FVTX detector system is composed of two identical endcap sections,
one in the front of the north muon spectrometer and one in the front of
the south muon spectrometer. Figure 77 shows a three dimensional model
of the two detectors, the geometrical parameters are shown in Table 4.
The VTX detector and the two FVTX endcap regions share an environmental
enclosure. The environmental enclosure is needed because the barrel
strip detectors must be operated at 0 deg C. The enclosure radius is 25
cm except close to the absorbers (the nose-cone surface) where the
enclosure extends out to at least 45 cm. The larger radius ends are used
for the barrel pixel layer transition electronics and all of the barrel
bus cables, power and cooling lines plus all of the utilities and cables
for the forward vertex system. An ongoing integration study of these
utilities and cable routing is being pursued for the VTX barrel upgrade.
The design of the enclosure and mechanical structure will include the
needs of both the barrel and the forward upgrades.

The four endcap disks contain 48 individual wedge shaped towers mounted
on a carbon composite support substrate. Each wedge supports silicon
sensors with readout chips wire bonded to the sensors, In addition,
adjacent wedges overlap by about 0.2 millimeter to give hermetic
coverage in the phi direction. The technology for the sensors will be
p-on-n detectors with the strips oriented so that the strips nearest the
beam pipe at a radius of 4.5 cm are short, \~2.9mm long in the phi
coordinate, and at the largest radius of 17 cm they are about 11.2 mm
long, i.e. individual strips fan out from the center of the 7.5 deg
wedge. The maximum occupancy at the inner strip is 2.9%. The total
number of readout strips in each endcap is \~ 553,000. The FPHX chips on
each edge of the sensor are connected to a flexible kapton bus that
takes the data to the outer radius of the wedge.

![](media/image101.jpeg){width="4.1125in" height="3.0833333333333335in"}

[]{#__RefHeading___Toc170092651 .anchor}Figure 77 - 3-D model of the
full vertex detector showing the barrel portion and the endcaps on left
and on the right. The Readout Out Cards are at either end of the
detector at a larger radius and visible in the exploded view on the
left.

[]{#__RefHeading___Toc170092685 .anchor}Table 4 - Summary of the
parameters of the FVTX disks.

  --------------- ------------------- ------- --------- --------- ---------
  FVTX            Disk                Z1      Z2        Z3        Z4

  Geometrical     z (cm)              18.7.   25.1      31.5      37.9

  Dimensions      R (cm) inner        4.5     4.5       4.5       4.5

                  R (cm) outer        10.6    17.0      17.0      17.0

  Unit Counts     \# of wedges        48      48        48        48

                  sensors/wedge       1       1         1         1

                  readout chips       12      26        26        26

                  Readout Channels            160k      160k      160k
                  73.7k                                           

  Radiation       Sensor (300 m)     0.3     0.3       0.3       0.3
  Length                                                          

                  Readout (300 m)    0.3     0.3       0.3       0.3

                  Bus                 0.2     0.2       0.2       0.2

                  Ladder&cooling      0.3     0.3       0.3       0.3

                  total               1.1     1.1       1.1       1.1
  --------------- ------------------- ------- --------- --------- ---------

[]{#__RefHeading___Toc170092652 .anchor}Figure 78 A block diagram of the
readout system required for the FVTX. The red block (ROC) and blue block
(FEM) are boards which will reside between the FPHX readout chip and the
DCM and are currently under development.

The data from the readout chips will go through two successive boards
before going in to the PHENIX DCMs, as indicated in . The first board,
the ROC, will reside inside the enclosure and will perform the functions
of: stripping the sync words out of the data, collecting the data of
several chips together, serializing it and sending it out on optical
fiber to the FEM. Additionally, the ROC will provide calibration pulses
for the PHX chips and route download and readback lines to and from the
chips.

The second board, the FEM will reside inside the counting house and will
receive data from the ROC(s), buffer it until a Lvl-1 accept is
received, retrieve the data of interest for the Lvl-1 accepts and
package the data for the DCMs. It will also perform the function of an
overall slow-controls manager: passing data to and receiving data from
the ROCs/FPHXs and the PHENIX DAQ system.

## FPHX Chip Development

The ASIC development Group at FNAL, led by Ray Yarema, has completed the
design for a readout chip that is specifically tailored to the FVTX
sensor. Within the Group, Tom Zimmerman is leading the analog section
design, and Jim Hoff is leading the digital data acquisition design
function of the chip. The chip design borrows heavily from previously
successful IC designs, FPIX2, FSSR, SVX4, etc. The FVTX custom IC has
been named the FPHX chip. Each chip is a 128 channel package with an
input pitch that that is slightly less than 70 microns.

![](media/image102.png){width="5.532638888888889in"
height="4.545833333333333in"}

[]{#__RefHeading___Toc170092653 .anchor}Figure 79 The FPHX amplifier
front end.

The schematic for one channel is shown in Figure 79. The front end
amplifier is designed to accept a positive charge (holes) input from the
p-on-n silicon sensor. It is optimized for the input capacitance range
of the strips from the inner most to outer most radius of the sensor.
The estimated capacitance range is 0.5 pF to 2 pF. The total charge gain
is 500 mV/fC. The CR-RC shaper has a peaking time of 60 ns (see Figure
80), and the shaping time can be adjusted through a programmable shaper
bias. The chip is dc-coupled and provides leakage current compensation
up to 100nA per strip. The noise floor of the analog section is 150e and
the noise slope is 140 e/pF Figure) The power consumption is 60-110 uW,
depending on the transistor bias current that is set.
![](media/image103.jpeg){width="4.252083333333333in"
height="2.801388888888889in"}

[]{#__RefHeading___Toc170092654 .anchor}**Figure 80 Pulse Shape before
and after shaper**.

![](media/image104.wmf){width="3.69375in" height="3.004166666666667in"}

[]{#__RefHeading___Toc170092655 .anchor}**Figure 81 Noise vs.
Capacitance**.

A \~70 um pitch on the FPHX chip will allow us to wire bond directly
from the sensor to the chip input without the need for an additional
pitch adapter. The smaller pitch also allows for space between adjacent
chips where bypass capacitors can be placed. One of the most important
reasons that drove the design layout to locate the readout chips on each
side of the sensor was to minimize possible noise problems associated
with long signal return paths between the sensor and the chip. This
mitigation is accomplished by locating a bias voltage bypass capacitor
as close as possible to the readout chip ground reference and the
silicon sensor bias.

The output, clock, and control pads are all located on the side of the
chip opposite from the inputs and they are wire bonded to a high density
interconnect (HDI) cable. The digital connections are arranged to
minimize their effect on the analog inputs.

The FPHX is designed to be a data push architecture. It incorporates
simultaneous read/write in a dead time free configuration. The FPHX
output provides a 7 bit address, a 6 bit time stamp, and 3 bits of ADC
for each hit. The chip will also output sync words comprised of 19 zeros
followed by a one, which are used by the downstream acquisition to
synchronize word boundaries. The functionality of the chip is separated
into four distinct phases; analog process the hit, zero suppress,
serialize1 and serialize2. The four-phase architecture assures that up
to four hits from a single event can be processed and delivered within
four beam crossover periods. If there are events in sequential beam
crossings, the data will be output, but in greater than a four beam
crossing time period.

## Silicon Mini-strip Sensors and Wedge Assembly

We plan on using existing technology for the silicon sensor. Standard
p-on-n silicon strip technology, which has been the baseline detector
technology for dozens of silicon trackers in Nuclear and High Energy
physics experiments, will be used for the FVTX mini-strips. In a p-on-n
detector, the output signal is generated by the collection of positive
charge carriers. The FPHX chip is being designed to be compatible with
positive charge collection. The FPHX is also being designed to have
leakage current compensation at the front-end, up to 100 nA/ strip. This
compensation circuitry allows us to design the sensors with dc output
connections to the FPHX chip, avoiding the additional process step to
create integrated coupling capacitors. The sensor readout strips will
operate at ground potential, and a positive bias voltage will be applied
to the backside of the sensor to fully deplete the sensor volume for
efficient charge collection. The large sensor wedge for disks 2,3,4 is
approximately 126.5 mm high,8.7 mm wide at the inner radius, and 25.3 mm
wide at the outer radius. The small sensor wedge for disk 1 is
approximately 103.5 mm high, 8.7 mm at the inner radius, and 16.5 mm at
the outer radius. Several, but not all vendors have 6-inch wafer
processing capability. The remainder employe 4-inch wafer processing
capability. The advantage to a 6-inch wafer is that an entire unit wedge
sensor fits within the useable wafer boundary. Whereas, a 4-inch wafer
forces us to design each full sensor wedge out of two component parts.
The final decision between the 4 and 6-inch wafer options will be made
through a wide-ranging market survey of the current silicon sensor
foundries, and a subsequent cost/benefit analysis based primarily on
cost, and secondarily on efficient use of the wafer area. Developing the
masks for this effort will be done in concert with the vendors of the
sensors. Lengthy and costly R&D for the sensors is not necessary. The
material and electrical specifications for the sensors are listed below.

**MATERIAL SPECIFICATION:**

Wafer diameter 6 inch preferred (152 mm**),** 4 inch (100 mm)

Crystal orientation \<111\> or \<100\>

Thickness 300 μm +10 μm --20 μm

Uniformity (across wafer) \< 10 μm

Wafer bowing after processing \< 50 μm (sagitta)

Doping of starting material: n-type

Resistivity: 2.0 -- 5.0 kohm KΩ cm

Uniformity of resistivity (wafer to wafer) ±25%

Polishing: Double sided

> Passivation: Covering junction-side except for wire-bond pads and
> reference marks. It can either be silicon oxide or silicon nitride.

**DESIGN PARAMETERS**

-   Devices shall be p-on-n mini-strips.*.*

-   The full design for the masks will be provided by us in electronic
    form, GDS file format.

-   Vendor will finalize the design details according to their design
    rules and process, and will work with us on the final design and
    mask layout..

-   Mask alignment precision within the same side : ±2um

-   Mask Alignment precision between front and back side: ±5um

The arrangement of the readout chips on each of the large wedge
assemblies is shown in Figure 82. The FPHX chips are located on the
vertical edges of both sides of the silicon wedge. The two columns of
strips are physically separated to the left and right of the centerline
of the sensor wedge. The FPHX input pads are located directly opposite
the strip bond pads, allowing for easy wire-bonding without the need for
fan-in circuitry. The location of the chips close to the sensor also
facilitates the effectiveness of the bias voltage filters. The total
number of 128-channel known-good FPHX chips that will be required is
11,290, which includes an estimate for spares. There are 3328(1536)
independent strips per large (small) wedge arranged into 2 columns. The
wedge assembly covers an angular range of 15 deg and the sensors cover
an angular range of 7.5 deg with 0.2 mm added on each edge for overlap
with the adjacent sensor located on the back side of a support plate.

The sensor wedge consists of a stack up of a carbon support backing,
kapton HDI, and sensor and chips as shown pictorially in Figure 83. The
carbon backing serves as a carrier on which the sensor, HDI, and chips
can be mounted separately from the cooling plate. This modular
arrangement allows us to fabricate and test all of the wedges
separately.

![](media/image105.jpeg){width="2.0368055555555555in"
height="3.4277777777777776in"}![](media/image106.jpeg){width="3.23125in"
height="3.2465277777777777in"}

[]{#__RefHeading___Toc170092656 .anchor}Figure 82 The large wedge
assembly on the left showing the location of the sensor and chips and
blow up the bottom of the wedge n more detail on the right.

The HDI stack up is shown on the left of Figure 83 and the wedge stack
up is shown on the right. Indicated on the HDI stack up is one signal
layer, one ground and one power layer. All control lines will be routed
under the sensor and all output lines will be routed towards the edge of
the wedge thus insuring that the output lines will not couple into the
signal lines on the sensor. The number of lines required (8 pairs for
the control lines and 2 signal pairs per chip for the output lines) will
be easily handled and the line pitch of the HDI will be very modest
allowing us to use conventional kapton PC techniques.

![](media/image107.jpeg){width="5.992361111111111in"
height="2.4305555555555554in"}

[]{#__RefHeading___Toc170092657 .anchor}Figure 83 The HDI and wedge
stack up. The radiation length of the wedge is 1.2%.

![](media/image108.wmf)

[]{#__RefHeading___Toc170092658 .anchor}Figure 84 The noise canceling
strategy for the HDI.

The layout of the wedge, chip, and HDI will have impact on the noise
figure of the system. To facilitate the HDI layout, Tom Zimmerman of
FNAL analyzed the electrical

layout of the wedge assembly to insure we did not increase the noise.
The strategy is shown in Figure 84 . In the figure one notices the two
noise canclling loops, one for the input side and one for the output
side of the chip. The location of the bypass capacitors will be
incorporated into the design of the HDI. In particular we will design
the length of the chip to allow us to place the bypass capacitor to the
backplane in between the chips. The digital supply bypass caps will
located on the edge of the wedge.

## Electronics Transition Module and FEM

As indicated in the block diagram in there are two boards (the ROC and
the FEM) which will need to be developed to get the data from the FPHX
chips in to the PHENIX DAQ system.

The FPHX chip will have the following connections to the ROC:

-   One calibration line in per chip

-   One analog and one digital voltage supply and associated grounds

-   6 LVDS lines required for downloading, clocking, and resetting the
    chip

-   2 LVDS data lines per chip sending the data out

The electronics transition module (ROC) will take the continuously
streaming data (data-push) from 56 FPHX chips via flexible cables into
an FPGA, strip the sync words from the data, combine the data of several
chips, serialize it and send it out via fiber to the FEM and the Lvl-1
boards. The time to receive all of the data to pass to the Level 1
trigger is expected to be less than four beam clocks or 424 nsec. In
addition to receiving the data, the ROC will provide calibration pulses,
route analog and digital power to the FPHX chips, and provide 6 LVDS
lines for downloading the chip and providing clocks and resets. The
location of the ROCs will be at the end of the silicon tracker enclosure
in the "big wheel" area, as indicated in Figure 85. A block diagram of
the ROC is shown in and a layout for a board which would service 4
layers\*4 sensor wedges is show in Figure 87. Twelve ROC boards will be
required to service one endcap and these boards will hold a total of 84
FPGAs.

![](media/image2.jpeg){width="5.495833333333334in"
height="4.129166666666666in"}

[]{#__RefHeading___Toc170092659 .anchor}Figure 85 The silicon tracker
region, indicating at the far right the location of the ROCs for the
FVTX.

![](media/image110.wmf){width="6.490277777777778in"
height="4.330555555555556in"}

![](media/image109.png){width="4.679921259842519in"
height="3.4236220472440944in"}

[]{#__RefHeading___Toc170092660 .anchor}**Figure 86 Block diagram of the
ROC which will take data from 56 chips, derserialize and strip off the
sync words, serialze the data and send it out on fiber**.

![](media/image111.wmf){width="5.996527777777778in"
height="5.9430555555555555in"}

[]{#__RefHeading___Toc170092661 .anchor}Figure 87 Layout of a ROC board
which would span 30° and service 4 layers\*4 sensor wedges. Shown are
the connectors would would receive signals from and route signals to the
FPHX chips, the FPGAs which would compress the data, serdes which
serialize the data and fiber drivers which sned the combined data to the
FEMs and Lvl-1 boards. Voltage regulators and LVDS repeaters are also
included above.

The power consumption required for the ROC is approximately 350 Watts
per arm. The details of this are shown in Table 5.

![](media/image112.wmf)

[]{#__RefHeading___Toc170092686 .anchor}Table 5 Power consumption
calculations for the FVTX ROC card components.

The FEM will buffer the data for 64 beam clocks (emulating the 64 beam
clock analog buffer of current PHENIX detectors), grab the data from the
appropriate beam clock upon a Level-1 trigger and reformat the data
before it is sent to the PHENIX DCMs. A data buffering concept which is
under development is shown in Figure 88. There is a 64 FIFO array, with
each FIFO storing the data from a particular beam counter. The FPHX data
is routed to a FIFO, selected by the beam clock counter that is embedded
in the datastream. The hits from the particular beam crossing stay in
the FIFO for not more than 64 clocks, otherwise they are marked as
expired. This strategy solves the problem of relatively short beam clock
counter wrap around. is routed by an FPGA chip to one of 64 buffers
corresponding to the beam clock number. The FPGA then allows the data
from the appropriate beam clock to be sent to the DCM when a LVL-1
trigger accept is received. Upon readout of the FIFO the hits from the
expired beam crossing are not being outputted. The existing PHENIX DCMs
can be used without modification.

The current FEM design has been successfully implemented on an XC4VSX35
Vertex-4 XILINX FPGA and tested at design speed. The buffering block is
capable of receiving 32 bit parallel data at up to 300 MHz and reliably
sends the data to the output buffer at 300 MHz. Copying of the data from
a particular FIFO to the output buffer should be done as fast as
possible as the data from the next beam crossing should arrive when the
previous crossing (64 clocks before in time) data have already been
read-out.

[]{#__RefHeading___Toc170092662 .anchor}Figure 88 -- Block diagram of
the data buffering for the FEM.

The buffering requirements of the ROC are expected to be modest with
\<20 kbits of data expected in Central Au+Au events for up to 56 chips
serviced by the same FPGA. Noise hits are expected to take even less
space. Some calculations of data sizes and readout times can be found in
Table 6, for various options of readout lines, chip "ganging", and
assuming the readout clock is synchronized to give an integral number of
beam clocks needed per data word. The proposed granularity of the
readout DAQ and the data rates at each point are shown in Figure 89.

![](media/image113.wmf)

[]{#__RefHeading___Toc170092687 .anchor}Table 6 - Buffer requirements
for the transition module for most challenging case of AuAu events,
various options of readout lines/chip, different levels of chip
"ganging", and a extremely conservative noise estimate. In addition the
time to readout an event is given for the same conditions.

![](media/image114.png){width="5.999305555555556in"
height="3.8048611111111112in"}

[]{#__RefHeading___Toc170092663 .anchor}Figure 89 Block diagram of the
FVTX readout electronics components.

## Radiation Environment and Component Selection

The evaluation of the FPGA technology available for use on the FVTX
Read-out Controller (ROC) primarily considers the effects of the
radiation on the performance of the overall system. Additional
considerations included I/O configurations, serial communication
capabilities and reconfiguration of the device within the system. The
choice of technology is primarily the choice of configuration memory
technology as logic implementation and density do not really impact our
application. The different configuration technologies and their
suppliers under consideration are as follows:

> SRAM Altera, Xilinx
>
> FLASH Actel ProASIC3
>
> Anti-fuse Actel Axcelerator

The primary concern for FVTX about FPGAs is the ability to operate in a
radiation environment. Considerable effort and investigation has gone
into this question by such organizations as NASA, DOD and CERN. The
concern here is to determine the radiation environment and its effects
on FPGA performance for the FVTX system. The radiation environment for
the FVTX is the environment of the PHENIX interaction area with either
RHIC I or RHIC II luminosities. The master's thesis *A scalable analytic
model for single event upsets in radiation-hardened field programmable
gate arrays in the PHENIX interaction region* by Steven Skutnik provided
invaluable information on defining these environments as did the ASIC
discussion section of the VTX TWIKI.

Based on the above, the upset rates in the PHENIX radiation environment
at 10 and 40 cm are as follows:

> RHIC I AuAu
>
> 10cm 1.6x10^-6^ /bit/hr
>
> 40cm 1.0x10^-7^ /bit/hr
>
> RHIC II AuAu
>
> 10cm 1.6x10^-5^ /bit/hr
>
> 40cm 1.0x10^-6^ /bit/hr
>
> RHIC II p+p
>
> 10cm 1.28x10^-4^ /bit/hr
>
> 40cm 8.0x10^-5^ /bit/hr

The primary elements of the FPGA that are affected by the radiation are
the SRAM memory elements, clocks and sequential logic. The primary
concern with Altera and Xilinx FPGAs is that the configuration or
functionality of the device is contained in SRAM and upsets in this
memory affect the function of the device and will cause it to no longer
perform the function as it was initially programmed. Both Xilinx and
Altera offer configuration "scrubbing" solutions that check the
configuration but they require a reload of the configuration if an error
is detected, which takes time. The configuration SRAM size dominates the
FPGA SEU rates as it is 3 to 10 times the size of the data SRAM
available. The configuration and data memory sizes for a mid-range
Statix II GX part and a high-end Cyclone II part are shown below:

> Altera EP2SGX60 Configuration SRAM = 16,951,824 Data SRAM = 6,747,840
>
> Altera EP2C70 Configuration SRAM = 14,319,216 Data SRAM = 1,152,000

The SEU rates for the SRAM based FPGAs must include both configuration
and data memories. The Altera and Xilinx devices are extremely similar
in regards to their radiation susceptibility so we use just the Altera
device as an example here. In consideration of the application in the
FPGA for FVTX, data memory upsets are ignored and triple redundancy
methods would be used on sequential logic to reduce upsets to negligible
levels. Therefore, considering only configuration SRAM upsets, the upset
rate for the Altera chips are as follows:

> EP2SGX60 27.12 upsets/hr RHIC I AuAu 10cm
>
> EP2C70 22.91 upsets/hr RHIC I AuAu 10cm
>
> EP2SGX60 271.2 upsets/hr RHIC II AuAu 10cm
>
> EP2C70 229.1 upsets/hr RHIC II AuAu 10cm
>
> EP2SGX60 2170 upsets/hr RHIC II p+p 10cm
>
> EP2C70 1833 upsets/hr RHIC II p+p 10cm
>
> EP2SGX60 1.70 upsets/hr RHIC I AuAu 40cm
>
> EP2C70 1.43 upsets/hr RHIC I AuAu 40cm
>
> EP2SGX60 16.95 upsets/hr RHIC II AuAu 40cm
>
> EP2C70 14.32 upsets/hr RHIC II AuAu 40cm
>
> EP2SGX60 135.6 upsets/hr RHIC II p+p 40cm
>
> EP2C70 114.6 upsets/hr RHIC II p+p 40cm

These upset rates are per device so the system upset rate is determined
by multiplying these rates by the number of devices in the system. For
the LDRD version of FVTX device count is between 12 (lower limit should
be 8 if you follow our design) and 48 and for the DOE FVTX system the
device count is between 48 and 192 devices. Even with configuration
scrubbing the SRAM FPGAs have an unacceptable down time because the
configuration reload time is between 1 and 2 seconds.

The Actel FPGAs do not have SRAM configuration memory so they are immune
to this form of upset. FLASH memories exhibit dissipation of the charge
on the floating gate after 20kRad of integrated dose. The dissipation is
not permanent damage and is remediated by reprogramming the device.
Flash memories also displayed SEE problems during programming during
radiation exposure that included gate punch-through, a destructive
effect. These types of SEEs are avoided by not programming the FLASH
under radiation exposure conditions, namely during machine operation.

The Actel FPGAs have a decided advantage over the SRAM based FPGAs since
they do not have configuration upsets.

The additional factors to consider for the selection of the FPGA are I/O
configurations, serial communication capabilities and reconfigurability
in the system.

The I/O configuration necessary for the ROC is to accept many input
differential LVDS pairs as that is the native signaling mode for both
the FPIX and PHX interface chips. The Actel devices allow for almost
100% of their I/O pins to be differential pairs. The Altera devices are
both less than 50% necessitating the inclusion of LVDS to CMOS
translators in order to use these devices.

The Altera Stratix II GX includes built-in SERDES for up to 6.375 Gbit/s
data links (and Xilinx does too right?). None of the other devices have
this feature and thus will require an external device for high speed
serial communications protocols (\> 600Mbits/sec). Each of the devices
have the capability for moderate speed (600 Mbit/sec) communications.

Finally, in-system reconfiguration is available for the Actel ProASIC 3
Flash based FPGA and the Altera devices. The Actel Axcelerator is a
one-time programmable device.

In consideration of all of these factors the Actel ProASIC 3 Flash based
FPGA provides the best solution to the FVTX ROC FPGA requirements
because it is immune to radiation problems, it provides the I/O
capabilities required, it allows reprogrammability. The following table
summarizes most of these factors for the different candidate FPGAs.

FVTX Read-out Controller FPGA Comparison

  -------------------------- --------------- ------------ ---------------- ----------------
                             **Actel         **Actel      **Altera Stratix **Altera Cyclone
                             Axcelerator**   ProASIC3**   II GX**          II**

  Model                      AX 2000         A3PE3000     EP2SGX60         EP2C70

  Configuration type         Anti-fuse       FLASH        SRAM             SRAM

  Radiation Tolerance        200kRad         200kRad      50kRad           50kRad

  Single-ended I/O /         684 / 342       616 / 300    534 / 78         622 / 262
  Differential I/O pairs                                                   

  Voltages                   1.5             1.5          1.2              1.2

  Power (Quiescent)          22mA            25mA         820mA            250mA

  Built-in SERDES            No              No           Yes              No

  I/O Rates                  LVDS - 700 Mb/s LVDS - 700   LVDS-6.375 Gb/s  LVDS-622 Mb/s
                                             Mb/s                          

  Configuration Errors       No              No           Yes              Yes

  SEE types                  clocks, data    clocks, data configuration,   configuration,
                             memory          memory       clocks, memory,  clocks, memory
                                                          SERDES           

  SRAM Memory- Data          294912          516096       6747840          1152000

  SRAM Memory- Configuration 0               0            16951824         14319216

  FLASH Memory-              0               0            32 Mbyte         16 Mbyte
  Configuration                                                            

  RHIC I AuAu SEU Rate - 10  0.00            0.00         27.12            22.91
  cm /hr-chip                                                              

  RHIC I AuAu SEU Rate - 40  0.00            0.00         1.70             1.43
  cm /hr-chip                                                              

  RHIC II AuAu SEU Rate - 10 0.00            0.00         271.23           229.11
  cm /hr-chip                                                              

  RHIC II AuAu SEU Rate - 40 0.00            0.00         16.95            14.32
  cm /hr-chip                                                              

  RHIC II p+p SEU Rate - 10  0.00            0.00         2169.83          1832.86
  cm /hr-chip                                                              

  RHIC II p+p SEU Rate - 40  0.00            0.00         135.61           114.55
  cm /hr-chip                                                              

  Total Integrated Dose      \>200k          \>200k       \>50k            \>50k

                                                                           

  **SEU Rates**                                                            

  RHIC I AuAu-10cm           1.60E-06                                      

  RHIC I AuAu-40cm           1.00E-07                                      

  RHIC II AuAu-10cm (200GeV) 1.60E-05                                      

  RHIC II AuAu-40cm (200     1.00E-06                                      
  GeV)                                                                     

  RHIC II p+p-10cm (500 Gev) 1.28E-04                                      

  RHIC II p+p-40cm (500 Gev) 8.00E-06                                      
  -------------------------- --------------- ------------ ---------------- ----------------

## Mechanical Structure and Cooling

The mechanical structures and cooling are part of the integrated design
of the barrel and endcaps. The majority of the support structure has
been designed as part of the barrel effort and remaining issues
concerning ladders and cooling specific to the endcaps will be part of
this proposal.

A conceptual design of the silicon vertex detector was commissioned by
the LANL group

to HYTEC, Inc. HYTEC provided the mechanical designs for the ATLAS
silicon pixel group and has 15 years of design experience with silicon
vertex detectors. For PHENIX they have also designed the station-1 muon
detectors and the station-2 spider and they also did the finite element
analysis for the station-3 octants. The VTX/FVTX mechanical conceptual
design was completed and a report written.

<http://p25ext.lanl.gov/~hubert/phenix/silicon/HTN-111003-0001.pdf>

Recently, in September 2005, the original concept was reanalyzed to
incorporate changes that have occurred over the intervening 2-½ years, a
report was issued in October 2005.

<http://pvd.chm.bnl.gov/twiki/pub/VTX/HYTEC/HTN-111004-0001.pdf>

We summarize the results of both reports:

For the internal support and cooling of the VTX and FVTX detector, the
major results of the conceptual design are:

> • The use of sandwich composites will satisfy the radiation length
> requirements and provide the required stiffness.
>
> • The outer frame structure should be a single diameter encompassing
> both the
>
> barrel and end-caps.
>
> • The modular clamshell design can satisfy the stability requirements
> provided the
>
> connection issues are studied further.
>
> • An octagon arrangement is suggested to facilitate utility routing
> and fabrication.
>
> • Structural end disks at either end of the structure are recommended
> to prevent
>
> deformation
>
> • The ladders should have a simple support at one end and floating
> support at the
>
> other end to minimize thermal strains

The R&D issues identified are:

> • Building prototypes of ladder assemblies to verify calculations.
>
> • Building full-scale prototype to test static and dynamic stiffness.
>
> • Develop connections of modules.
>
> • Develop support design.
>
> • Refine calculations and develop full concept for 0 deg operation.

### Design Criteria

The goal of the study was to establish a feasible design and to identify
outstanding design issues. The study was based on a preliminary list of
design requirements and a straw-man layout of the detector structure. To
adequately address all structural and mounting issues, a fully
integrated design, which includes the barrel detectors and future
end-caps extension, is needed. This design needs to address all
integration issues not only for the barrel and the end-cap vertex
trackers, but also with other potential PHENIX upgrades.

The design requirements of the conceptual study were,

> • Modular Design
>
> o End-caps detectors can be mounted independently at a later time
>
> o Support structure separated vertically into two half shells
>
> • Detector Coverage
>
> o Hermetic design
>
> o Four barrel layers
>
> o Four end-cap layers in each forward section
>
> o Fiducial volume \< 20 cm radius, z \< 40cm
>
> • Radiation length goal \< 1% per layer
>
> • Room temperature operation desirable, 0 deg Celsius if needed
>
> • Dimensional stability \< 25 microns

### Structural Support

The selection of materials for the support structure is based upon the
above criteria where the most important material properties are low
radiation length, low density, high stiffness, and availability. Out of
three candidates (i) beryllium, (ii) graphite fiber reinforced plastic
(GFRP), and (iii) Carbon-Carbon, the GFRP was chosen for the study
because of its wide availability, works well in sandwich composites, and
has good radiation length and strength properties. The GFRP is still the
material of choice.

#### Structural Analysis

The structural analysis includes two studies, a first study using finite
element analysis models and the resulting modal frequencies to look at
dynamic stiffness of tracker concepts and a second study to look at the
static stiffness with mass loaded structures. The lower modal frequency
limit is set at 70 Hz on a fully loaded structure so that the natural
frequencies due to environmental conditions such as pumps, traffic, etc.
do not couple into the structure and cause instabilities greater than 25
microns.

![](media/image115.png){width="5.997916666666667in"
height="1.5319444444444446in"}

[]{#__RefHeading___Toc170092664 .anchor}Figure 90 Design concepts
studied for the vertex detector support structures. The center most
concept with the constant outer diameter shell had the highest
fundamental frequency.

![](media/image116.jpeg){width="2.875in"
height="2.0069444444444446in"}![](media/image117.jpeg){width="2.873611111111111in"
height="1.975in"}

[]{#__RefHeading___Toc170092665 .anchor}Figure 91 First mode shape that
dominated the dynamic structural stiffness analysis

Various support structures shown in Figure 90 were studied. The center
most structure has the highest frequency limit.

The dumbbell shaped structure has the lowest mode frequencies below 53
Hz while the concept with the uniform shell with constant outside
diameter has the lowest fundamental mode at 132 Hz, well above 70 Hz. In
Figure 91 the associated first mode shape of the concept that has the
highest fundamental frequency is shown

The static analysis under gravitational load is shown in Figure 92 for
the concept with the uniform shell. A 1.0 G load is applied vertically
to the fully loaded structure. The maximum displacement is 14.5 microns
and the maximum stress is 130 psi. These satisfy the design criteria so
the uniform shell with constant diameter has been chosen as the concept
to be pursued.

![](media/image118.jpeg){width="2.748611111111111in"
height="1.8930555555555555in"}![](media/image119.jpeg){width="2.748611111111111in"
height="1.8930555555555555in"}

[]{#__RefHeading___Toc170092666 .anchor}Figure 92 Displacement and
principle stress from a 1.0g gravity load on a full mass loaded
structure

### Endcap Ladder Wedge Structure

The forward regions consist of 4 disk arrays of wedge modules oriented
normal to the beam pipe. Conceptually, we have chosen a flat panel
structure with sensors and electronics mounted on either side of the
panel so that we can achieve hermetic coverage.

![](media/image120.jpeg){width="3.120138888888889in"
height="2.338888888888889in"}![](media/image121.jpeg){width="2.7416666666666667in"
height="2.0555555555555554in"}

[]{#__RefHeading___Toc170092667 .anchor}Figure 93 The forward region
disk assembly is shown on the left and a close up of the detail showing
the individual wedges is at right.

The forward region disk array is shown in Figure 93. The new PHX chip
has a heat load of 90 uW per channel so the total for each end cap is
\~50 W. In comparison to the barrel this is a very small heat load and
greatly simplifies the removal of heat. The disk panel structure
consists of thermally conducting carbon composite with cooling tubes
mounted on the outer radius. Heat generated by the wedge assemblies is
conducted through the carbon composite to the outer radius cooling
tubes. Thermal and gravity sag calculations were performed and no
serious distortions were observed. The results of thermal calculations
are shown in Figure 94. With only the outer radius cooled the
temperature gradient is only 2.5 deg C verifying that the wedge stackup
design is adequate. This is primarily because the heat load of the wedge
is quite small ( .3 W) and the carbon backing is an excellent heat
conductor.

![](media/image122.png){width="5.663385826771654in"
height="4.2220472440944885in"}![](media/image123.png){width="2.8346456692913384in"
height="0.3610236220472441in"}![](media/image124.png){width="2.748425196850394in"
height="0.5125984251968504in"}

[]{#__RefHeading___Toc170092668 .anchor}Figure 94 Thermal analysis of
the wedge assembly. The temperature gradient from top to bottom is 2.5
deg C.

Thermal and gravity distortion of the FVTX has been done and the results
are shown in Figure 95. Evident in this picture is the first model
frequency of 83.9 Hz seen as a pivoting about the attachment fixture at
the top and bottom.

The FVTX disk distortion summary is shown in Table 7 FVTX distortions
from gravity and temperature gradients.. The largest distortions come
from gravity sag but are still only 24 microns. Since this is a static
deformation, it can be removed either by metrology of the assemble
endcap or by using high energy straight through particles.

![](media/image125.png){width="2.6770833333333335in"
height="3.033333333333333in"}

[]{#__RefHeading___Toc170092669 .anchor}Figure 95 The FVTX modal
analysis. The first modal frequency is 83.9 Hz is seen as a pivoting
about the attachment points.

![](media/image126.wmf){width="6.498611111111111in"
height="1.5090277777777779in"}

[]{#__RefHeading___Toc170092688 .anchor}Table 7 FVTX distortions from
gravity and temperature gradients.

### Analysis of the Full VTX/FVTX Structure

Since the VTX design effort has been proceeding and construction is now
beginning, it was important for the FVTX to keep pace with its design so
that we could insure that the two projects could coexist in the same
enclosure without interference. A complete mechanical study has been
completed. The results of the FEA of the complete structure demonstrate
that the FVTX introduces no change in the VTX first mode and does not
change the VTX deformation. The FEM model is shown in Figure 96

![](media/image127.png){width="4.25in" height="3.245833333333333in"}

[]{#__RefHeading___Toc170092670 .anchor}Figure 96 FEA model of the
combined VTX and FVTX. The first modal frequency is 38.5 Hz

A full system level analysis has also been finished for the combined
system. The model is shown in Figure 96.

![](media/image128.png){width="2.4277777777777776in"
height="3.497916666666667in"}

[]{#__RefHeading___Toc170092671 .anchor}Figure 97 Full system FEA. The
first frequency mode is 24 Hz.

## Endcap Analysis Summary

######## The conceptual design studies revealed the following: {#the-conceptual-design-studies-revealed-the-following .unnumbered}

######## Single phase cooling is well suited to the endcaps. 

-   Only one cooling loop is required on the outer radius of the disk.

-   2mm cooling tubes and panel thickness are adequate.

-   The radiation length of the octant panel exclusive of sensor and
    electronics is \~ 0.6 %.

-   The FVTX and VTX coexist in the enclosure without interference.

-   No mechanical show stoppers.

The R&D issues consist of refining the calculations, designing
attachment points to the main support structure, and prototyping the
octant panels.

## Assembly and Integration 

### Assembly

We can categorize the assembly into a few distinct categories; wedge,
disk, cage, electronics.

#### Wedge

The wedge assembly consists of putting the HDI, sensor, and chips onto
the backplane, affixing the passive components, wirebonding, testing and
potting the wire bonds. We generally will use precision jigs to
accomplish this assembly. We expect to do three wedges per day when the
production cycles starts. The concept for attaching the HDI to the
backplane is shown in the left panel inFigure 98. Vacuum jigs hold the
two pieces in each jig and the jigs are glued together as shown. Pins
align the two jigs. For attaching the sensor to the HDI we first
optically align the sensor to the alignment pin holes in the jig using
fiducial marks on the sensor (shown in the right panel in Figure 98) and
then put the two sides together. It will take 8-24 hours for the glue to
cure so we will have 3 identical setups for these assembly tasks.

![](media/image129.wmf){width="2.3756944444444446in"
height="1.7305555555555556in"}
![](media/image130.wmf){width="2.3756944444444446in"
height="1.738888888888889in"}

[]{#__RefHeading___Toc170092672 .anchor}Figure 98 Assembly jigs for
Backplane to HDI in the left panel and the sensor to HDI in the right
panel.

At this stage the sensor, HDI, backplane is complete and the next step
is to send the completed units to a vendor for chip and passive
component attachment and wire bonding. A QA system test will be done on
the completed unit and then the wire bonds will be potted for protection
before the completed wedge assembly is shipped back. A second QA
procedure will be done when received. The details of the QA procedures
will ultimately wait until a later date but but the outline is given in
section 4.9.

#### Disk

The wedges populate both sides of the disk. An exploded view is shown in
Figure 99. Visible around the inner and outer radius are the alignment
pins for the wedge assemblies. These pins locate the wedge assemblies to
an accuracy \< 25 m. The assembly procedure will be to place the
certified wedge assemblies onto the disk and fasten with nylon screws.

![](media/image131.wmf){width="4.5in" height="2.670138888888889in"}

[]{#__RefHeading___Toc170092673 .anchor}Figure 99 Exploded view of the
disk showing the series of alignment pins on the outer and inner radius.
The alignment pins accurately locate the wedges on the disk.

#### Cage

A holding jig assembly will be fabricated that will allow the disk to be
held while the wedges are placed. After assembly the disk assembly will
be surveyed to accurately locate the sensors to \~10 m.

The assembly into the cage is reasonably straight forward owing to the
simplicity of the disk assembly. The disk assembly has three tabs at the
outer boundary for attachment to the cage assembly. As shown in Figure
100 the tab contains an alignment pin hole and a screw hole for
fastening the disk in place. The general procedure for the cage assembly
will be to, attach the disks in the following order, 1,2,3,4 and as each
disk is mounted route the cable with the cable extensions to the rear of
the cage. The cable extensions will be connected to the FVTX back plate
that holds the Readout Cards (ROC), It has not been determined whether
the cage and back plate will be assembled as a unit (preferred) and then
inserted into the VTX enclosure or the cage is first inserted into the
VTX enclosure and then the back plate is attached.

![](media/image132.wmf){width="3.501388888888889in"
height="2.204861111111111in"}

[]{#__RefHeading___Toc170092674 .anchor}Figure 100 Closeup view of the
outer boundary of the disk assembly showing the tab for attachment to
the FVTX cage. Located at three points on the circumference, the disk is
pinned accurately to the cage and then fastened with a screw.

### Integration

Integration involves coordinating the mechanical and electronic
activities within the FVTX project and across subsystem boundaries with
the VTX, NCC, and the rest of PHENIX. We have put in place integration
engineers who are responsible for ensuring that the FVTX integrates
seamlessly into the VTX and other subsystems. The two integreation
engineers, Eric Mannel and Walt Sondheim, have identical
responsibilities in the VTX and the FVTX projects. In addition, Robert
Pak is working with both projects as the responsible person for
infrastructure and mechanics and provides the interface to the BNL
engineering team and the external subsystems.

#### Mechanical Integration

The mechanical integration has been an ongoing task for the FVTX since
FY2006-7. Supported under R&D funds we have provided substantial input
to the efforts by the VTX group to keep the design of the FVTX moving
along as the VTX design evolves so that no show stoppers remain and the
VTX effort can procede on schedule. This has been very successful and
the FVTX design has matured to the point where we have been able to do
the thermal and finite element analysis of the entire VTX-FVTX system to
ensure that the two projects coexist without interference. This is an
ongoing effort that will last the full length of the project. Periodic
reviews will be held.

#### Electronic Integration

Electrical Integration:

The tight space constraints of the VTX enclosure and the close proximity
of the electronics for the the VTX detector requires that close
attention be paid to the electrical integration of the detector. To
facilitate this, the project electrical engineer will develop a set of
plans, with the assistance of the subsystem managers from both the VTX
and FVTX projects, along with members of the PHENIX experimental team
responsible for overall electronics at PHENIX. The integration can be
broken into three separate sub-tasks; power and ground, systems control,
and electrical design review.

Power and Ground:

A preliminary plan for power and ground for the VTX and FVTX projects
requires that the three subdetectors, VTX pixels, VTX stripixels, and
FVTX be electrically isolated from each other to minimize crosstalk and
noise. Each of the three systems will provide the means for all grounds
to be tied together at a single point, most likely at the power
supplies. It is envisioned that the detectors will have several
independent grounds within the detector - digital, analog, and shield -
which will be specific to each of the detectors and requirements of the
electronics chosen in the design. During the design phase of the
electrical components, each detector system needs to insure that their
grounding plans are appropriate and provide the flexibility to connect
or isolate grounds at different points to allow for studies of crosstalk
and noise issues, if necessary.

The three subdetectors will also have their own power requirements and
it is up to the design teams to specify the power requirements,
voltages, current, and noise limits, during the design phase. To
maintain the electrical isolation, each of the subdetectors will have
their own power supplies. Once full power specifications are known based
on the measurements during the proto-type stages, power systems will be
evaluated based on performance and cost. However, to minimize the effort
required, it is planned that the three subdetectors will use the same
vendor if possible.

Systems Control and PHENIX Integration:

Overall electrical integration into PHENIX requires the coordination of
the VTX and FVTX design teams and various teams from PHENIX responsible
for the overall operations of PHENIX. The project electrical engineer
will be responsible for coordinating with the electrical group
responsible for power and ground within PHENIX, the DAQ group
responsible for data readout of all PHENIX detectors, and the Online
Computing Group(ONC) that oversees the slow control and monitoring
systems. The project engineer will work with each of these groups to
ensure that when the FVTX detector is ready for installation, the
detector can be quickly integrated into the PHENIX DAQ and Control
systems.

Design Review:

Performing internal design reviews of the electronics is a critical step
to ensure that the final design meets not only the readout requirements
of the detector, but is compatible with PHENIX overall, and meets all
PHENIX, BNL CA-D and BNL safety requirements. The FVTX project will use
a review procedure similar to the one developed and implemented by the
VTX project.

The over all design phase has three primary stages, proto-type,
pre-production, and final production. Once the proto-type testing has
been completed, and the pre-production design work is nearing
completion, the project electrical engineer will call for an internal
electronics review of the component design. The review process will be
headed up by the project electrical engineer, and will include other
electronics experts from within PHENIX with strong knowledge of the
PHENIX detector and DAQ system. The design team will be required to
provide in advance sufficient information for the review team to make an
assessment as to the viability of the unit to perform to the required
specifications and work within the PHENIX detector. This information
should include, but is not limited to, electrical schematics, layout
files, component list and data sheets, fpga/pld code, power and heat
loads as measured on the proto-type, and a detailed Q/A and testing
plan. This documentation will be archived for future reference. Once the
design has been approved by the review team, pre-production can go
forward. Should significant design changes be required following the
pre-production review, then a second review may be required. Once the
the pre-production units have been made and tested, a second mini-review
will be held to verify the performance of the unit and address any final
changes that might be required. Upon second approval, full production
may go forward. In the case of simple designs, or cases where only a
couple of modules are needed, the electrical project engineer can reduce
the scope or wave the review process in consultation with the design
team, FVTX project management, and PHENIX project management.

## Q/A procedures

The FVTX is a complex assembly of silicon sensors, electronics,
mechanical support and thermal management components. The individual
pieces that comprise the final complete assembly will be designed,
tested and produced at different stages of the project. The Q/A plan
will contain a detailed set of test procedures, along with specific
pass/fail criteria, to guide the various stages of the project from
prototype to Q/A test, from Q/A test to production, and from production
to Q/A acceptance for assembly.

### Silicon sensors, design and prototype

The design of the silicon sensor will be initiated within the FVTX
project. The responsibility for the layout design will be shared by LANL
and the Prague collaborators. Major sensor design parameters include:

Wafer diameter and thickness 6"(preferred), 300m

Implant Width min 25 m

Metallization Width min 25 m

Readout pitch 75 m

Polysilicon resistors 1-5M

Capacitor oxide specifications ≥ 200pf

Passivation material SiO~2~ or SiNi

Bond Pad Area min 50 m

Test Pad Area min 50 m

Guard ring structure \>1 with bond pads

Scratch pad for sensor ID and pass/fail marks

Scribe lines for cutting

Alignment targets for metrology

Test Structures (Large Area Diode, polysilicon, capacitor)

The CAD design will be sent to the vendor and the vendor will evaluate
the design in the context of the company's design rules. The final mask
design will be created by the vendor, and will be the result of
iteration between the FVTX and the vendor. The LANL and Prague
collaborators responsible for the sensor design will perform a final
review of the proposed mask set, and mutually agree that it is correct,
before giving the vendor permission to produce the mask set. The
produced mask set will be qualified by the vendor according to their
process rules.

The vendor will produce a prototype round of sensors from the mask set.
The FVTX project will present a set of performance criteria to the
vendor, which must be achieved in order to qualify each sensor for
acceptance. Major acceptance criteria with typical values will include:

Wafer resisitivity 2-5 kohm

Wafer thickness and planarity 300 m, \< 10 m

Maximum leakage current 2 A/cm^2^

Maximum slope of leakage current versus voltage

Sensor capacitance versus voltage

Minimum sensor breakdown voltage 200V

Polysilicon resistor value (if applicable) 1-5M

Integrated capacitor value (if applicable) 200pf

Oxide breakdown voltage \>50V

Visual inspection for defects and flaws

The prototype batch of silicon sensors will be re-tested by the FVTX
project. The exact location where these tests will take place is
undetermined at this time, but laboratories with suitable equipment
exist at Prague and at UNM. The test laboratory should have an adequate
clean area and a semiconductor characterization station.

-   
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-   
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-   
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All the acceptance criteria tests that the vendor performs will be
repeated by the project. The sensor depletion voltage and breakdown
voltage will be measured on each individual sensor. The overall sensor
leakage current/voltage characteristic will also be measured on each
sensor. Additionally, we will design a custom probe card that exactly
matches the test pad geometry on the sensors. We will measure the
leakage current/voltage characteristic on each individual strip using
this probe card. Deviation from a relatively uniform characteristic
across the sensor could be indicative of problems in the interstrip
isolation or the quality of the passivation layer. We will measure the
polysilicon resistance on test resistors on the wafer. We will measure
the capacitance/voltage characteristic on a MOS test structure on the
wafer. Another test structure will be used to measure the oxide
breakdown voltage. Almost all of the test measurements will be
controlled by a software interface, such as Labview. The program will
record and store all the test data. We will use scratch pads on the
wafer to record pass/fail results for each sensor.

A subset of the prototype detectors will be more extensively tested with
radioactive sources and a 1064 nm laser diode to evaluate signal
response performance of the sensor. Both methods can produce signals
with large enough amplitude that the detector output can be recorded
without an amplifier. The amplitude and pulse shape response to source
or laser will test the quality of the integrated coupling capacitors and
the sensor depletion voltage characteristics versus bias voltage. By
scanning the sensor with the laser diode, we will be able to evaluate
the charge sharing characteristic of the sensor.

A typical anticipated yield for sensors fabricated in 4-inch wafer
technology is approximately 70%. Because most sensor failures are due to
volume defects in the silicon wafer, the number of defects scales with
sensor area. We can expect a higher incidence of defects, and therefore
a lower yield for sensors fabricated in 6-inch wafer technology. A
minimum 50% yield in the prototype round would suggest that the failures
were caused by material defects, and probably not process related. This
would be sufficient basis to authorize the production run.

#### Silicon Sensors, Production Runs

The same procedures and criteria used for the prototype sensor Q/A will
be used for the production runs.

###  {#section-1 .unnumbered}

### FPHX Readout Chips, Design and Prototyping

The FVTX project will work with the electronics design group at Fermilab
to develop the performance specifications of the FPHX readout chip. LANL
is leading this effort for the FVTX project. These specifications
include:

Front end coupling, ac/dc

Amplification

Shaping time

Noise floor and noise slope

ADC

Zero suppression

Channel mask

Test inject

Kill

Readout architecture and controls

Clock speeds

Data format

Power

The Fermilab design group and the FVTX project, led by LANL, will
iterate between the design specifications provided by the project and
the chip layout designed by the Fermilab group. The final prototype
design will be reviewed by the FVTX project and approved before it is
released for submission to the foundry. The Fermilab group will work
with the foundry to ensure that the chip layout conforms to the
foundry's process rules. The foundry will produce the mask set, and they
will be responsible for reviewing and accepting the mask set.

The foundry will perform in-house quality checks on the wafer; however
these will likely be basic tests which will not reflect die performance.

The Fermilab team will have a vested interest in qualifying the
prototype round of wafers. We will work with them to prepare a probe
station at Fermilab and to write software to perform a variety of
automated measurements using the probe station. The Fermilab team will
write specifications regarding the set points for reference voltages,
filter requirements, and the performance metrics. We will test all the
die on the wafers before they are diced. Die that fail to meet the
acceptance criteria are typically inked on the wafer. The wafers will be
sent to a vendor to have them thinned and diced. The die that have
passed the acceptance test will be grouped according to similar
performance characteristics.

Once they are diced, a subset of the readout chips will be tested
extensively in the lab to gather as much operating experience as
possible with the chips. Some number of die will be powered for
approximately 72 hours to determine if there is any infant mortality
concern. Die will be tested with various input configurations, both
varying input capacitance over the expected range, and with a range of
input amplitudes. The signal-to-noise will be measured over this range
of input conditions. The front-end saturation response will be measured.
The sensitivity of the chip performance to bias voltages and other
hardware and programmable set points will be studied. The ADC pedestals
and linearity will be measured. A variety of test patterns using the
masking capability will be exercised to look for crosstalk or
neighboring channel correlations. Clock frequencies will be varied and
measurements made to look for edge coupling from the clock to the other
parts of the circuitry. Kill and reset functions will be tested. Test
data will be readout under a variety of operating conditions and clock
speeds. Tests will be performed to determine failure modes of the data
output. Some die will be wire-bonded to a prototype sensor, and the
response to an injected charge, either a source or laser diode, will be
measured. The filter components between the sensor and the readout chip
will be tested and optimized. The ambient temperature can be manipulated
to test the system with elevated leakage currents in the sensor. A test
in a particle beam would be useful, but not considered necessary to
decide whether to move forward to full production of the readout wafers.

If, during these tests, a serious flaw or performance deficiency is
found in the readout chip, there will be another design round. This is
explicitly written into the Project schedule.

### High Density Interconnect (HDI)

There will be an initial prototype round of the HDI. The first test of
the HDI is a careful visual inspection. Common failure modes in kapton
circuits are opens in the traces, and (often tiny) metal hairs that
short adjacent traces. The quality of the trace edge is also an
important indicator of good high frequency isolation. The kapton circuit
is a precision component in the overall wedge assembly, and so accurate
metrology will be performed to measure length, height, width, thickness
die pad locations, and sensor bias pad location. The LCR characteristics
of the kapton circuit will be tested with test pulses. The fidelity of a
test signal will be measured end-to-end. Cross talk between output lines
will be studied and electrical characteristics of the HDI will be
measured at operating frequencies. UNM is leading the HDI effort

### Composite Backplane (Support/Heat Spreader)

Hytec Inc. will determine the composition and specifications for the
backplane based on finite element simulations which indicate that our
operating temperature specification will be maintained. On receipt of
the first articles, we will perform metrology to confirm the length,
width, thickness, and planarity of the composite backplane. We will
measure the thermal conductivity, in consultation with Hytec. These
tests will most likely take place at LANL or at Hytec.

### Adhesives

The wedge assembly components are mainly glued together. The kapton HDI
will be glued to the composite backplane. The bond must have adequate
strength, a uniform and repeatable bead deposition pattern, provide a
flat assembly, and provide adequate rigidity under the wire bond pads on
the HDI to ensure reliable wire bonding from the readout chip to the
HDI. There are two classes of adhesives that we will evaluate; adhesive
tape and epoxies. Types of adhesives will include electrically
conductive, non-conductive and thermally conductive. We will evaluate
various products in close consultation with Hytec, because the company
has experience and expertise with these products. If we choose to work
with epoxies, we may have to evacuate the mix to get rid of bubble
formation. It is very likely that we would use an automated glue
dispenser in order to achieve a reproducible epoxy bead pattern.

We will perform precision metrology on the assembly to evaluate the
accuracy of the assembly procedure. We will perform a heat conduction
evaluation using a suitable heat source on top of the HDI and measuring
the temperature distribution on the backplane. We will thermal cycle the
assembly to test for mechanical integrity and to determine whether the
assembly retains acceptable planarity.

The sensor will be glued to the HDI/backplane. In addition to the
requirements stated above, the bias connection has to be made to the
underside of the sensor and brought to the perimeter of the HDI. This
will most likely be done using a conductive adhesive. We will also test
this assembly as above for thermal and mechanical characteristics.

Each of these assemblies will require custom designed vacuum jigs and
precision location tooling. The lab where these assemblies and tests
will take place has not yet been determined.

### Wedge Assembly

The wedge assembly will be built in the following sequence.

Kapton HDI glued to composite backplane

Sensor glued to HDI plus composite backplane

Filter components and bias resistors soldered to HDI

FPHX chips glued to HDI

FPHX output pads wire bonded to HDI

Sensor outputs wire bonded to FPHX input pads

Wire bonds encapsulated

Production quantities of the wedge assembly, prior to wire bonding, can
be done at a lab within the project, or at the vendor who does the wire
bonding. This will be determined according to cost/benefit. If the
assembly is done at the vendor, the work will be carried out in
accordance to written procedures, specifications and measurements, and
it will be monitored by someone from the FVTX project.

The filter components, bias resistors and FPHX die will likely be
attached at the vendor. The surface mount components will be soldered
and the FPHX will be attached with adhesive. We will work with the
vendor to approve component and die attach procedures. The readout wafer
thinning and sawing into individual die will be performed by a qualified
vendor, either the one who is awarded the wire bond contract or a
different source. The vendor will use a diamond saw, and we will
visually inspect the die under a microscope to ensure good cut-edge
quality from the saw before sawing the entire wafer lot.

The wire bonding from sensor to readout chip and from readout chip to
the HDI will be performed by an approved vendor. We expect the vendor to
use a semi-automated wedge bonder and to use aluminum bond wire. The
vendor will qualify a process to achieve bonds with reproducible length
and loop height. Test bonds will be made to ensure bond strength of
approximately 7 grams or greater pull strength.

The wire bonds on the wedge will be encapsulated to protect them during
shipping and handling. There are several candidate products, opaque and
clear, that will be evaluated. We have had experience using both clear
and opaque encapsulant. The advantage to the clear product is that one
can observe if a wire is bent over to its neighbor during application of
the viscous encapsulant, and this can be corrected before the
encapsulant sets. The encapsulant will most likely be applied by the
vendor who is selected to do the wire bonding. We would evaluate the
integrity of prototype assemblies before we had them encapsulated. We
would require visual inspection to confirm that the wire bond pattern is
correct on subsequent production assemblies before they are
encapsulated.

# R+D Schedule, Responsibilities and Budget

## R+D Areas

The R&D associated with the endcaps involves designing the FPHX chip,
developing the interface between the FPHX chip and the existing PHENIX
DCMs, sensor design, developing the wedge structure, and developing the
bus and flex cable. The FPHX and data interface is the most involved of
the R&D projects. The rest are starting from existing technology or use
standard commercial concepts. The R&D for the endcaps will be supported
at LANL and BNL. At LANL we will complete the R&D for the interface, the
mechanical support and ladder, and the sensor design. BNL will support
the R&D for the FPHX design and modification.

### FPHX 

The FPHX chip design will borrow elements from previously successful
chips such as the FPIX2, SVX4, FSSR, etc. The FPHX is a 1 column x 128
channel structure designed for holes rather than electron collection. It
has a data-push architecture similar to the FPIX2.1 chip and \~ 70
micron channel pitch. The R&D issues involve optimizing the front-end
for the mini-strips, designing the digital readout specifically for the
PHENIX DAQ and converting the chip to wire bonds. FNAL electronics group
( Ray Yarema, head) has completed the conceptual design of FPHX and the
next phase will be to do the wafer layout and prototype. We expect that
this phase will proceed in mid calendar 2007.

### Sensor

The sensor will be a standard p on n DC coupled silicon diode. This is a
very conventional design that is available from many vendors. The R&D
consists of mainly developing the prototype masks and producing
prototypes for testing. We have begun the process of identifying vendors
and the Czech group has started designing the sensor. We expect to
procure a prototype in the spring of 2007.

### Interface 

The ROC and FEM boards that will connect between the PHX chip and PHENIX
DCMs will need to provide the following functions:

-   Strip the sync words out of the data stream, retaining only data
    words

-   Combine the data from several chips into one serial stream which
    will go via fiber to a FEM

-   Provide buffering of the continuously streaming data from the PHX
    chips for 64 beam clocks, and this buffering must be adequate for
    everything from pp running to central Au-Au events

-   Upon a lvl-1 accept, retrieve the data from the buffer for the
    appropriate beam clock and package it into a format acceptable by
    the DCM

-   Pass beam clock to the PHX chip, assure sychronization

-   Provide an interface to download initialization settings to the PHX
    chips

-   Perhaps provide ability to reset PHX chip(s)

We expect the board designs to be largely completed by our LDRD grant
which will put a prototype forward silicon tracker in to PHENIX, and
will be using FPIX chips which will have very similar digital output to
the FPHX chips. Some details will need to be modified to accept the
somewhat different segmentations of the FVTX detector compared to the
LDRD detector. A large portion of the designs have already been
prototyped via efforts at LANL and Columbia, using FPIX chips and FPGA
evaluation boards. The FPIX chips have been successfully read out, with
one or more data lines per chip, the data have been buffered into 64
clock buffers, and the correct event from a given chip has been shown to
be properly pulled out from the clock buffers upon a trigger.
Prototyping will begin in mid 2007.

## Schedule

The schedule for the FTVX project is shown in Figure 101. Included in
the schedule is the R&D timeline. We have assumed R&D money begins in
the second quarter of FY06 and construction funds begin in the second
quarter of FY08. Task durations are based on previous experience of the
engineering teams and quotes. The total project duration is due
primarily to the sensor and PHX R&D and procurement times.

![](media/image133.png){width="5.986805555555556in"
height="6.626388888888889in"}

![](media/image134.png){width="5.986805555555556in"
height="5.999305555555556in"}

![](media/image135.png){width="5.986805555555556in"
height="6.127777777777778in"}

![](media/image136.png){width="5.986805555555556in"
height="3.248611111111111in"}

[]{#__RefHeading___Toc170092675 .anchor}Figure 101 -- PHENIX Forward
Silicon Vertex (FVTX) project timeline.

###  Cost

Since the FVTX will be added to the existing barrel vertex detector,
VTX, much of the needed infrastructure, cooling, enclosure, cable
routing, installation procedures, etc. will already have been done and
be in place. In this cost estimate only those items needed for fitting
the FVTX into the VTX enclosure are considered. The costs in Table 8 are
generally obtained from cost estimates by the engineering team who will
be doing the work and from cost estimates for work already done by those
teams. For example, the cost estimate for the FPHX chip came from the
FNAL engineers who designed the FPIX2 chip. The HYTEC engineering team
previously designed the ATLAS pixel mechanical structures and is
currently working on the VTX and that forms the basis for the mechanical
cost estimates. The cost basis for the sensors are from quotes from ON
Semiconductor Inc. in Prague, Czech Republic and CIS Semiconductor
obtained in 2006 and on drawings of the wafers with the FVTX wedges. The
contingency analysis method is listed in Appendix A (Section 6).

![](media/image137.wmf)

[]{#__RefHeading___Toc170092689 .anchor}Table 8 -- Cost estimate for the
FVTX endcaps with contingency. The methodology used for contingency is
in Appendix A (Section 6).

### Project Management and Responsibilities

The LANL Group will work together with HYTEC inc. to develop the design
for the Endcap mechanical ladder and cooling. LANL has formed
collaboration with FNAL to design, prototype and test the PHX readout
chip. An MOU with PHENIX, BNL physics department and FNAL for R&D of the
PHX chip was signed in 2004.

The organizational chart for the FVTX project is shown inFigure 102.

![](media/image138.png){width="5.99375in" height="4.009722222222222in"}

[]{#__RefHeading___Toc170092676 .anchor}Figure 102 - Organizational
Chart for the FVTX project.

Institutional Responsibilities

Los Alamos National Laboratory

LANL coordinate work to design and procure the silicon sensors, work
with FNAL on the development of the FPHX chip, development of the
interface to PHENIX DAQ, and on the simulation effort with NMSU. Los
Alamos is currently leading the mechanical engineering and the
integration effort for the barrel detector, and will continue those
efforts for the FVTX.

Brookhaven National Laboratory

Brookhaven is responsible for the overall Mechanical Integration and
Infrastructure for the VTX project and will do the same for the FVTX.
They will coordinate activities at BNL and also work on simulations.

Columbia University

Columbia University will have the responsibility of the wedge assembly.
The wedge is the fundamental unit for the FVTX. Columbia will be
involved with all aspects of the design and specification of the
components that form the wedge. They will work with LANL and FNAL on the
FPHX and sensors and with UNM on the HDI. They will be responsible for
the assembly and testing of the wedge assembly, wire bonding and doing
all QA. If other institutions are involved, they will coordinate all of
the activities. Columbia is also responsible for the overall electronic
integration.

Iowa State University

Iowa State University is currently working on management details with
the barrel detector and working on an (funded) SBIR effort addressing
the level 1 trigger capabilities of the FVTX. They are also involved
with the interface module.

Charles University, Czech Technical University, Institute of Physics,
Academy of Sciences, Prague, Czech Republic

Charles University has been active in the development, testing,
assembly, and commissioning of the ATLAS pixel sensors. They will do the
same for the FVTX effort and additionally participate in software
development.

New Mexico State University

NMSU will work on comprehensive simulations for the FVTX effort. The
will work on the wedge assembly and are responsible for the coordination
of the assembly of the disks and cages.

University of New Mexico

UNM has experience in testing, Q/A and a laboratory for characterization
of sensors. They are currently working on the barrel strip sensors and
will do the same for the FVTX effort. UNM is responsible for the HDI,
flex, and fiber cables and will assist with sensor QA and testing.

Saclay

Saclay will work on software. 

Yonsei University, Seoul, Korea

The Yonsei group has worked on electronics and software for the muon
system. They have not defined their scope of work.

University of Jyvaskyla, Finland

The university of Jyvaskyla will work on simulations and assist in
assembly.

# Appendix A -- Contingency Analysis

## Contingency Analysis

The average contingency for the FVTX is 25.2 %.

This section describes how the contingency for a given WBS element was
calculated.  Risk is a function of the following factors:  the
sophistication of the technology, the maturity of the design effort, the
accuracy of the cost sources and the impact of delays in the schedule. 
Risk analysis is performed for each WBS element at the lowest level
estimated.  Results of this analysis are related to a contingency, which
is listed for each WBS element.  The goal is to make the method of
contingency determination uniform for all project WBS elements.

> **Definitions**
>
> **Base Cost Estimate** -- The estimated cost of doing things correctly
> the first time. Contingency is not included in the base cost.
>
> **Cost Contingency** -- The amount of money, above and beyond the base
> cost, that is required to ensure the project\'s success. This money is
> used only for omissions and unexpected difficulties that may arise. 
> Contingency funds are held by the Project Manager.
>
> **Risk Factors**
>
> **Technical Risk** -- Based on the technical content or technology
> required to complete the element, the technical risk indicates how
> common the technology is that is required to accomplish the task or
> fabricate the component.  If the technology is so common that the
> element can be bought \"off-the-shelf\", i.e., there are several
> vendors that stock and sell the item, it has very low technical risk,
> therefore a risk factor of 1 is appropriate.  On the opposite end of
> the scale are elements that extend the current \"state-of-the-art\" in
> this technology.  These are elements that carry technical risk factors
> of 10 or 15.  Between these are: making modifications to existing
> designs (risk factor 2-3), creating a new design which does not
> require state-of-the-art technology (risk factor 4 & 6), and creating
> a design which requires R&D, and advances the state-of-the-art
> slightly (risk factor 8 & 10).
>
> **Cost Risk** -- Cost risk is based on the data available at the time
> of the cost estimate.  It is subdivided into 4 categories.
>
> The first category is for elements for which there is a recent price
> quote from a vendor or a recent catalog price. If the price of the
> complete element, or the sum of its parts, can be found in a catalog,
> the appropriate risk factor to be applied is 1. If there is an
> engineering drawing or specification for the element, and a reliable
> vendor has recently quoted a price based on these, the cost risk
> factor to be applied is 2. Similarly, if a vendor has quoted a price
> based on a sketch that represents the element, and the element\'s
> design will not change prior to its fabrication, the appropriate cost
> risk factor would be 3.
>
> The second category is for elements for which there exists some
> relevant experience.  If the element is similar to something done
> previously with a known cost, the cost risk factor is 4.  If the
> element is something for which there is no recent experience, but the
> capability exists, the cost risk is 6.  If the element is not
> necessarily similar to something done before, and is not similar to
> in-house capabilities, but is something that can be comfortably
> estimated, the risk factor is 8.
>
> The third category is for elements for which there is information
> that, when scaled, can give insight into the cost of an element or
> series of elements.  The cost risk factor for this category is 10. 
>
> The fourth category is for elements for which there is an educated
> guess, using the judgment of engineers or physicists.  If there is
> experience of a similar nature, but not necessarily designing,
> fabricating or installing another device, and the labor type and
> quantity necessary to perform this function can be estimated
> comfortably, a cost risk factor of 15 is appropriate.
>
> **Schedule Risk** -- If a delay in the completion of the element could
> lead to a delay in a critical path or near critical path component,
> the schedule risk is 8.  If a delay in the completion of the element
> could cause a schedule slip in a subsystem which is not on the
> critical path, the schedule risk is 4.  Only elements where a delay in
> their completion would not affect the completion of any other item
> have schedule risks of 2.
>
> **Design Risk** -- is directly related to the maturity of the design
> effort. When the element design is nearly complete, quantity counts
> and parts lists finished, the risk associated with design is nearly
> zero; therefore a risk factor of 0 is applied.  This is also the case
> when the element is an \"off-the-shelf\" item and the parts counts and
> quantities are finalized.  When the element is still just an idea or
> concept, with crude sketches the only justification for the cost
> estimate, the risk associated with design state is high or 15. 
> Between these two extremes are the stages of conceptual design and
> preliminary design.  In conceptual design, when layout drawings of the
> entire element are approaching completion, some preliminary scoping
> analyses have been completed, and parts counts are preliminary, the
> design risk factor is 8.  During preliminary design, when there are
> complete layout drawings, some details worked out, complete parts
> counts, and some analysis for sizing and showing design feasibility,
> the appropriate design risk is 4.
>
> **Weighting Factors**
>
> The weight applied to the risk factors depends on whether there are
> multiple or single risks involved in completing an element. 
>
> The weights applied to technical risk depend upon whether the element
> requires pushing the current state-of-the-art in design,
> manufacturing, or both.  If the element requires pushing both, the
> weight to be applied is high, or 4; if either the design or
> manufacturing are commonplace, the weighting factor is 2.
>
> For weights applied to cost risk, the two factors are material costs
> and labor costs.  If either of these are in doubt, but not both, the
> weight to be applied to cost risk is 1.  If they are both in doubt,
> the weight applied is 2.
>
> The weight factor given to schedule risk is always 1.
>
> The weight factor given to design risk is always 1 and so is not shown
> explicitly.
>
> ** Procedure**
>
> The following procedure is used for estimating contingency.
>
> **Step 1 --** The conceptual state of the element is compared with
> Table 4 to determine risk factors.  A technical risk factor is
> assigned based on the technology level of the design.  A design risk
> factor is assigned based upon the current state (maturity) of the
> design.  A cost risk factor is assigned based on the estimating
> methodology used to arrive at a cost estimate for that element. 
> Similarly, a schedule risk factor is identified based on that
> element\'s criticality to the overall schedule.
>
> **Step 2 --** The potential risk within an element is compared with
> Table 5 to determine the appropriate weighting factors. 
>
> **Step 3 --** The individual risk factors are multiplied by the
> appropriate weighting factors and then summed to determine the
> composite contingency percentage.
>
> **Step 4 --** This calculation is performed for each element at its
> lowest level.
>
> **Step 5 --** The dollar amount of contingency for an element is
> calculated by multiplying the base cost by the composite contingency
> percentage.

  ---------- ------------------ ----------------- --------------- ---------------
  **Risk     **Technical**      **Cost**          **Schedule**    **Design**
  Factor**                                                        

  0          Not used           Not used          Not used        Detail design\
                                                                  \> 50% done

  1          Existing design    Off-the-shelf or  Not used        Not used
             and\               catalog item                      
             off-the-shelf H/W                                    

  2          Minor              Vendor quote      No schedule     Not used
             modifications to   from  established impact on any   
             an existing design drawings          other item      

  3          Extensive          Vendor quote with Not used        Not used
             modifications to   some design                       
             an existing design sketches                          

  4          New design;\       In-house estimate Delays          Preliminary
             nothing exotic     based on previous completion of   design \>50%
                                similar           non-critical    done; some
                                experience        subsystem item  analysis done

  6          New design;        In-house estimate Not used        Not used
             different from     for item with                     
             established        minimal                           
             designs or         experience but                    
             existing           related to                        
             technology         existing                          
                                capabilities                      

  8          New design;        In-house estimate Delays          Conceptual
             requires some R&D  for item with     completion of   design phase;
             but does not       minimal           critical path   some drawings;
             advance the\       experience and    subsystem item  many sketches
             state-of-the-art   minimal in-house                  
                                capability                        

  10         New design of new  Top-down estimate Not used        Not used
             technology;        from analogous                    
             advances           programs                          
             state-of-the-art                                     

  15         New design; well   Engineering       Not used        Concept only
             beyond current\    judgment                          
             state-of-the-art                                     
  ---------- ------------------ ----------------- --------------- ---------------

[]{#__RefHeading___Toc170092690 .anchor}Table 9 - Technical, cost and
schedule risk factors.

  --------------- ---------------------------------------- ------------------
  **Risk Factor** **Condition**                            **Weighting
                                                           Factor**

  **Technical**   Design OR Manufacturing                  2

                  Design AND Manufacturing                 4

  **Cost**        Material Cost OR Labor Rate              1

                  Material Cost AND Labor Rate             2

  **Schedule**    Same for all                             1

  **Design**      Same for all                             1
  --------------- ---------------------------------------- ------------------

[]{#__RefHeading___Toc170092691 .anchor}Table 10 - Technical, cost,
schedule and design weighting factors.

# Appendix B -- The FVTX Level-1 Trigger System

## Introduction

In this Appendix we present the current status of a conceptual design
for a Level-1 trigger system utilizing the FVTX detector. While many of
the details remain to be worked out, the design outlined here is a
powerful, flexible trigger system that exploits synergies between many
PHENIX upgrades and can address a wide array of physics observables.

We begin by summarizing the additional required event rejection for
single and di-muon physics with the PHENIX detector beyond that
currently available with the existing Muon Identifier Local Level-1
(MuID LL1). We outline a trigger strategy starting with an FVTX LL1
system for the identification of tracks from both the primary and
displaced vertices. This trigger strategy requires combining the FVTX
LL1 output with additional information from the PHENIX Muon Trigger
Upgrade, which we describe in detail. We then report on the current
hardware research and development effort, and conclude with a cost
estimate for the FVTX LL1

## Required Event Rejection

The required event rejection for heavy flavor physics with the PHENIX
muon arms in future RHIC and RHIC-II running can be divided into two
classes of trigger signals -- single muons and muon pairs.

The existing trigger option for single muons is to trigger on at least
one deep muon road in the Muon Identifier (MuID). A deep road is defined
as a track in LL1 that penetrates all layers of the MuID. The achieved
rejection factors for the 1-Deep MuID LL1 trigger in both p+p and Au+Au
are shown in Table 11 (taken from Table 26 in this proposal). Also shown
are the required rejections for the end of RHIC-I running as well as for
RHIC-II. The required rejections are what are needed to ensure that the
triggers are not prescaled (Table 27 this proposal). Prescaling means
that valid triggers are not written to disk because the rate exceeds a
bandwidth limit at Level-1 (1kHz). For convenience the required
rejections are factorized into the current rejection and the required
improvement.

[]{#__RefHeading___Toc170092692 .anchor}Table 11 - Event rejection
required beyond the MuID LL1 for RHIC-I (2008) and RHIC-II running for
single muon triggers.

+-----------------+-----------------+-----------------+-----------------+
| Existing        | Achieved        | Rejection       | Rejection       |
| Trigger         | Rejection       | needed 2008     | needed RHIC-II  |
|                 |                 |                 |                 |
| MuID 1-Deep     |                 |                 |                 |
+-----------------+-----------------+-----------------+-----------------+
| p+p             | 478             | 478\*21         | 478\*71         |
+-----------------+-----------------+-----------------+-----------------+
| Au+Au           | 5               | 5\*15           | 5\*116          |
+-----------------+-----------------+-----------------+-----------------+

Table 12 demonstrates that a new Level-1 trigger needs to increase the
rejections already at the end of RHIC-I era (2008) and definitely by
RHIC-II in order to maximize the collected statistics on open charm and
bottom from a given time running the experiment.

The existing trigger option for muon pairs is to trigger on two roads in
the MuID LL1. In order to maximize the efficiency for the physics
signals of interest, combinations with shallow roads (only utilizing the
first three MuID gaps) are used in p+p collisions, where the MuID
occupancy is low. The achieved rejection factors for the 1-Deep
1-Shallow trigger in p+p and 2-Deep trigger in Au+Au are shown in the
Table 12 (taken from Table 26 in this proposal). Also shown are the
required rejections for the end of RHIC-I running as well as for
RHIC-II. Again, the required rejections are factorized into the current
rejection and the needed improvement.

[]{#__RefHeading___Toc170092693 .anchor}Table 12 - Event rejection
required beyond the MuID LL1 for RHIC-I (2008) and RHIC-II running for
di-muon triggers.

+---------------------+--------------+---------------+---------------+
| Existing Trigger    | Achieved     | Rejection     | Rejection     |
| MuID                | Rejection    | needed 2008   | needed        |
|                     |              |               | RHIC-II       |
+---------------------+--------------+---------------+---------------+
| p+p                 | 23500        | \< 23500      | 23500\*1.4    |
|                     |              |               |               |
| 1-Deep 1-Shallow    |              |               |               |
+---------------------+--------------+---------------+---------------+
| Au+Au               | 15.7         | 15.7\*5       | 15.7\*37      |
|                     |              |               |               |
| 2-Deep              |              |               |               |
+---------------------+--------------+---------------+---------------+

Table 12 demonstrates that a new Level-1 trigger needs to increase the
rejections already at the end of Au+Au RHIC-I era (2008) and definitely
by RHIC-II in order to get the most statistics in
the$B \rightarrow \frac{J}{\psi}$ channel from a given time running the
experiment. Another way of expressing this is that if no increase in
rejection is obtained, then in Au+Au 2008 only one in every 5 produced
$B \rightarrow \frac{J}{\psi}$ will be recorded, the other events will
have to be prescaled away. Note that for p+p running very little to no
increase in muon pair trigger rejection is needed.

## FVTX LL1 Trigger Strategy

Based on the physics that the FVTX is designed to address and on the
expected collision rates of p+p and A+A collisions at RHIC, there are
three main types of triggers that a new Level-1 trigger needs to
deliver; displaced single tracks for use in open charm and bottom
production, a pair trigger for $B \rightarrow \frac{J}{\psi}$ and
upsilon production, and an event-trigger to improve the efficiency of
min-bias and ultra-peripheral collisions. More details on each are given
below. We begin by presenting details of the trigger strategy to be used
in the FVTX, followed by a combination with the downstream Muon Trigger.

### Single Displaced Tracks

The goal of this trigger is to select events that have a track in the
FVTX (comprised of hits in three to four stations) that are displaced
from the collision vertex. Large additional sources of displaced tracks
are pion and kaon decays, that have a much larger decay lifetime. This
leads to a strategy of requiring tracks that are displaced from the
collision vertex but are still within several charm/bottom lifetimes to
reduce the contamination from pions and kaons. As an example consider a
trigger on z-displacement, how far the z-coordinate of the track is from
the collision vertex (a similar cut could be placed on the radial
distance of closest approach, or DCA)

$${\Delta z}_{\text{LOWER}} < \Delta z < {\Delta z}_{\text{UPPER}}$$

Since most charm and bottom decays occur close to the collision vertex
(exponential decay is largest at t=0), you would like to make
${\Delta z}_{\text{LOWER}}$ as small as possible while still maintaining
an acceptable rejection factor. Since the resolution of pointing back to
the collision vertex depends on the momentum, you may be able to afford
a tighter ${\Delta z}_{\text{LOWER}}$ cut at higher momentum in order to
catch more of the charm and bottom decays.

![](media/image139.png){width="3.0006944444444446in"
height="2.7493055555555554in"}

[]{#__RefHeading___Toc170092677 .anchor}Figure 103 - A schematic
representation a displaced vertex cut in the FVTX Level-1 as a function
of momentum. The upper limit is designed to reject muons from pion and
kaon decays, while the lower cut defines a minimum distance from the
event vertex. To avoid potential bias against high momentum decays and
still achieve a reasonable rejection factor, it will be necessary to
change the upper cut as a function of momentum.

A different reason compels us to also consider that the
${\Delta z}_{\text{UPPER}}$ cut also needs to be momentum dependent. One
would like to make ${\Delta z}_{\text{UPPER}}$ as small as possible that
is consistent with catching several lifetimes of charm/bottom decays
(cτ \~ 300-500 μm). The smaller you can make
${\Delta z}_{\text{UPPER}}$, the fewer pion decays you trigger on and
the better the trigger rejection. This is shown schematically in Figure
103.

The need to have ${\Delta z}_{\text{LOWER}}$ and
${\Delta z}_{\text{UPPER}}$ cuts momentum dependent drives the need for
information to be combined from the displaced tracks of the FTVX LL1 and
the momentum information from tracks in the downstream Muon Trigger.

### Muon Pair Trigger

The requirements for the two main physics cases are exactly
complementary: the $B \rightarrow \frac{J}{\psi}$ requires a trigger on
two tracks that are both displaced, while the upsilon and continuum
physics require a trigger on two tracks that come from the main
collision vertex.

A potentially powerful pair trigger is to require that both FVTX tracks
come from a region that is within a distance a few times the track
resolution, or $({\Delta z}_{1} - {\Delta z}_{2}) < n\sigma$, where
n=2-3. This trigger will only achieve a sizeable rejection if both FVTX
tracks are matched to muon tracks in the downstream Muon Trigger,
otherwise the trigger will be satisfied by any pair of primary tracks
that do not decay (primary protons, for example). This trigger satisfies
all the pair physics goals and should remove many of the random
combinations of decaying pions, and therefore it has the potential to
reach high rejections.

## Combined Forward Muon Trigger 

As emphasized above, much of the physics to be addressed by the FVTX
requires the ability to trigger effectively on the presence of a
displaced vertex which results in a downstream track in the PHENIX Muon
Tracker (MuTr) and Muon Identifier (MuID) detectors. While the FVTX is
designed to accurately measure tracks whose origin is displaced from the
main event vertex, it cannot identify these tracks as muons nor classify
them according to momentum (for large momenta). Because of this, the
FVTX LL1 is envisioned to operate as a key part of a combined forward
physics trigger that makes use of additional information from the
existing PHENIX MuID Local Level-1 and the planned Muon Trigger Upgrade
funded by the National Science Foundation.

In the sections that follow we introduce and describe the PHENIX Muon
Trigger Upgrade and describe how the FVTX and MuonTrigger systems can be
combined to provide a trigger that can address a wide array of physics
observables.

### The PHENIX Muon Trigger Upgrade

The planned PHENIX Muon Trigger Upgrade is designed primarily to address
the needs of the PHENIX spin program in polarized p+p collisions at
$\sqrt{s} =$`<!-- -->`{=html}500 GeV. In order to measure the antiquark
contribution to the nucleon spin, it is necessary to trigger on very
high momentum muons originating from the decay of polarized *W* bosons.
Low momentum muons from pion and kaon decay, as well as from charm (and
to some extent, bottom) decays occur at a substantial rate, so that a
trigger is required that can select muons based on momentum as measured
in the PHENIX muon arm.

![](media/image140.png){width="5.997222222222222in"
height="3.5854166666666667in"}

[]{#__RefHeading___Toc170092678 .anchor}Figure 104 - The PHENIX Muon
Trigger Upgrade is designed to provide an effective trigger on muons
from the decay of polarized W bosons in polarized p+p collisions at
500GeV. Such muons dominate the inclusive muon production above a
momentum of \~20GeV/c. The location of the additional RPC chambers that
will be added to the PHENIX muon arm are shown at right.

The Muon Trigger Upgrade will consist of three additional resistive
plate chambers (RPC's), two of which will provide tracking in the
magnetic field volume and a third that will be used for the rejection of
beam-associated backgrounds. These chambers are planned to have a
segmentation of 1^o^ in the phi angle, with 24 segments in theta,
although current plans only call for two theta segments at the trigger
level. The momentum of the track is measured by the difference in angle
between the track hit at the first and second RPC stations. A cut at
2^o^ corresponds roughly to a cut at a muon momentum of 12 GeV and
yields sufficient rejection for the spin program, although the
possibility of simultaneously selecting lower-momentum regions (possibly
prescaled) will be retained. Finally, track candidates in the RPC
chambers will be matched to deep roads in the existing MuID LL1 trigger
system. This matching will be done by passing the deep road information
along a backplane in the trigger crate to the new Muon RPC (MuPC)
Level-1 trigger.

The hardware for the RPC-based Level-1 trigger system will be based on
an improved design of the trigger boards used for the MuID LL1. These
boards, designated GenLL1 Rev2, are based on a generic design that uses
Xilinx FPGA's to implement the trigger algorithm and incorporate up to
twenty 1Gbit fiber transceivers as input. We plan to make use of the
generic nature of this design to implement the Combined Trigger
Processor (described below) that will combine the output of the FVTX and
Muon Level-1 trigger into an extremely flexible and powerful trigger
system.

The Muon Trigger Upgrade is funded by a grant from the National Science
Foundation, and is planned to be installed and commissioned in PHENIX in
2007-2008, and ready for operation in 2009.

## Combining the FVTX with the Downstream Muon Trigger

We envision a trigger strategy where the information from the FVTX is
combined and matched with track momentum information from the downstream
Muon Trigger. Because the displaced vertex cut needs to be a function of
momentum, and the FVTX does not accurately determine the track momentum,
it will generate several sets of trigger primitives based on assumed
momentum range. Likewise, the Muon Trigger will generate primitives for
a selection of candidate momenta. The exact granularity of the trigger
primitives in ∆z and track momentum will need to be determined by
simulation and event rejection requirements.

![](media/image141.png){width="3.6479166666666667in"
height="2.9506944444444443in"}

[]{#__RefHeading___Toc170092679 .anchor}Figure 105 - Block diagram
showing the communication between the FVTX and combined MuID and MuRPC
triggers with the Combined Trigger Processor. Each LL1 system will have
the ability to send trigger data to Global Level-1 (GL1) for independent
triggering, or the primitives can be combined in the Combined Trigger
Processor (as described in the text) to generate trigger primitives
based on information from both systems.

This primitive information will be sent to a combined in a Combined
Trigger Processor, as shown in Figure 105 Assuming four FVTX sets of
trigger primitives, corresponding to a "low" and "high" momentum
assumption (and therefore cut as outlined in Figure 105) combined with a
displaced or primary track, and three sets of momentum regions defined
by the Muon Trigger as "low", "middle" and "high" we show in Table 13
possible combinations of trigger primitives for different physics
signals. For the sake of being concrete we assume p+p collisions at
$\sqrt{s} =$`<!-- -->`{=html}500GeV and therefore the inclusive muon
distribution shown in Figure 50. The Muon Trigger momentum selections
correspond to regions where charm ("low"), bottom ("middle") or W decay
("high") dominate the inclusive muon spectra.

+--------------------------+--------------+----------------+----------+
| **Physics Signal**       | **FVTX       | **Muon Trigger | **Min.   |
|                          | Primitives** | Primitives**   | No. of   |
|                          |              |                | Tracks** |
+--------------------------+--------------+----------------+----------+
| $                        | displaced    | "low" and      | 1        |
| $D,B \rightarrow \mu X$$ | vtx ("low"   | "middle"       |          |
|                          | and "high")  | momentum       |          |
| (single muon, displaced  |              |                |          |
| vertex)                  |              |                |          |
+--------------------------+--------------+----------------+----------+
| $$B \rig                 | displaced    | "low" and      | 2        |
| htarrow \frac{J}{\psi}$$ | vtx ("low"   | "middle"       |          |
|                          | and "high")  | momentum       |          |
| (pair, displaced vertex) |              |                |          |
+--------------------------+--------------+----------------+----------+
| $$\                      | primary      | "low" and      | 2        |
| frac{J}{\psi},\psi^{'}$$ | vertex       | "middle"       |          |
|                          | ("low" and   | momentum       |          |
| (pair, primary vertex)   | "high")      |                |          |
+--------------------------+--------------+----------------+----------+
| *ϒ, μμ* continuum        | primary      | "low" and      | 2 (same  |
|                          | vertex       | "middle"       | arm,     |
| (pair, primary vertex)   | ("low" and   | momentum       | high η)  |
|                          | "high")      |                |          |
|                          |              |                | 2        |
|                          |              |                | (        |
|                          |              |                | opposite |
|                          |              |                | arm,     |
|                          |              |                | central) |
+--------------------------+--------------+----------------+----------+
| $$W                      | (not         | "high"         |          |
|  \rightarrow \text{μν}$$ | required)    | momentum       |          |
+--------------------------+--------------+----------------+----------+

[]{#__RefHeading___Toc170092694 .anchor}Table 13 - Physics signals and
potential FVTX and muon trigger primitive combinations that could be
used to generate Level-1 triggers.

### Hardware Integration of FVTX and Muon Trigger Systems

In previous sections we have outlined a trigger strategy that requires
the integration of trigger information from the downstream muon arm with
information from the FVTX. We plan to do this by transmitting trigger
primitives from both the FVTX LL1 and the Muon Level-1 trigger to a
Combined Trigger Processor. We envision that the primitives will consist
of mappings of candidates in (θ,ϕ) space at the back of the FVTX
detector with a granularity that is determined by the resolution of the
RPC trigger. Each element in the mapping will be a "1" if the system
detected a candidate matching a set of requirements in that (θ,ϕ)
element, and a "0" otherwise. There may be several groups of these
primitives based on momentum region of interest and vertex origin of the
FVTX tracks, as described above.

The combination of the trigger primitive mapping is relatively
straightforward in the Combined Trigger Processor, and is essentially an
AND operation on the individual map elements. The generation of the
trigger data sent to the Global Level-1 trigger will then consist of a
count of the number of elements in each combined primitive map that
satisfies the AND operation.

As an example, a trigger on a pair of tracks originating away from the
event vertex (for example, the decay $B \rightarrow \frac{J}{\psi}$)
would be generated by a trigger primitive map from the FVTX trigger for
tracks originating within a window away from the event vertex and a
trigger primitive map (or several maps) from the Muon Trigger indicating
candidates within selected momentum ranges. If more than two elements in
the trigger primitive array survive the AND operation between the FVTX
and Muon Trigger, the pair trigger is satisfied.

The exact method by which trigger primitive data is pushed from the FVTX
and Muon Trigger LL1 systems into the Combined Trigger Processor will be
determined based on the number of maps (and hence the amount of data)
that will need to pass between the systems. It is possible that all
three systems could coexist in a single crate for each arm, or that
individual crates for each system will communicate over fiber or copper
links.

We note that some modification of the Muon Trigger design may be
necessary to allow an optimal combined trigger. While it is already
envisioned that the Muon Trigger will allow lower momentum selections
(possible prescaled at GL1) to allow triggering on tracks from charm and
bottom decay, it is possible that additional segmentation in theta will
be required by the combined trigger, especially in the heavy ion
environment. Simulations are underway to determine the required
segmentation and the potential impact on the Muon Trigger.

Finally, we note that additional elements could be incorporated into
this Combined Trigger Processor approach could be used to incorporate
additional PHENIX detectors into the trigger if required by the physics
program. For example, the PHENIX Nose Cone Calorimeter is a calorimeter
proposed to cover the same rapidity region as the PHENIX muon arms. Such
a calorimeter could be included to provide an isolation cut at the
trigger level, for example.

## Research and Development on FVTX LL1 Trigger Design

An FY2005 Phase I Small Business Technology Transfer (STTR) award was
granted to to Northern Microdesign and ISU. The key personnel in this
project are

-   Bill Black, President Northern Microdesign previously at Xilinx,
    Inc. (until September 2003) where he was responsible for the analog
    portion of the 10Gb/s serial transceivers on the newly introduced
    Virtex II Pro-X chips

-   Nader Badr, Engineer Northern Microdesign with experience in
    high-speed chip to chip communications and protection circuits

-   Gary Sleege, Engineer Iowa State University who has worked on
    previous PHENIX Level-1 trigger projects, including the MuID LL1

-   John Lajoie, Craig Ogilvie at Iowa State University

A Phase II STTR has since been awarded to this group for FY06/07 to
continue the Phase-I development and produce a hardware prototype.

During the Phase I project displaced vertex calculations were
successfully run on an FPGA using simulated events into one FVTX arm
with the simulated event preloaded into memory. The goals of Phase I
were to

-   Develop a starting algorithm for displaced vertices

-   Test if the calculation is feasible for central Au+Au, i.e. to
    calculate DCAs for all tracks within the maximum PHENIX Level-1 of
    4μs.

Single and multiple-track events were simulated using standard PHENIX
packages of GEANT for zero magnetic field. This case was chosen as the
simplest starting algorithm to set the overall scale for the size and
timing of the tracking algorithm. Extension of the Phase-1 algorithms to
nonzero magnetic fields is being developed in Phase II.

Within the FPGA we implemented a pipelined four stage algorithm that
consisted of (see Figure 106):

1.  Hit sorting and preparation

2.  Straight-line finding

    a.  Hits in station 0 paired with max/min collision point

    b.  Searched for hits in station 1 within tolerance

    c.  Line between station-0 and station-1 hits

    d.  Searched for hits in 2, 3 within tolerance

3.  Collision vertex from found lines

4.  DCA from collision vertex calculated for each track

The timing for this algorithm was established for single- and
multiple-track events then scaled to the full central Au+Au event. The
test was done for a single Xilinx XC2VPX70 FPGA, but the scaling for a
full central Au+Au event assumes eight XC4VLX200 FPGAs on a board (or
equivalent logic in a smaller number of units, such as the Virtex-4).
Such a prototype board is the major goal of the Phase-II STTR grant. The
timing for the algorithm is shown in Table 14.

+-----------------------------------+-----------------------------------+
| > Task                            | > Time (ns)                       |
|                                   | >                                 |
|                                   | > Central Au+Au                   |
+-----------------------------------+-----------------------------------+
| > Hit Format converter            | > 30                              |
+-----------------------------------+-----------------------------------+
| > Hit Sorter                      | > 30                              |
+-----------------------------------+-----------------------------------+
| > Line-finder                     | > 960\*                           |
+-----------------------------------+-----------------------------------+
| > Collision Vertex                | > 70                              |
+-----------------------------------+-----------------------------------+
| > Secondary Tracks                | > 120                             |
+-----------------------------------+-----------------------------------+
| > Total                           | > 1210                            |
+-----------------------------------+-----------------------------------+

[]{#__RefHeading___Toc170092695 .anchor}Table 14 - Time budget for the
STTR Phase-I FVTX algorithm as described in the text. Notes that the
time required for the line finding algorithm could be reduced with added
parallelization.

Since the time required to calculate track DCA's is less than the
maximum PHENIX Level-1 latency of 4 μs, it seems that an FVTX
displaced-vertex trigger is feasible for Au+Au collisions.

![](media/image142.png){width="4.813194444444444in"
height="5.611805555555556in"}

[]{#__RefHeading___Toc170092680 .anchor}Figure 106 - Block diagram of
the FVTX LL1 trigger algorithm, as implemented by Northern Microdesign
for STTR Phase-1 feasibility testing.

The major goal of the Phase-II STTR is to produce a prototype board that
could be used with the prototype FVTX being installed in PHENIX using
LANL's LDRD grant. The result of this development should be a
well-developed design for the trigger hardware required for the full
FVTX LL1.

## FVTX LL1 Cost Estimate 

The full FVTX detector consists of 48 wedges per station, four stations
per arm, with 5632 channels per wedge. We plan to develop a Level-1
trigger board that can service eight wedges over four stations, or a
total of 5632 x 8 x 4 = 180k channels.

Each wedge will send a single fiber to the trigger board, for a total of
32 fibers per trigger board. For a AuAu event, assuming 1.5% occupancy
and 24 bits per hit channel yields 8.3kB per event input to the trigger
tile, or 0.259kB per fiber. This can be easily accommodated in a modern
7.5Gbit/s serial link (the Xilinx Virtex-4 FPGA's incorporate
transceivers capable of speeds up to 10Gbit/s).

+--------------------------------------------------+-------------------+
| **Item Description**                             | **Est. Cost**     |
+--------------------------------------------------+-------------------+
| **Trigger Tile Boards:**                         | **\$510k**        |
|                                                  |                   |
| **(assumes 12 boards + 3 spares)**               |                   |
+--------------------------------------------------+-------------------+
| Cost Breakdown per board:                        |                   |
+--------------------------------------------------+-------------------+
| Board Manufacture                                | \$3k              |
+--------------------------------------------------+-------------------+
| Assembly                                         | \$2k              |
+--------------------------------------------------+-------------------+
| Interface, Monitoring and Control Logic          | \$5k              |
|                                                  |                   |
| (Ethernet interface)                             |                   |
+--------------------------------------------------+-------------------+
| Xilinx Virtex-4 FPGA's                           | \$20k             |
|                                                  |                   |
| (four per board @ \$5K per FPGA)                 |                   |
+--------------------------------------------------+-------------------+
| Fiber Transceivers                               | \$4k              |
+--------------------------------------------------+-------------------+
| Total Cost Per-Board:                            | \$34k             |
+--------------------------------------------------+-------------------+
|                                                  |                   |
+--------------------------------------------------+-------------------+
| **Combined Trigger Processor:**                  | **\$25k**         |
|                                                  |                   |
| **(assumes 1+1 spare)**                          |                   |
+--------------------------------------------------+-------------------+
|                                                  |                   |
+--------------------------------------------------+-------------------+
| **Engineering Design:**                          | **\$60K**         |
+--------------------------------------------------+-------------------+
| Production Board Design                          | \$20k             |
+--------------------------------------------------+-------------------+
| Systems Integration Support                      | \$20k             |
+--------------------------------------------------+-------------------+
| Backplane Design                                 | \$10K             |
+--------------------------------------------------+-------------------+
| Combined Trigger Processor FPGA Design           | \$10K             |
+--------------------------------------------------+-------------------+
|                                                  |                   |
+--------------------------------------------------+-------------------+
| **Crates, Power Supplies and Controllers**       | **\$25k**         |
+--------------------------------------------------+-------------------+
|                                                  |                   |
+--------------------------------------------------+-------------------+
| **Estimated Total System Cost:**                 | **\$620k**        |
+--------------------------------------------------+-------------------+

[]{#__RefHeading___Toc170092696 .anchor}Table 15 - Cost estimate
breakdown for the FVTX LL1 trigger. The estimate is based on the
conceptual design as outlined in the proposal and assumes that the
prototype board design is completed as part of the Northern Microdesign
Phase-II STTR. The Combined Trigger Processor is assumed to be a GenLL1
Rev2 board, as used in the Muon RPC trigger, so the costs shown are for
materials and additional programming.

A breakdown of the estimated cost of a full FVTX LL1 system, consisting
of 12 FVTX LL1 trigger boards with two spares and all required
infrastructure, is shown in Table 15. This cost estimate assumes the use
of Xilinx Virtex-4 FPGA's based on current prices; however, we emphasize
that no final technology choice has been made. We also assume that we
will be able to use the existing design of the GenLL1 Rev2 boards to
implement the Combined Trigger Processor, so that new hardware for this
purpose does not need to be developed. The costs listed in Table 1 are
based on price quotations for the FPGA's as well as our previous
experience in designing trigger hardware.

The cost estimate presented in Table 15 should be viewed as setting that
expected scale of the cost of the Level-1 trigger project. Additional
refinement will be possible once continued development has refined
trigger algorithms that can achieve the required rejections.

Note that the cost listed in Table 15 is not included in the baseline
FVTX budget. It is assumed that once the FVTX project is approved we
will pursue additional independent funding for this FVTX trigger. We
also view the triggering problem as an issue to spans multiple forward
PHENIX subsystems that should be addressed in a global way.

#  {#section-2 .unnumbered}

#  {#section-3 .unnumbered}

# Appendix C -- Estimates for Rates and Triggers for the PHENIX FVTX

## Cross sections, branching ratios and acceptances:

### D → mu X

We take the PHENIX result from hep-ex-/0508034,

$$\sigma_{c\overline{c}} = \text{920} \pm \text{150} \pm \text{540}\mu b$$

which gives a single-charm cross section of 1840 μb.

We get the branching ratio to a muon from the PDB and use the average of
the charged and neutral D branching ratios (since the number of charged
and neutral D's is about equal),

$D^{+} \rightarrow l + X$ is 17.2%.

$D^{0} \rightarrow \mu + X$ is 6.6%,

and use 11.9%

For the acceptance we use a Pythia simulation which gives 2.32% (after
taking out the branching ratio) for muons with theta 10-35 degrees and a
total momentum greater than 2.5 GeV. An additional factor of 0.84 is
included on top of the Pythia acceptance to account for octant boundary
gaps, etc.

3826/1000000 muons pass the 10-35 degree and p\>2.5 GeV cuts, so,

Acc = 3826/1000000/11.9%\*84% = 2.32%

Pythia version 6.205 is used with CTEQ5L, M~charm~ = 1.25 GeV and K=1.

To estimate the p~T~ dependence of the yields we use the p~T~ shape of
the spectra from the above simulations, given as follows as fractional
yield in each bin:

  ----------- ------------ ------------ ------------ ------------ ------------
  All         0\<p~T~\<1   1\<p~T~\<2   2\<p~T~\<3   3\<p~T~\<4   4\<p~T~\<5

  1.00        0.68         0.31         0.012        0.00073      0.000147
  ----------- ------------ ------------ ------------ ------------ ------------

### B → mu X

We take the $b\overline{b}$ cross section from Ramona Vogt's FONNL
calculations as shown in her RHIC-II workshop talk (April 2005),

$$\sigma_{b\overline{b}} = 2\mu b$$

(Her calculations, see below, varied between 1.25 and 2.7 μb for
different parameters)

![](media/image143.wmf){width="5.996527777777778in"
height="3.640972222222222in"}

[]{#__RefHeading___Toc170092681 .anchor}Figure 107 - Cross section
calculations for bottom with FONNL for various parameters from Ramona
Vogt.

Which gives a single-bottom cross section of 4 μb.

For the branching ratio we take 10.87% from the PDB for an admixture of
B^+^/B^0^.

For the acceptance we use 14.5% from a Pythia simulation that requires
the muon be within theta 10-35 degrees and with a total momentum above
2.5 GeV. An additional factor of 0.84 is included on top of the Pythia
acceptance to account for octant boundary gaps, etc.

1880/100000 muons pass the 10-35 degree and p\>2.5 GeV cuts

Acc = 1880/100000/10.87%\*84% = 14.5%

  --------- ------------ ------------ ------------ ------------ ---------- ------------
  All       0\<p~T~\<1   1\<p~T~\<2   2\<p~T~\<3   3\<p~T~\<4   4\<pT\<5   5\<p~T~\<6

  1.00      0.131        0.572        0.234        0.0496       0.0103     0.00258
  --------- ------------ ------------ ------------ ------------ ---------- ------------

### B → J/ψ X

We use the 4 μb cross section for B given above.

For the combined branching ratio we use 1.094% (B → J/ψX) and 5.9% (J/ψ
→ μμ) which gives 0.065%

For the acceptance we use 4.6% from a Pythia simulation that requires
both muons to lie within theta 10-35 degrees and have a total momentum
above 2.5 GeV. An additional factor of 0.70 for a pair is included on
top of the Pythia acceptance to account for octant boundary gaps, etc.

(42/1000000)/(1.094%\*5.9%)\*0.7 = 4.6%

A Z~vtx~\>1 mm vertex cut is made with an efficiency for B → J/ψX of
39%.

## Luminosities

We use the RHIC-II luminosities from T. Roser as given at,

[[]{#OLE_LINK20
.anchor}http://www.phenix.bnl.gov/phenix/WWW/publish/leitch/rhicii-forward/RHIC_II_Luminosity_Roser.xls](http://www.phenix.bnl.gov/phenix/WWW/publish/leitch/rhicii-forward/RHIC_II_Luminosity_Roser.xls)

Table 16 - Luminosity estimates for RHIC-II from Thomas Roser.

  ------------------ ------------- --------- --------- ------------- ----------- ----------- ---------- ---------- ----------- ------------- -----------
  W. Fischer, T.                                                                                                                             
  Roser, I. Ben-Zvi,                                                                                                                         
  A. Fedotov, BNL                                                                                                                            
  C-AD, 16-Mar-2005                                                                                                                          

                                                                                                                                             

  Classical proton   1.53E-18                                                                                                                
  radius \[m\]                                                                                                                               

                                                                                                                                             

  **Maximum                                                                                                                                  
  Luminosity                                                                                                                                 
  Estimates for RHIC                                                                                                                         
  II**                                                                                                                                       

  **Beams**          **unit**      **p**     **p**     **unit**      **Si**      **Cu**      **d**      **p**      **Au**      **unit**      **Au**

  Charge number Z    ...           1         1         ...           14          29          1          1          79          ...           79

  Mass number A      ...           1         1         ...           28          63          2          1          197         ...           197

  Relativistic γ     ...           108       271       ...           108         108         107        108        107         ...           107

  Revolution         kHz           78.2      78.2      kHz           78.2        78.2        78.2       78         78.2        kHz           78.2
  frequency                                                                                                                                  

  Normalised         mm mrad       12        12        mm mrad       12          12          12         12         12          mm mrad       10
  emittance, 95%,                                                                                                                            
  min                                                                                                                                        

  Ions/bunch,        10^9^         200       200       10^9^         10.7        5.2         150        200        1.0         10^9^         1.0
  initial                                                                                                                                    

  Charges per bunch  10^9^e        200       200       10^9^e        150         150         150        200        80          10^9^e        80

  No of bunches      ...           110       110       ...           110         110         110        110        110         ...           110

  Average beam       mA            275       275       mA            206         206         206        275        110         mA            110
  current/ring                                                                                                                               

  **Luminosity at    **unit**      **p-p**   **p-p**   **unit**      **Si-Si**   **Cu-Cu**   **d-Au**   **p-Au**   **Au+Au**   **unit**      **Au+Au**
  one IP**                                                                                                                                   

  Beam-beam          ...           0.0123    0.0123    ...           0.0046      0.0043      0.0024     0.0048                 ...           0.0024
  parameter per IP                                                                                                                           

                                                                                             0.0036     0.0048                                

  β∗                 m             1.0       0.5       m             1.0         1.0         2.0        2.0                    m             0.5

  Peak luminosity    10^30^        150       750       10^28^        42          10          28         37                     10^26^        90
                     cm^-2^s^-1^                       cm^-2^s^-1^                                                             cm^-2^s^-1^   

  Peak / average     ...           1.5       1.5       ...           1.3         1.3         1.5        1.5                    ...           1.3
  luminosity                                                                                                                                 

  Average store      10^30^        100       500       10^28^        32          8           19         25                     10^26^        70
  luminosity         cm^-2^s^-1^                       cm^-2^s^-1^                                                             cm^-2^s^-1^   

  Time in store      \%            55        55        \%            55          55          55         55                     \%            60

  Luminosity/week    pb^-1^        33        166       nb^-1^        108         25          62         83                     nb^-1^        2.5

  Luminosity/week,   pb^-1^        0.9                 nb^-1^                    2.4         4.5                               nb^-1^        0.16
  achieved                                                                                                                                   
  ------------------ ------------- --------- --------- ------------- ----------- ----------- ---------- ---------- ----------- ------------- -----------

and to get an estimate of RHIC-I luminosities we scaled these down
according the ratios for average store luminosity given also by T. Roser
in a RHIC-II talk,

pp: 1.5x10^32^ / 5x10^32^ = 0.3

AuAu: 8x10^26^ / 70x10^26^ = 0.114

For dAu we take the RHIC-I luminosity from the PHENIX Run6 BUP for dAu
in Run7 of 2.8 nb^-1^/wk.

These luminosities per week are:

[]{#__RefHeading___Toc170092698 .anchor}Table 17 - Summary of
luminosities used in these rate calculations for RHIC-II and RHIC-I
(2008).

  ------------------ --------------------------- -------------------------
  **collision**      **RHIC-II**                 **RHIC-I (2008)**

  **Pp**             33 pb^-1^/wk                9.9 pb^-1^/wk

  **dAu**            62 nb^-1^/wk                2.8 nb^-1^/wk

  **AuAu**           2.5 nb^-1^/wk               0.327 nb^-1^/wk
  ------------------ --------------------------- -------------------------

## Reality factors

We use the following reality factors for pp:

-   55% for \|Zvtx\| \< 10 cm

-   60% PHENIX duty factor

-   79% for the min-bias part of the pp trigger

-   90% trigger efficiency

-   90% reconstruction efficiency

For AuAu we use the same factors except:

-   90% for min-bias part of the AuAu trigger

-   70% reconstruction efficiency

##   {#section-4 .unnumbered}

## Summary of Changes from Old Numbers

Changes from older estimates include:

-   Explicit calculation of the B → μ X acceptance which is much larger
    than the D → μ X given the higher momentum muons from the B.

-   Use FONNL calculations of the B cross section.

-   Use the PHENIX measured D cross section.

-   Update the branching ratios from the latest online Particle Data
    Book (PDB).

-   Adding various efficiency and reality factors.

-   Using the \'Roser luminosities

-   Lowering the single-muon momentum threshold to 2.6 GeV from 2.5 GeV.

[]{#__RefHeading___Toc170092699 .anchor}Table 18 - Comparison of new and
old values for various parameters used in these rate calculations.

  ------------ ------- -------- -------- ---------- ------------ ------------
               D → μ X          B → μ X             B → J/ψ X →  
                                                    μ μ X        

               new     old      New      old        New          old

  σ(pair)      920 μb  325 μb   2 μb     0.73 μb    2 μb         0.73 μb

  BR           11.9%   9.6%     10.87%   10.49%     1.094% •     1.2% • 5.9%
                                                    5.9%         

  Acc(1-arm)   2.32%   4.7%     14.5%    2.08%      4.6%         2.83%

  eff          84%     1        84%      1          70%          1

  p~T~\> (Gev) 2.5     2.6      2.5      2.6        2.5          2.6

  eff~vtx~     1       n/c      1        n/c        39%          n/c
  ------------ ------- -------- -------- ---------- ------------ ------------

## Rates

  ------- ------- -------- --------- -------- -------- -------- --------- ------- --------
  pp      Ccbar                                                                   

                                                                                  

          (μb)    Acc      BR        Type     (pb-1)   Counts   Reality   Dzvtx   dzvtx

  Dμ     920     0.0232   0.119     RHICII   33       3.4E08   7.1E07    1       7.1E07

          920     0.0232   0.119     2008     9.9      1.0E08   2.1E07    1       2.1E07

  Bμ     2       0.145    0.1087    RHICII   33       4.2E06   8.8E05    1       8.8E05

          2       0.145    0.1087    2008     9.9      1.2E06   2.6E05    1       2.6E05

  Bj/ψ   2       0.046    0.00065   RHICII   33       7.9E03   1.7E03    0.39    6.5E02

          2       0.046    0.00065   2008     9.9      2.4E03   5.0E02    0/39    2.0E02
  ------- ------- -------- --------- -------- -------- -------- --------- ------- --------

[]{#__RefHeading___Toc170092700 .anchor}Table 19 Estimated rates per
week for p+p collisions

  --------- ---------------------------- ---------------------------- ---------------------------- ---------------------------- ---------------------------- ----------------------------
  **pp**    **[0\<pT\<1]{.underline}**   **[1\<pT\<2]{.underline}**   **[2\<pT\<3]{.underline}**   **[3\<pT\<4]{.underline}**   **[4\<pT\<5]{.underline}**   **[6\<pT\<6]{.underline}**

  D -\> mu  4.8E+07                      2.2E+07                      8.5E+05                      5.2E+04                      1.0E+04                      \-\--

            1.4E+07                      6.6E+06                      2.5E+05                      1.6E+04                      3.1E+03                      \-\--

  B -\> mu  1.2E+05                      5.0E+05                      2.1E+05                      4.4E+04                      9.1E+03                      2.3E+03

            3.5E+04                      1.5E+05                      6.2E+04                      1.3E+04                      2.7E+03                      6.8E+02
  --------- ---------------------------- ---------------------------- ---------------------------- ---------------------------- ---------------------------- ----------------------------

[]{#__RefHeading___Toc170092701 .anchor}Table 20 -- p+p rates vs p~T~
for same estimates as in Table 19.

  --------------------------- ------------------------ ----------------------- ---------------------- ------------------------ -------------------------- -------------------------- --------------------------- ------------------------- -------------------------
  **dAu**                     **ccbar**                                                                                                                                                                                                    

                              **Sigma**                **1-arm**                                      **Lumi**                 **Lumi**                                              **with**                    **eff**                   **with**

  **[process]{.underline}**   **[(ub)]{.underline}**   **[Acc]{.underline}**   **[BR]{.underline}**   **[type]{.underline}**   **[(nb-1)]{.underline}**   **[counts]{.underline}**   **[reality]{.underline}**   **[dzvtx]{.underline}**   **[dzvtx]{.underline}**

  D → μ                       920                      0.0232                  0.119                  RHIC-II                  62                         2.5E+08                    6.0E+07                     1                         6.0E+07

                              920                      0.0232                  0.119                  2008                     2.8                        1.1E+07                    2.7E+06                     1                         2.7E+06

  B→ μ                        2                        0.145                   0.1087                 RHIC-II                  62                         3.1E+06                    7.4E+05                     1                         7.4E+05

                              2                        0.145                   0.1087                 2008                     2.8                        1.4E+05                    3.3E+04                     1                         3.3E+04

  B → J/ψ                     2                        0.046                   0.0007                 RHIC-II                  62                         5.8E+03                    1.4E+03                     0.39                      5.5E+02

                              2                        0.046                   0.0007                 2008                     2.8                        2.6E+02                    6.3E+01                     0.39                      2.5E+01
  --------------------------- ------------------------ ----------------------- ---------------------- ------------------------ -------------------------- -------------------------- --------------------------- ------------------------- -------------------------

[]{#__RefHeading___Toc170092702 .anchor}Table 21 Estimated rates per
week for d+Au collisions.

  ---------- ---------- ---------- ---------- ---------- ---------- ----------
  dAu        0\<pT\<1   1\<pt\<2   2\<pt\<3   3\<pt\<4   4\<pt\<5   5\<pt\<6

  D → μ      4.1E07     1.9E07     7.2E05     4.4E04     8.8E03     

             1.8E06     8.4E05     3.2E04     2.0E03     4.0E02     

  B→ μ       9.7E04     4.2E05     1.7E05     3.7E04     7.6E03     1.9E03

             4.4E03     1.9E04     7.8E03     1.7E03     3.4E02     8.6E01
  ---------- ---------- ---------- ---------- ---------- ---------- ----------

[]{#__RefHeading___Toc170092703 .anchor}Table 22 d+Au rates vs p~T~ for
same estimates as inTable 21.

  --------- ------- -------- --------- -------- -------- -------- --------- ------- --------
  AuAu                                                                              

            Sigma   1-arm              Lumi     Lumi              With      Eff     With

  Process   (ub)    Acc      BR        Type     (nb-1)   Counts   Reality   Dzvtx   Dzvtx

  D → μ     920     0.0232   0.119     RHICII   2.5      9.9E08   1.8E08    1       1.8E08

            920     0.0232   0.119     2008     0.327    1.3E08   2.4E07    1       2.4E07

  B→ μ      2       0.145    0.1087    RHICII   2.5      1.2E07   2.3E06    1       2.3E06

            2       0.145    0.1087    2008     0.327    1.6E06   3.0E05    1       3.0E05

  B → J/ψ   2       0.046    0.00065   RHICII   2.5      2.3E04   4.3E03    0.39    1.7E03

            2       0.046    0.00065   2008     0.327    3.0E03   5.7E02    0.39    2.2E02
  --------- ------- -------- --------- -------- -------- -------- --------- ------- --------

[]{#__RefHeading___Toc170092704 .anchor}Table 23 Estimated rates per
week for Au+Au collisions.

  ---------- ---------------------------- ---------------------------- ---------------------------- ---------------------------- ---------------------------- ----------------------------
  **AuAu**   **[0\<pT\<1]{.underline}**   **[1\<pT\<2]{.underline}**   **[2\<pT\<3]{.underline}**   **[3\<pT\<4]{.underline}**   **[4\<pT\<5]{.underline}**   **[6\<pT\<6]{.underline}**

  D → μ      2.2E+07                      1.0E+07                      3.9E+05                      2.4E+04                      4.8E+03                      

             1.6E+07                      7.5E+06                      2.9E+05                      1.8E+04                      3.5E+03                      

  B → μ      3.0E+05                      1.3E+06                      5.4E+05                      1.1E+05                      2.4E+04                      5.9E+03

             3.9E+04                      1.7E+05                      7.0E+04                      1.5E+04                      3.1E+03                      7.7E+02
  ---------- ---------------------------- ---------------------------- ---------------------------- ---------------------------- ---------------------------- ----------------------------

[]{#__RefHeading___Toc170092705 .anchor}Table 24 Au+Au rates vs p~T~ for
same estimates as in Table 23.

## Rates for Prompt Vector Mesons: J/ψ, ψ' and ϒ

Although the rates for the prompt vector mesons, J/ψ, ψ' and ϒ, have
been estimated elsewhere (e.g. in Tony Frawley's RHIC-II studies[^49]);
we give estimates here that are consistent with the single heavy-quark
rates estimates above. The following inputs are used and the rates for
one RHIC-II week are shown in Table 25.

-   For the cross sections we use the recently published J/ψ cross
    section of 2.61 μb from PHENIX\]. For the ψ' we use the cross
    section ratio of 14% to the J/ψ from Ref. [^50]; and for the ϒ we
    use the preliminary estimate from PHENIX at QM05 of 2.1 nb.

-   We take the Branching ratios from the particle data book as 5.9%
    (J/ψ), 0.76% (ψ') and 2.1% (ϒ); where the latter is an average over
    the three Upsilon states as calculated in PHENIX Analysis Note
    AN401.

-   For the acceptance we use values from recent PHENIX analysis: 1.08%
    (J/ψ) and 1.19% (ϒ). And we assume the ψ' acceptance is the same as
    that for the J/ψ.

[]{#__RefHeading___Toc170092706 .anchor}Table 25 - Counts for prompt
vector mesons per week into both muon arms at RHIC-II luminosity.

<table style="width:100%;">
<colgroup>
<col style="width: 1%" />
<col style="width: 11%" />
<col style="width: 5%" />
<col style="width: 9%" />
<col style="width: 13%" />
<col style="width: 10%" />
<col style="width: 6%" />
<col style="width: 18%" />
<col style="width: 3%" />
<col style="width: 17%" />
<col style="width: 3%" />
</colgroup>
<tbody>
<tr class="odd">
<td></td>
<td colspan="2"><strong>Signal</strong></td>
<td colspan="2"><strong>Luminosity/week</strong></td>
<td colspan="2"><strong>J/ψ → μμ</strong></td>
<td><strong>ψ’→ μμ</strong></td>
<td colspan="2"><strong>ϒ → μμ</strong></td>
<td></td>
</tr>
<tr class="even">
<td></td>
<td colspan="2">Au+Au</td>
<td colspan="2">2.5 nb<sup>-1</sup></td>
<td colspan="2">60k</td>
<td>1.1k</td>
<td colspan="2">200</td>
<td></td>
</tr>
<tr class="odd">
<td></td>
<td colspan="2">d+Au</td>
<td colspan="2">62 nb<sup>-1</sup></td>
<td colspan="2">20k</td>
<td>360</td>
<td colspan="2">65</td>
<td></td>
</tr>
<tr class="even">
<td></td>
<td colspan="2">p+p</td>
<td colspan="2">33 nb<sup>-1</sup></td>
<td colspan="2">23k</td>
<td>420</td>
<td colspan="2">77</td>
<td></td>
</tr>
<tr class="odd">
<td colspan="2"></td>
<td colspan="2"><p>Although not shown in the table, the rates for ϒ’s at
y=0 from detecting their decay into one muon in each of the two muon
arms is approximately equal to the rate into one muon arm shown in Table
25.</p>
<h2 id="trigger-considerations">Trigger considerations</h2>
<h3 id="rejection-factors">Rejection factors</h3>
<p>For pp triggers we use Lajoie’s estimate from run5 data and
simulations oof 478 (1-deep), 23500 (1-deep &amp; 1-shallow) and 133500
(2-deep). An independent check of these numbers was done by looking at
the run5 pp triggers for several runs (179809, 170190, 174696, 177185)
where one sees about a factor of 500 rejection for 1-deep muons (south
arm) and 10<sup>4</sup> rejection for 1d1s dimuons (south arm).</p>
<p>For AuAu we use simulations of the level-1 run on 2004 AuAu raw data
files (since the level-1 hardware was not working fully during that run
yet). Lajoie gets rejection factors of 5 for 1-deep and 1-deep *
1-shallow triggers and 15.7 for 2-deep triggers.</p>
<p>As shown in Table 26, we will then use the averages over the two
arms, with the North arm generally being somewhat worse than the South
due to its coverage at smaller angles with its smaller piston.</p>
<p><span id="__RefHeading___Toc170092707" class="anchor"></span>Table 26
- Level-1 muon trigger rejection factors for pp and AuAu based on
previous data and simulations of the level -1 triggers.</p>
<p><strong>Species</strong></p></td>
<td colspan="2"><strong>Arm</strong></td>
<td colspan="3"><strong>Source</strong></td>
<td colspan="2"><strong>Trigger</strong></td>
</tr>
<tr class="even">
<td colspan="2"><strong>Reject. factorpp</strong></td>
<td colspan="2">N</td>
<td colspan="2">Run5</td>
<td colspan="3">1-deep</td>
<td colspan="2">580</td>
</tr>
<tr class="odd">
<td colspan="2"></td>
<td colspan="2"></td>
<td colspan="2">“</td>
<td colspan="3">1-deep &amp; 1-shallow</td>
<td colspan="2">28700</td>
</tr>
<tr class="even">
<td colspan="2"></td>
<td colspan="2"></td>
<td colspan="2">“</td>
<td colspan="3">2-deep</td>
<td colspan="2">20000</td>
</tr>
<tr class="odd">
<td colspan="2"></td>
<td colspan="2">S</td>
<td colspan="2">“</td>
<td colspan="3">1-deep</td>
<td colspan="2">376</td>
</tr>
<tr class="even">
<td colspan="2"></td>
<td colspan="2"></td>
<td colspan="2">“</td>
<td colspan="3">1-deep &amp; 1-shallow</td>
<td colspan="2">18300</td>
</tr>
<tr class="odd">
<td colspan="2"></td>
<td colspan="2"></td>
<td colspan="2">“</td>
<td colspan="3">2-deep</td>
<td colspan="2">67000</td>
</tr>
<tr class="even">
<td colspan="2"></td>
<td colspan="2">N&amp;S avg</td>
<td colspan="2">“</td>
<td colspan="3">1-deep</td>
<td colspan="2">478</td>
</tr>
<tr class="odd">
<td colspan="2"></td>
<td colspan="2"></td>
<td colspan="2">“</td>
<td colspan="3">1-deep &amp; 1-shallow</td>
<td colspan="2">23500</td>
</tr>
<tr class="even">
<td colspan="2"></td>
<td colspan="2"></td>
<td colspan="2">“</td>
<td colspan="3">2-deep</td>
<td colspan="2">133500</td>
</tr>
<tr class="odd">
<td colspan="2"><strong>AuAu</strong></td>
<td colspan="2">N</td>
<td colspan="2">Sim on run4 prdf</td>
<td colspan="3">1-deep</td>
<td colspan="2">5.1</td>
</tr>
<tr class="even">
<td colspan="2"></td>
<td colspan="2"></td>
<td colspan="2">“</td>
<td colspan="3">1-deep &amp; 1-shallow</td>
<td colspan="2">5.3</td>
</tr>
<tr class="odd">
<td colspan="2"></td>
<td colspan="2"></td>
<td colspan="2">“</td>
<td colspan="3">2-deep</td>
<td colspan="2">15.3</td>
</tr>
<tr class="even">
<td colspan="2"></td>
<td colspan="2">S</td>
<td colspan="2">“</td>
<td colspan="3">1-deep</td>
<td colspan="2">4.8</td>
</tr>
<tr class="odd">
<td colspan="2"></td>
<td colspan="2"></td>
<td colspan="2">“</td>
<td colspan="3">1-deep &amp; 1-shallow</td>
<td colspan="2">5.3</td>
</tr>
<tr class="even">
<td colspan="2"></td>
<td colspan="2"></td>
<td colspan="2">“</td>
<td colspan="3">2-deep</td>
<td colspan="2">16.1</td>
</tr>
<tr class="odd">
<td colspan="2"></td>
<td colspan="2">N&amp;S avg</td>
<td colspan="2">“</td>
<td colspan="3">1-deep</td>
<td colspan="2">5</td>
</tr>
<tr class="even">
<td colspan="2"></td>
<td colspan="2"></td>
<td colspan="2">“</td>
<td colspan="3">1-deep &amp; 1-shallow</td>
<td colspan="2">5</td>
</tr>
<tr class="odd">
<td colspan="2"></td>
<td colspan="2"></td>
<td colspan="2">“</td>
<td colspan="3">2-deep</td>
<td colspan="2">15.7</td>
</tr>
</tbody>
</table>

### Trigger Rates and Needed Rejection Factors

For these estimates we will use a 2-deep (2d) dimuon trigger in AuAu and
a 1-deep & 1-shallow (1d1s) trigger in pp.

We use the luminosities quoted above in the discussion of FVTX rates. To
calculate the peak luminosity from the average, we will follow Tony's
example again and use a factor of 4.48 from the average instantaneous
luminosity.

Min-bias rates are calculated from luminosities using the full inelastic
cross sections for pp and AuAu of 42 mb and 6847 mb respectively. This
assumes that the FVTX itself can provide a min-bias trigger that is very
close to 100% of the inelastic cross section. In any case this is an
upper limit on the min-bias trigger rate.

We use event sizes of 180 kb and 250 kb for pp and AuAu respectively.
These sizes will need to be updated as the additional contributions from
the various PHENIX upgrades become clear.

Additional trigger rejections needed from the FVTX (or from combination
with other upgrades such as the muon RPC trigger upgrade) will be
calculated assuming a 60 Mb/s limit for each muon trigger, which
corresponds to 10% of an assumed DAQ limit of 600 Mb/s. I.e. if one uses
½ of the 600 Mb/s for min-bias, and the remaining 300 Mb/s is split
between 5 types of triggers, then that leaves 60 Mb/s per trigger (sum
over the two arms).

[]{#__RefHeading___Toc170092708 .anchor}Table 27 -- Estimated trigger
rates and addition rejection factors needed for p+p and Au+Au collisions
in PHENIX.

  ------ ----------------------- ------- -------------------------- ------ -------------------------- ------- -------------------------- ------ ----------------------- ----- ------ ------------------------ ------------------------- ----- ------------------------ ---- -------------------------- ------ ------------------------ ----- ------------------------ ----- -------------------------- ----
                                                                                                                                                **MB**                               **evt**                  **1d**                                                        **1d**                            **1d1s**                                                      **1d1s**                   

                                         ***L*/wk**                        **Zvtx**                           ***L* pk**                        **pk rate**                          **size**                 **pk rate**                     **1d**                        **presc.**                        **pk**                         **1d1s**                       **presc.**                 

         **[era]{.underline}**           **[(pb-1)]{.underline}**          **[\<10cm]{.underline}**           **[10\^32]{.underline}**          **[Mhz]{.underline}**                **[(kb)]{.underline}**   **[(khz)]{.underline}**         **[Mb/s]{.underline}**        **[needed]{.underline}**          **[(hz)]{.underline}**         **[Mb/s]{.underline}**         **[needed]{.underline}**   

  pp     RHICII                          33                                0.55                               1.34                              5.65                                 180                      23.63                           4253                          71                                481                            87                             1.4                        

         2008                            9.9                               0.55                               0.40                              1.69                                 180                      7.09                            1267                          21                                144                            26                             0.4                        

                                                                                                                                                                                                                                                                                                                                                                                                       

                                                                                                                                                **MB**                               **evt**                  **1d**                                                        **1d**                            **2d**                                                        **2d**                     

                                         ***L*/wk**                        **Zvtx**                           ***L* pk**                        **pk rate**                          **size**                 **pk rate**                     **1d**                        **Presc.**                        **pk rate**                    **2d**                         **presc.**                 

         **[era]{.underline}**           **(nb-1)**                        **[\<10cm]{.underline}**           **[10\^26]{.underline}**          **[khz]{.underline}**                **[(kb)]{.underline}**   **[(khz)]{.underline}**         **[Mb/s]{.underline}**        **[needed]{.underline}**          **[(hz)]{.underline}**         **[Mb/s]{.underline}**         **[needed]{.underline}**   

  AuAu   RHICII                          2.5                               0.55                               101.85                            69.74                                250                      27.9                            6974                          116                               8884                           2221                           37                         

  2008                           0.327                              0.55                              13.32                              9.12                           250   3.65                                                      912                            15                              1162                            291                            4.8                              
  ------ ----------------------- ------- -------------------------- ------ -------------------------- ------- -------------------------- ------ ----------------------- ----- ------ ------------------------ ------------------------- ----- ------------------------ ---- -------------------------- ------ ------------------------ ----- ------------------------ ----- -------------------------- ----

# Appendix D -- Synergy with other PHENIX Upgrades

Although the FVTX detector adds a lot of important physics, as has been
discussed at length in the body of the proposal, it also can work
together with many of the ongoing or other proposed upgrades to
strengthen or add physics capability beyond what any subsystem of PHENIX
brings by itself. Here we will discuss briefly some of these
strengthened or added capabilities. Since integration with the muon
tracker and muon identifier has already been extensively discussed, we
will not repeat that discussion here.

## Central Barrel Vertex Detector (VTX) Upgrade

The most obvious coupling of the upgrades is with the VTX detector,
which provides similar vertexing capability in the central rapidity
region to what this FVTX detector provides. When used together they can
provide a very accurate primary vertex which can then be used by both
detectors as a origination point for determining detached vertices for
the various processes already discussed in this proposal. As shown in
Section 3.3, the FVTX can do this quite well by itself even in p+p
collisions and can do it at the level-1 trigger level for fast triggers;
but the VTX can improve this further. Unfortunately the VTX does not
give a fast output and cannot contribute at the fast trigger level.

Together the two detectors, as has been discussed in the body of this
proposal, give a quite large range in rapidity, -2.2 to +2.2. However at
the boundary between them, some tracks will give hits in both detectors.
This should help with internal alignment between the two vertex
detectors and will also help make a smooth picture of the physics across
the boundary between the VTX and FVTX parts of the vertex detector.

## Muon Trigger Upgrade

The Muon Trigger Upgrade is a NSF funded upgrade with the main goal
being to allow selective triggering on very high momentum (\> 10 GeV)
muons from W decays for measurements of the flavor dependence of spin
structure functions. Three Resistive Plate Cathode strip (RPC) detector
planes will be added to each muon arm with one in just in front of
station-1, one in between station-3 and the front of the muon
identifier, and a third plane behind the muon identifier. The RPC's will
have 1^0^ segmentation in φ (the bend direction in the muon magnet's
field) and up to 24 segments in the radial direction.

<http://www.npl.uiuc.edu/phenix/publish/nsf/muon-mri.pdf>

The coarse momentum resolution of the MuTrig can provide a momentum
measurement (fast enough to be used for a level-1 trigger) that would
help to:

-   Allow momentum dependence vertex cuts in the FVTX or prescaling of
    lower momentum ranges.

-   Help eliminate any tracks that do not point to the primary vertex
    and do not satisfy time-of-flight cuts for tracks originating from
    the primary vertex.

-   Allow track matching at the fast trigger level between roads through
    the MuTrig RPC's and the muon identifier with the FVTX tracks.

-   Help eliminate soft pion tracks in the FVTX that do not match tracks
    above.

-   And also provide a space (x-y) point to help the muon tracker
    pattern recognition in high occupancy events (central Au+Au
    collisions) that will reduce incorrect tracks in the muon tracker.
    This will also benefit the FVTX by providing cleaner muon tracks to
    match with.

## Nose Cone Calorimeter (NCC) Upgrade

The NCC upgrade would turn the present copper nosecone absorbers, that
lie in front of the muon magnets and behind where the FVTX would go,
into an active Silicon-tungsten electromagnetic and partial hadronic
calorimeter for detecting various particles including photons and
neutral pions. This would extend much of the capability of the PHENIX
central arms calorimeters into the forward and backward regions now
covered only for muons. Highlights of the physics this upgrade could add
include direct photons, extending the study of pion suppression to these
rapidities and measurements of the χ~C~ by its decay into a photon and a
photon. The proposal for this upgrade, along with out FVTX proposal, is
now being prepared for submission to DOE for funding, although
contributions from RIKEN may also help fund the total \$7M cost of two
NCC endcaps.

<https://www.phenix.bnl.gov/WWW/publish/seto/NCC/ncccdr.pdf>

A number of physics issues could be addressed with the combination of
the NCC and the FVTX, these include:

-   Identification of hadron jets in the NCC to help reduce backgrounds
    for single muons from punch-through hadrons that penetrate deep into
    the muon identifier and otherwise look like muons. Although the FVTX
    in combination with the muon tracker can eliminate many of these,
    the possibility of reducing punch-throughs further could be quite
    valuable. A detailed study of shower probabilities and
    characteristics in the 1.5 lamba NCC needs to be made in order to
    make a quantified estimate of the level to which the NCC can help
    here.

-   Can aid in the study of associated particle production with hard
    processes such as J/ψ production, especially by adding detection
    capability for neutral particles such as π^0^'s and photons. These
    associated particles, may help understand the production mechanism
    for J/ψ and could also give information on the interaction with
    co-moving light quarks in heavy ion collisions.

-   The combination of the FVTX and NCC in the forward and backward
    rapidity regions would allow detection of charm and bottom decays
    via their decay to electrons with the electron identification coming
    from the NCC and the detached vertex from the FVTX. This would give
    a second measurement of these heavy quarks, in addition to that with
    single muons; and might even allow extending these measurements to
    lower momentum with the electrons compared to the \~2.5 GeV momentum
    threshold for detection via detached vertices with muons.

-   The additional measurements in the NCC might also help in overall
    definition of the muon track in combination with the FVTX mini-strip
    hits, muon tracker cathode-strip hits, muon identifier hits and
    MuTrig RPC hits. (if one NCC plane has smaller pixels, it would help
    most -- need to check NCC proposal about this) It may also be able
    to help identify kinks in tracks that result from decay-in-flight of
    hadrons to muons, and thereby reduce the contributions of these
    decays-in-flight to the final single muon spectra.

-   This matching between FVTX and NCC might also help with low energy
    tracks in the forward direction, by looking for consistency between
    the multiple scattering of the track in the FVTX and the energy
    observed for the matching track in the NCC.

-   Electrons and muons, both with detached vertices, could be combined
    into $D\overline{D} \rightarrow \mu e$pairs which would provide a
    additional wayto study the di-lepton continuum under and near the
    J/ψ peak. Identification of these lepton pairs would also help in
    isolating the Drell-Yan di-leptons which are otherwise over-whelmed
    by copious random pairs from heavy quark decays. This could include
    back-to-back μe pairs where an electron is seen in one endcap and a
    muon in the other.

-   The FVTX can act as a charged particle veto for the NCC, to help
    solidify the identification of neutral particles, e.g. photons and
    π^0^'s.

## Muon Piston Calorimeter (MPC)

The Muon Piston Calorimeter (MPC) is a small electromagnetic calorimeter
composed of an array of PbWO^4^ crystals (240/arm) with photo-diode
readout that is installed inside the muon magnet piston of each muon
arm, and adds detection jets in the 3 to 4 rapidity range, providing
measurements of jets, pions and eta's for the study of spin asymmetries
in the very forward region in p+p collisions and to search for effects
of shadowing or the color glass condensate in that region in d+A
collisions. Like the NCC, it may be useful in sampling particles near
those in the FVTX, e.g. in terms of associated particle production for
instance. But it has no tracking, only calorimetry -- so would likely
not be useful in Au+Au collisions.

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