***PROPOSAL***

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

***for the PHENIX Experiment***

***January 12, 2006***

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

*draft author list - not complete, not confirmed*

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, 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

J.G. Boissevain, M.L. Brooks, S. Butsyk, H.W. van Hecke, J. Kapustinsky,
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, S. Pate, X.R. Wang

New Mexico State University, Las Cruces, NM, USA

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

University of New Mexico, Albuquerque, NM, USA

**Other Interested Institutions:**

Don Geesaman, Roy Holt, Paul Reimer

Argonne National Laboratory, Argonne, IL 60439, USA

O. Drapier, A. Debrain, F. Gastaldi, M. Gonin, R. Cassagnac de Granier,
F. Flueret, A. Karar

LLR, Ecole Polytechnique, Palaiseau, France

A.D. Frawley

Florida State University, Tallahassee, FL 32306, USA

B. Hong

Korea University, Seoul, Korea

N. Saito, M. Togawa, M. Wagner

Kyoto University, Kyoto 606, Japan

J. Gosset, H. Pereira

CEA Saclay, Gif-sur-Yvette, France

J.H. Kang, D.J. Kim

Yonsei University, Seoul, Korea

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

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

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

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

[2.1.2 Open Charm and Beauty Enhancement
11](#open-charm-and-beauty-enhancement)

[2.1.3 J/ Suppression and Comparisons with Open charm, ' and
13](#j-suppression-and-comparisons-with-open-charm-and)

[2.1.4 Reaction Plane and Azimuthal Asymmetries
14](#reaction-plane-and-azimuthal-asymmetries)

[2.2 Proton(Deuteron)+Nucleus Collisions and Nuclear effects on Gluons
in Nuclei
19](#protondeuteronnucleus-collisions-and-nuclear-effects-on-gluons-in-nuclei)

[2.2.1 Shadowing or Gluon Saturation via Heavy-quarks Measurements
19](#shadowing-or-gluon-saturation-via-heavy-quarks-measurements)

[2.2.2 Disentangling the Physics of J/ and Quarkonium Production in
Nuclei
22](#disentangling-the-physics-of-j-and-quarkonium-production-in-nuclei)

[2.2.3 Heavy-quarks: Charm and Beauty Mesons
27](#heavy-quarks-charm-and-beauty-mesons)

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

[2.2.5 Drell-Yan Measurements 32](#drell-yan-measurements)

[2.2.6 Summary of Physics Addressed by the FVTX in d(p)-A Collisions
33](#summary-of-physics-addressed-by-the-fvtx-in-dp-a-collisions)

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

[2.3.1 The Role of the Silicon Vertex Detector
36](#the-role-of-the-silicon-vertex-detector)

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

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

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

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

[3 Simulations and Required Performance for the FVTX Upgrade
51](#simulations-and-required-performance-for-the-fvtx-upgrade)

[3.1 Charm Measurements 54](#charm-measurements)

[3.1.1 Single muons from semi-leptonic D meson decays:
$D \rightarrow \mu X$
54](#single-muons-from-semi-leptonic-d-meson-decays-d-rightarrow-mu-x)

[3.1.2 Muon Pairs from J/ and ' Decays: J/ ^+^, ' ^+-^
57](#muon-pairs-from-j-and-decays-j--)

[3.1.3 Charm Pair Decays to Dimuons and Electron-muon Pairs:
$D\overline{D} \rightarrow \mu^{+}\mu^{-}X$**,**
$D\overline{D} \rightarrow \mu\text{eX}$
59](#charm-pair-decays-to-dimuons-and-electron-muon-pairs-doverlined-rightarrow-mumu-x-doverlined-rightarrow-mutextex)

[3.2 Open Beauty Measurement 59](#open-beauty-measurement)

[3.2.1 B Meson Decays:
$B \rightarrow \frac{J}{\psi} \rightarrow \mu^{+}\mu^{-}$**,**
$B \rightarrow \mu X$
60](#b-meson-decays-b-rightarrow-fracjpsi-rightarrow-mumu--b-rightarrow-mu-x)

[3.2.2 Muon Pairs from Upsilon Decays: ^+-^
61](#muon-pairs-from-upsilon-decays--)

[3.3 Heavy Quark Energy Loss and Flow
63](#heavy-quark-energy-loss-and-flow)

[3.4 Trigger Plans 63](#trigger-plans)

[3.5 Si Endcap Event Rates 63](#si-endcap-event-rates)

[3.6 Matching to Muon Spectrometers 64](#matching-to-muon-spectrometers)

[3.7 Integration with PHENIX 64](#integration-with-phenix)

[4 FVTX Detector system 66](#fvtx-detector-system)

[4.1 Overview 66](#overview)

[4.2 Silicon Readout Chip - PHX 67](#silicon-readout-chip---phx)

[4.3 Silicon Mini-strip Sensors 70](#silicon-mini-strip-sensors)

[4.4 Electronics Transition Module 75](#electronics-transition-module)

[4.5 Mechanical Structure and Cooling
77](#mechanical-structure-and-cooling)

[4.5.1 Design Criteria 78](#design-criteria)

[4.5.2 Structural Support 78](#structural-support)

[4.5.3 The Enclosure and Environmental Envelope
79](#the-enclosure-and-environmental-envelope)

[4.5.4 Endcap Ladder Structure 79](#endcap-ladder-structure)

[4.5.5 Radiation Length 81](#radiation-length)

[4.6 Endcap Analysis Summary 81](#endcap-analysis-summary)

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

[5.1 R+D Areas 81](#rd-areas)

[5.1.1 PHX 82](#phx)

[5.1.2 Sensor 82](#sensor)

[5.1.3 Interface 82](#interface)

[5.2 Schedule 83](#schedule)

[5.2.1 Cost 85](#cost)

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

[6 Appendix A 89](#appendix-a)

[6.1 Contingency Analysis 89](#contingency-analysis)

[Appendix B. Level 1 Trigger 93](#appendix-b.-level-1-trigger)

[Estimate of the Level 1 Trigger Rejection Factor
93](#__RefHeading___Toc124816735)

[Summary of Level 1 Prototype Trigger Hardware
93](#__RefHeading___Toc124816736)

[Estimated Cost of Level I Trigger 93](#__RefHeading___Toc124816737)

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

[6.2 Cross sections, branching ratios and acceptances:
94](#cross-sections-branching-ratios-and-acceptances)

[6.2.1 D μ X 94](#d-μ-x)

[6.2.2 B μ X 95](#b-μ-x)

[6.2.3 B J/ X 96](#b-j-x)

[6.3 Luminosities 96](#luminosities)

[6.4 Reality factors 97](#reality-factors)

[6.5 98](#section-3)

[6.6 Summary of Changes from old numbers
98](#summary-of-changes-from-old-numbers)

[6.7 Rates 98](#rates)

[6.8 Trigger considerations 99](#trigger-considerations)

[6.8.1 Rejection factors 100](#rejection-factors)

[6.8.2 Trigger rates and needed rejection factors
100](#trigger-rates-and-needed-rejection-factors)

**List of Figures**

[Figure 1 - Conceptual layout of the PHENIX FVTX showing the four
lampshade silicon planes of each endcap.
4](#__RefHeading___Toc124816751)

[Figure 2 - Suppression of high-p~T~ hadrons and pions as seen in Au+Au
vs d+Au collisions. 8](#__RefHeading___Toc124816752)

[Figure 3 - Large elliptic flow for light hadrons in Au+Au collisions is
near the hydrodynamic limit. 8](#__RefHeading___Toc124816753)

[Figure 4 - In PHENIX preliminary results shown at QM05, even charm
seems to suffer energy loss at mid-rapidity.
9](#__RefHeading___Toc124816754)

[Figure 5 - Preliminary results for charm from single electrons in
PHENIX and STAR shows flow for small p~T~ and conflicting results from
PHENIX and STAR as to whether the flow returns to zero for larger p~T~.
9](#__RefHeading___Toc124816755)

[Figure 6 - Single electron data of PHENIX compared with two extreme
models of charm p~T~ distribution. 10](#__RefHeading___Toc124816756)

[Figure 7 - Charm enhancement expected at RHIC from ref. 8. 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. 12](#__RefHeading___Toc124816757)

[Figure 8 - 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
13](#__RefHeading___Toc124816758)

[Figure 9 - Mass spectra for the J/ and \', showing the substantial
improvement in separation expected with a vertex detector (yellow, 100
MeV resolution) compared to that without a vertex detector (black, 150
MeV resolution). The number of J/ and ' in this plot represents our
expectation for a \~25 pb^-1^ p+p run. 14](#__RefHeading___Toc124816759)

[Figure 10 - 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. 15](#__RefHeading___Toc124816760)

[Figure 11 - 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 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.
16](#__RefHeading___Toc124816761)

[Figure 12 - 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.
17](#__RefHeading___Toc124816762)

[Figure 13 - 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 reactionplane resolution. The reaction plane resolution of
0.75 estimated in figure 4 would result is a 65 precent confidence level
if binning the reaction plane into 3 bins. Two bins (delta phi = 90
degrees) will give a confidence level of 85 precent for the \'true
reaction plane\' being in the measured bin.
18](#__RefHeading___Toc124816763)

[Figure 14 - 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. 19](#__RefHeading___Toc124816764)

[Figure 15 - 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.
20](#__RefHeading___Toc124816765)

[Figure 16 - Gluon shadowing prediction from Frankfurt and Strikman,
which shows substantially larger gluon shadowing than that of EKS^13^.
21](#__RefHeading___Toc124816766)

[Figure 17 - 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 FGS for different Q values.
22](#__RefHeading___Toc124816767)

[Figure 18 - J/ψ nuclear dependence versus rapidity compared to
theoretical predictions with several types of gluon shadowing^16^.
23](#__RefHeading___Toc124816768)

[Figure 19 - Alpha versus x~2~ and x~F~ from measurements at three
different energies 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)^16^, E866/NuSea (s = 39 GeV) and NA3 (s = 19 GeV).
24](#__RefHeading___Toc124816769)

[Figure 20 - Dimuon mass spectrum in dAu collisions for one muon at
positive and one muon at negative rapidity, showing the large
combinatoric background from random muon pairs (black) that dominates
the μ^+^μ^-^ spectrum (red points with error bars) starting a little
below 5 GeV in mass. The (unobserved) would appear as a peak at 9.46
GeV. 26](#__RefHeading___Toc124816770)

[Figure 21 - The PHENIX 2003 dAu dimuon mass spectrum (top panel) with
the combinatoric background shown in black and the total μ^+^μ^-^ pairs
in red; and (bottom panel) the spectrum with the background subtracted
where a hint of the ψ' peak (at 3.7 GeV) has been fit. The ψ' is not
well determined, due to the statistical uncertainty contributed by the
subtraction and the poor mass resolution (\~170 MeV).
27](#__RefHeading___Toc124816771)

[Figure 22 - Nuclear modification factor in dAu collisions, RdAu, for
prompt muons in the forward and backward rapdity regions versus p~T~.
The prompt muons are primarily from the decays of charm and beauty
mesons although perhaps 10% are from other processes such as light meson
decays. 29](#__RefHeading___Toc124816772)

[Figure 23 - Nuclear modification factor in dAu collisions (RdAu) for
hadrons decaying into muons in the forward (red) and backward (blue)
rapidity directions (PHENIX Preliminary).
31](#__RefHeading___Toc124816773)

[Figure 24 -- Nuclear modification in dAu 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/.
32](#__RefHeading___Toc124816774)

[Figure 25 - Dimuon mass spectrum from E866/NuSea, showing the Drell-Yan
mass region used in their analysis, which excluded masses below 4 GeV.
Lower masses were excluded because of the large backgrounds from open
charm decays (labeled Randoms) in that region.
33](#__RefHeading___Toc124816775)

[Figure 26 - 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 parametrizations of these distributions.
35](#__RefHeading___Toc124816776)

[Figure 27 - 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 \[T. Gehrmann and W. J. Stirling, Z. Phys. C65, 461
(1995)\]. 36](#__RefHeading___Toc124816777)

[Figure 28 - Higher order semi-inclusive DIS is used to explore gluon
distribution. 37](#__RefHeading___Toc124816778)

[Figure 29 - At RHIC-SPIN, quarks and gluons interact directly at
leading order. 38](#__RefHeading___Toc124816779)

[Figure 30 - PHENIX preliminary results (blue points) for prompt single
muons (mostly from open charm decay) measurement from run2 pp data. Two
sources of background are shown. 40](#__RefHeading___Toc124816780)

[Figure 31 -- Expected size of double-spin asymmetries (lines) in the
observation of single muons from open charm and bottom production. The
projected uncertainties (points with error bars) are shown for a few
values of *p*~T~. 41](#__RefHeading___Toc124816781)

[Figure 32 - 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 beauty (red).
42](#__RefHeading___Toc124816782)

[Figure 33 - Partonic origin of charged pions produced within the
acceptance of muon spectrometer in pp collisions at sqrt(s) = 200 GeV.
43](#__RefHeading___Toc124816783)

[Figure 34 - Model calculation of double spin asymmetry for charged
pions within the muon spectrometer acceptance.
43](#__RefHeading___Toc124816784)

[Figure 35 - J/ measurement from run5 pp run. The J/ peak clearly stands
out from the background. The background fraction is about 25% under the
J/ mass peak. 44](#__RefHeading___Toc124816785)

[Figure 36 - The first measurement of double spin asymmetry from
polarized *pp* collisions at RHIC. 44](#__RefHeading___Toc124816786)

[Figure 37 - Expected experimental sensitivities of double spin
asymmetry measurements with prompt J/ (not from *B* decay).
45](#__RefHeading___Toc124816787)

[Figure 38 -- W production and decay to a muon plus a neutrino.
46](#__RefHeading___Toc124816788)

[Figure 39 - Inclusive muon production showing punch-through hadrons in
red. 47](#__RefHeading___Toc124816789)

[Figure 40 - Expected flavor dependent polarized quark distribution
functions measured by the PHENIX muon spectrometers.
48](#__RefHeading___Toc124816790)

[Figure 41 -- Predicted double spin asymmetry for charmonium at RHIC.
The asymmetry value depends on the final state charmonium polarization,
which can be tested experimentally. 49](#__RefHeading___Toc124816791)

[Figure 42 - Principle of operation of the 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. 51](#__RefHeading___Toc124816792)

[Figure 43 - Top panels: Simulated z-vertex resolution (microns) versus
muon momentum (in GeV) and strip width (microns.) For example, with 50
micron strip spacing, a 5 GeV muon provides a z-vertex resolution of
\~200 microns. Bottom panels: The corresponding resolution in terms of
distance of closest approach is about three times smaller. The dca
resolution for the 5 GeV muon is \~ 70 microns.
52](#__RefHeading___Toc124816793)

[Figure 44 - 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.
53](#__RefHeading___Toc124816794)

[Figure 45 - Single muon p~T~ distributions for charm, beauty and
backgrounds from low-mass meson decays, as expected for the 2003 d+Au
run. Note that the light-meson decays are above charm up to near 4
GeV/c. The black curve is for pion and kaon decays, green is charm and
red is beauty. 55](#__RefHeading___Toc124816795)

[Figure 46 - The p~T~ distribution of muons that decay within 1 cm of
the collision vertex. The red histogram is for charm decays while the
black is for pion and kaon decays. 55](#__RefHeading___Toc124816796)

[Figure 47 - The p~T~ distribution of negative prompt muons, decay muons
and punch-through hadrons at pseudorapidity () = -1.65. The
punch-throughs become the dominant background for p~T~ values above 3
GeV. The curves are simulations, while the data are PHENIX measurements.
56](#__RefHeading___Toc124816797)

[Figure 48 - Left panel: Correlation between x~1~ and p~Z~ of muons from
D meson decays (PYTHIA simulation.) Right panel: Correlation between
x~2~ and p~T~. 57](#__RefHeading___Toc124816798)

[Figure 49 -- Fraction of dimuon pair background containing decay muons
versus dimuon mass. At the J/ mass (3.1 GeV), about 60% of the total
background contains at least one decay muon, which can be rejected using
the FVTX. 58](#__RefHeading___Toc124816799)

[Figure 50 - PHENIX preliminary dimuon mass spectrum from 2004 for the
most central Au-Au collisions. Top panel: The red histogram is for
opposite sign muon pairs, while the black histogram is for smoothed like
sign pairs. Bottom panel: The opposite sign spectrum after background
subtraction. The peak at 3.1 GeV is the J/. Note that the signal to
background ration is less than 1:10. 59](#__RefHeading___Toc124816800)

[Figure 51 - The Z-decay length for semi-leptonic B decays (black
histogram). The black line is an exponential fit to the beauty decays,
with an average lifetime of 970 microns. The red line is a fit to the
charm decays, with an average lifetime of 785 microns.
60](#__RefHeading___Toc124816801)

[Figure 52 - The reconstructed Z-vertex distribution for J/ from B
decays (black line) and for prompt J/ (red line). Note that the J/ yield
has been scaled down by a factor of 100. The relative yield of J/ from B
decays versus prompt J/is estimated to be about 1%.
62](#__RefHeading___Toc124816802)

[Figure 53 - Left panel: Correlation between gluon x1 and p~Z~ of J/
from B meson decays (PYTHIA simulation.) Right panel: Correlation
between x2 and p~T~. 62](#__RefHeading___Toc124816803)

[Figure 54 - 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 pix hits) 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.
65](#__RefHeading___Toc124816804)

[Figure 55 - 3-D model of the full vertex detector showing the barrel
portion and the endcaps on left and on the right. Also shown is the VTX
mounting fixture in the bottom of the picture.
67](#__RefHeading___Toc124816805)

[Figure 56 - The FNAL FPIX2 pixel readout chip
68](#__RefHeading___Toc124816806)

[Figure 57 - Conceptual layout of the PHX pixel readout chip. The left
side graphic depicts the general layout of the chip. Green is the area
for bonding, blue the programming interface, red the discriminator,
orange the pipeline and yellow the digital interface. The left side
graphic shows the bonding layout, the bump spacing is 200 micron. The
signal and power bus will be routed on the surface on the chip and
bonded via the bump bonds on the ends of the chip.
69](#__RefHeading___Toc124816807)

[Figure 58 - The equivalent noise charge (ENC) versus capacitance.
70](#__RefHeading___Toc124816808)

[Figure 59 - Three silicon detector sizes will be used. The largest will
have 6 chips reading out two rows of 1536 strips, the intermediate
silicon will have 5 chips reading out two rows of 1280 strips and the
smallest silicon is half the size of the largest with 3 chips reading
out two rows of 768 strips. (All dimensions are in millimeter)
73](#__RefHeading___Toc124816809)

[Figure 60 - A wedge assembly will have 24 carbon panels (one shown here
in brown) in azimuth, each of them carrying 4 silicon detectors (blue),
two in the front and two in the back. They overlap on the edges by a few
millimeters to avoid dead areas. The bus on a silicon assembly is routed
on the chips as described above, the connection of the inner silicon
detectors is realized via a kapton bus (golden).
73](#__RefHeading___Toc124816810)

[Figure 61. Each station carries 24 wedges, i.e. 96 silicon detectors.
The stations are placed at \~20, 26, 32 and 38 cm from the interaction
point. 74](#__RefHeading___Toc124816811)

[Figure 62. Each endcap will have 4 stations of silicon detectors. The
inner station has a reduced size in order to not interfere with other
PHENIX detectors. 75](#__RefHeading___Toc124816812)

[Figure 63 - The transition module concept proposed by Columbia.
76](#__RefHeading___Toc124816813)

[Figure 64 - An isometric view of the VTX showing all of the internal
features coaxial with the beam tube: (moving out from the beam tube),
two cylinders of pixel detectors, two cylinders of strip detectors, the
GRFP structure (gray in color), and finally, the cylindrical enclosure
wall. 79](#__RefHeading___Toc124816814)

[Figure 65 - 3D model of octagonal disk like structures for the endcap
ministrips. Cooling tubes are to demonstrate both the number and
routing. 80](#__RefHeading___Toc124816815)

[Figure 66 - The octagon panel structure is on the right with the
cooling channel shown. A heat load of 0.1 W/cm\*\*2 is assumed.
80](#__RefHeading___Toc124816816)

[Figure 67 - Illustration of an embedded cooling passage arrangement in
the composite sandwich used in the endcap thermal and static
calculations. The upper panel depicts a circular tube with supports and
the bottom panel shows a flattened tube that enhances heat transfer and
provides a thinner sandwich. 80](#__RefHeading___Toc124816817)

[Figure 68 - Estimated normal radiation length for the endcap octant
panel for different tube diameters. 81](#__RefHeading___Toc124816818)

[Figure 69 -- PHENIX Forward Silicon Vertex (FVTX) project timeline.
84](#__RefHeading___Toc124816819)

[Figure 70 - Silicon wafer layout used for wedge sensor cost estimate.
86](#__RefHeading___Toc124816820)

[Figure 71 -- Organizational Chart for the FVTX project.
87](#__RefHeading___Toc124816821)

[Figure 72 - Cross section calculatations for beauty with FONNL for
various parameters from Ramona Vogt. 95](#__RefHeading___Toc124816822)

**List of Tables**

[Table 1 -- 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 semileptonic decay rates are before application of a
vertex cut. 64](#__RefHeading___Toc124816837)

[Table 2 - Summary of the parameters of the FVTX disks.
67](#__RefHeading___Toc124816838)

[Table 3 - 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. 77](#__RefHeading___Toc124816839)

[Table 4 -- Cost estimate for the FVTX endcaps with contingency. The
methodology used for contingency is in Appendix A.
85](#__RefHeading___Toc124816840)

[Table 5 - Technical, cost and schedule risk factors.
92](#__RefHeading___Toc124816841)

[Table 6 - Technical, cost, schedule and design weighting factors.
92](#__RefHeading___Toc124816842)

[Table 7 - Luminosity estimates for RHIC-II from Thomas Roser.
96](#__RefHeading___Toc124816843)

[Table 8 - Summary of luminosities used in these rate calculations for
RHIC-II and RHIC-I (2008). 97](#__RefHeading___Toc124816844)

[Table 9 - Comparison of new and old values for variouse parameters used
in these rate calculations. 98](#__RefHeading___Toc124816845)

[Table 10 - Estimated rates per week for p+p collisions.
98](#__RefHeading___Toc124816846)

[Table 11 - Estimated rates per week for d+Au collisions.
99](#__RefHeading___Toc124816847)

[Table 12 - Estimated rates per week for Au+Au collisions.
99](#__RefHeading___Toc124816848)

[Table 13 - Level-1 muon trigger rejection factors for pp and AuAu based
on previous data and simulations of the level -1 triggers.
100](#__RefHeading___Toc124816849)

[Table 14 -- Estimated trigger rates and addition rejection factors
needed for p+p and Au+Au collisions in PHENIX.
101](#__RefHeading___Toc124816850)

# Executive Summary

We propose the construction of two Forward Silicon Vertex Trackers
(FVTX) for the PHENIX experiment at RHIC. These would extend the vertex
capability of the PHENIX Silicon Vertex Tracker (VTX) to forward and
backward rapidities with secondary vertex capability in front of the
PHENIX muon arms.

The primary technical improvement provided by the FVTX (as well as the
VTX) is to allow for the identification of secondary (also called
"separated") vertices near the original event vertex. With an expected
z-vertex resolution of better than 200 m, we will see improvement in
both tracking from the original vertex as well as through identifying
the location of secondary vertices caused by the in-flight decay of
particles.

The identification of secondary vertices opens up a wide variety of
improvements in the understanding of primary physics processes. In heavy
quark (charm and beauty) production, the lifetime of the heavy meson
(combined with a significant boost) allows travel of a few millimeters
before decaying into a lepton and/or other products. For example, this
permits identification of beauty production through the channel B J/ψ X.
We will see that this affects a number of areas of physics exploration.
Also, numerous pions and kaons decay into muons and other products in
the first few centimeters of their travel, and the event-by-event
identification and rejection of this voluminous source of secondary
muons will reduce the level of background in a variety of physics
channels. Combining secondary vertex identification with the existing
muon spectrometers provides a powerful improvement in the capabilities
of the muon detector system and extends our physics reach in the large
rapidity () and low momentum-fraction (*x*) regions.

As a result of this proposed upgrade, numerous areas of physics
exploration will be made more 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 beauty
        measurements over a much broader x range than available with the
        barrel VTX detector alone and with much greater precision than
        is possible with the muon detectors alone. This allows the
        extension of studies of the geometrical and dynamical effects
        into the forward and backward rapidity regions of the hot-dense
        matter created in high-energy heavy-ion collisions.

    -   More precise open charm and beauty measurements will provide a
        solid \"denominator\" for comparison with production of bound
        states of heavy quarks (J/ψ and ). 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.

    -   Permit the direct measurement of s at mid-rapidity 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'.

    -   Allow for an unambiguous measurement of the Drell-Yan and
        heavy-flavor dimuon continuum with elimination of the
        backgrounds from light mesons.

    -   Provide a more accurate reaction plane for studies of many other
        signals, given the much larger rapidity coverage provided by the
        FVTX.

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

    -   Permit the study of the gluon structure function modification in
        nuclei at small *x* values, where gluon saturation or shadowing
        is thought to be important.

    -   Determine the initial state for AA collisions and provide a
        robust baseline for cold-nuclear matter effects in studies
        hot-dense matter in heavy-ion collisions.

    -   Help untangle the intricate physics of J/ψ and 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/.

```{=html}
<!-- -->
```
-   Polarized p+p collisions, and the contribution of the gluon to the
    spin of the nucleon:

    -   Provide a much larger x range (from x = 10^-2^ down to 10^-3^)
        over which the mostly unknown gluon polarization (*∆G/G*) can be
        determined. Without the FVTX the range covered is likely to not
        be sufficient to study the shape of any polarization or to
        determine its peak value.

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

    -   Enable a clean measurement of W/Z bosons by rejecting muons from
        light and heavy hadron decays at high p~T~.

The main experimental benefits provided by the FVTX detector are in the
following areas:

-   Identification and rejection of muons from long-lived and K meson
    decays

-   Identification of charm and beauty decays via displaced vertices

-   Explicit identification of beauty production through the channel BJ/

-   Significant improvement of signal-over-background in all dimuon
    measurements by rejecting decay muons from pions and kaons combined
    with the rejection of punch-through hadrons

-   Improvements in vector meson mass resolutions, e.g., the J/, ' and

With the present PHENIX detector, heavy-quark production in the forward
and backward directions has been measured indirectly via the observation
of single muons. These 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 statistical nature of
the analysis does not allow for a model-independent separation of the
charm and beauty contributions. The FVTX detector will provide vertex
tracking with a resolution better than 200 m over a large coverage in
rapidity (1.2 \< \|\| \< 2.2) with full azimuthal coverage. This will
allow for vertex cuts which separate prompt particles, decay particles
from short-lived heavy quark mesons and decay particles from long-lived
light mesons (pions and kaons). In addition, beauty measurements can be
made directly via B J/X by looking for a displaced J/ vertex, which will
allow charm and beauty contributions to be separated in semi-inclusive
single lepton measurements. Therefore, with this device significantly
enhanced and qualitatively new data can be obtained. A more robust and
accurate measurement of heavy-quark production over a wide kinematic
range will be possible. This new reach to forward and backward
rapidities complements that already planned for the central barrel
vertex (VTX) silicon detector, which will cover \|\| \< 1.2.

The precision of the J/ and other dimuon measurements in AuAu collisions
are currently limited by the large amount of combinatorial background
that must be subtracted from under the signal. With added rejection
power for muons from pion and kaon decays, the significance of all
dimuon measurements will greatly improve. Further improvement in these
measurements result from the improved mass resolution, which will be
attained because of the more accurate determination of the opening
angles of the dimuons. All together, these will result in greatly
improved dimuon data as well as providing access to several new
measurements: separation of ' from J/, extraction of Drell-Yan from the
dimuon continuum and measurement of upsilons at central rapidity.

The FVTX will be composed of two endcaps, with four silicon mini-strip
planes each, covering angles (10 to 35 degrees) that match the two muon
arms. Each silicon plane consists of wedges of mini-strips with 50 μm
pitch in the radial direction and lengths in the phi direction varying
from 1.9 mm at small angles to 13.5 mm at 35 degrees. A resolution in
z~vertex~ of 200 μm can be achieved at a maximum occupancy per strip in
central Au-Au collisions of less than 1.5%.

![](media/image1.png){width="5.383333333333334in" height="3.55in"}

[]{#__RefHeading___Toc124816751 .anchor}Figure 1 - Conceptual layout of
the PHENIX FVTX showing the four lampshade silicon planes of each
endcap.

The FVTX will have about 1.8 million strips that will be read out with a
Fermilab PHX chip, which is flip-chip assembled (bump-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 140-840 Mbps to an intelligent readout board
containing FPGAs. There the data is prepared in a standard PHENIX format
and, in parallel, a fast \"level-1\" trigger algorithm can be run to
select interesting heavy-quark events.

The PHX chip is a slightly modified version of the Fermilab FPIX2.1
front end ASIC developed for BTEV. The silicon mini-strip sensor will be
based on a similar wedge design developed for the CMS experiment. The
FPIX chip and CMS sensors are both mature designs.

A collaboration of 8 institutions with approximately 40 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, 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/ physics, small-x nuclear effects, gluon
structure functions and polarization, various other physics 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 to be installed in the RHIC beam
at the same time as the barrel pixel detector (FY08). As part of this
effort LANL, Columbia and ISU will advance the R&D for the FVTX by fully
designing the interface electronics that connects the PHX 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 the design of the mechanical ladder and support
structure.

We anticipate that the full project will be funded by the DOE Office of
Nuclear Physics at a total cost of \$4.0M (\$3.0M + 35% contingency). As
a first step in parallel and in preparation for construction of the full
project, a prototype endcap vertex detector covering approximately 1/8
of one endcap is being funded by the LANL LDRD-DR grant of \$1.25M/yr
over three years. This will be built during FY06-FY08 and operated for
an initial semi-leptonic charm decay measurement by the end of that
period. Construction of the full detector should proceed on a time scale
that will allow installation of the final/full detector starting in late
FY08. The full installation would be complete by the end of FY09.

A preliminary management plan of the VTX 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 proposed measurements
    are documented in section 2.

-   The feasibility of these measurements and the required detector
    performance are discussed in section 3.

-   Section 4 gives a detailed description of the 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.

#   {#section .unnumbered}

# Physics Goals of the FVTX Endcap Upgrade

The PHENIX Forward Vertex Detector (FVTX) endcaps complement the barrel
vertex detector (VTX) already being built for PHENIX by providing much
larger coverage in rapidity (two additional units of rapidity compared
to about one), extending the sensitivity to gluon momentum fraction (x)
down to x\~10^-3^ , and providing a broad reach in transverse momentum.
Heavy-quark mesons and bound states of heavy-quarks (quarkonia) coming
from beauty meson decay can be identified by their short detached
vertices, and the light-meson yields that ordinarily comprise most of
the backgrounds to these measurements can be largely eliminated
according to their large detached vertices. Prompt muons and kaons which
punch through the muon system can be eliminated by their lack of a
displaced vertex.

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 nuclear collisions, and finally those that related to
polarized proton collisions.

## Heavy-ion Collisions and the Quark Gluon Plasma

The main goal of the RHIC 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 in this dense matter as seen by the
suppression in the yields at high transverse momentum for light quarks,
the large flow seen at small momenta indicative of early thermalization,
and other signatures observed by the RHIC experiments point to large
densities created in these collisions. But the composition of this
high-density matter, whether or not it is deconfined, and what the
degrees of freedom are, remain beyond the reach of present measurements.
The FVTX detector coupled with the muon detector systems will allow for
precision measurements of open charm and beauty versus rapidity, p~T~
and reaction plane, much improved measurements of vector mesons (J/, ',
) as well as an unambiguous measurement of dimuons from Drell-Yan in
heavy-ion collisions. These measurements will allow one to understand
heavy quark energy loss and flow in heavy-ion collisions, contributions
of prompt production and quark recombination to vector meson production,
separation of initial-state and final-state modifications to charmonium
production, and provide important reference measurements from Drell-Yan.

### Energy Loss and Flow of Heavy Quarks

One of the most significant physics results in the first several years
of RHIC operations was the strong suppression of high-p~T~ light
particle production, shown in Figure 2, that is interpreted as energy
loss in dense matter for the outgoing particles or jets. A large
elliptical flow (asymmetry with respect to the reaction plane) is also
seen for the light hadrons as shown in Figure 3.

![](media/image2.png){width="3.123611111111111in"
height="2.1333333333333333in"}

[]{#__RefHeading___Toc124816752 .anchor}Figure 2 - Suppression of
high-p~T~ hadrons and pions as seen in Au+Au vs d+Au collisions.

![](media/image3.png){width="2.75in" height="2.7416666666666667in"}

[]{#__RefHeading___Toc124816753 .anchor}Figure 3 - Large elliptic flow
for light hadrons in Au+Au collisions is near the hydrodynamic limit.

More recent measurements are beginning to give some evidence that even
heavy quarks (charm and beauty) suffer substantial energy loss in the
final state (see Figure 4) and even appear to flow, though the flow
measurements at high p~T~ are rather imprecise and even somewhat
inconsistent between the PHENIX and STAR measurements (Figure 5). These
results have primarily come from the central rapidity detectors although
some early results from the muon spectrometers are beginning to emerge.
But for all these measurements large backgrounds and the necessity to
calculate non-heavy-quark contributions to the single lepton spectra and
then statistically subtract these to isolate the heavy-quark component
with low signal/background ratios give large systematic errors and limit
the accuracy of these measurements. Also there is not a clean way to
separate the charm and beauty components of the resulting subtracted
spectra. The FVTX detector will address both of these issues with heavy
flavor measurements.

![](media/image4.png){width="2.875in" height="2.796527777777778in"}

[]{#__RefHeading___Toc124816754 .anchor}Figure 4 - In PHENIX preliminary
results shown at QM05, even charm seems to suffer energy loss at
mid-rapidity.

![](media/image5.jpeg){width="3.2465277777777777in"
height="2.326388888888889in"}

[]{#__RefHeading___Toc124816755 .anchor}Figure 5 - Preliminary results
for charm from single electrons in PHENIX and STAR shows flow for small
p~T~ and conflicting results from PHENIX and STAR as to whether the flow
returns to zero for larger p~T~.

One can pose several important classes of questions related to the
interaction of heavy quarks with the hot-dense (QGP) matter created in
central heavy-ion collisions that will be addressed by the FVTX upgrade:

-   How does energy loss and flow differ between light and heavy quarks?

```{=html}
<!-- -->
```
-   What is the rapidity dependence of the suppression or energy loss of
    heavy quark production in heavy-ion collisions and how can one
    understand it taking into account the density and geometry of the
    hot-dense matter that is created? For example, given the additional
    boost of heavy quarks in the forward direction and differences of
    the time-dependence of the hot-dense region in the longitudinal
    versus transverse directions, the rapidity dependence should
    characterize these differences and help us understand the dynamics
    and properties of the dense medium.

-   How will the flow at lower momentum or the asymmetry with respect to
    the reaction plane change as one goes more forward and how can this
    be understood theoretically? This should be sensitive to the density
    left behind from the collision or to stopping and its evolution,
    with differences between forward and mid rapidity.

-   Can the high p~T~ dependence of heavy quark production distinguish
    between large flow, hydrodynamical behavior and production without
    final state interactions?

Predictions before the most recent data were that heavy quarks would not
lose much energy in hot-dense matter due to the \"dead-cone\"
effect[^1], but this appears inconsistent with the emerging results.
Recent studies suggest that the magnitude of the
dead-cone[^2]^,^[^3]^,^[^4] may be smaller than anticipated in reference
Error: Reference source not found, which would lead to an energy-loss
for heavy quarks closer to that for light quarks. Djordjevic and
GyulassyError: Reference source not
found^,Error:\ Reference\ source\ not\ found^ have proposed that the
energy-loss for heavy-quarks is further reduced due to a plasmon
frequency cut-off effect in a thermalized medium. As a result precise
measurement of heavy-quark energy loss through open charm may enable a
measurement of partonic effective thermal masses in the medium.

At the opposite extreme, Batsouli *et al*[^5] have suggested that the
first electron measurements at RHIC, which showed N~Binary~ scaling of
heavy quark production in AuAu collisions, can be reproduced by assuming
that charm particles flow hydro-dynamically, i.e. the charm particles
interact with the medium with a large cross-section. To distinguish
between these effects and to explore this physics will require precise
measurements of the *p*~T~ spectra for open charm at high transverse
momentum, out to several GeV/c. This point is illustrated in Figure 6.
The figure, taken from reference Error: Reference source not found,
illustrates that the *p*~T~ distribution of *D* mesons and single
electrons from charm have little difference in the two extreme scenarios
of no medium effect (shown in dashed curves) and a hydrodynamic model
(shown in solid curves), within the *p*~T~ range accessible by the
current PHENIX setup. Obviously, a much more precise measurement at much
higher *p*~T~ range is required to distinguish the models. Such a
measurement is not feasible without the FVTX and VTX upgrades due to the
large backgrounds and ambiguity of charm and beauty contributions.

![](media/image6.jpeg){width="4.054166666666666in"
height="3.438888888888889in"}

[]{#__RefHeading___Toc124816756 .anchor}Figure 6 - Single electron
dataError: Reference source not found of PHENIX compared with two
extreme models of charm p~T~ distribution.

Other theoretical pictures[^6] suggest that heavy and light quarks will
behave quite differently because the heavy quarks will fragment or
hadronize within the dense matter, while the light quarks will fragment
outside. So for heavy quarks the process is more complicated with both
quark energy loss and fragmentation occurring in the medium. This
behavior would presumably depend on the rapidity of the observed leading
particles or jets. Thus the large coverage in rapidity provided by the
FVTX will be quite important.

Clearly the FVTX detector upgrade will be critical in helping to
determine which of the above theoretical pictures are reflected by the
real data as it will provide much more precise heavy quark cross section
and flow measurements, combined with the VTX will cover a very large
rapidity range, will much improve the p~T~ coverage at forward rapidity,
and will allow for separation of charm and beauty components to the
heavy quark spectra.

### Open Charm and Beauty 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[^7]^,^[^8]^,^[^9]. Heavy quarks are produced in
different stages of a heavy ion reaction. In the early stage charm and
beauty 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 (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.

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 7 (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 accuracy and precision is therefore required to
establish a potential charm enhancement.

![](media/image7.jpeg){width="2.7222222222222223in"
height="3.0375in"}![](media/image8.jpeg){width="2.428472222222222in"
height="2.9763888888888888in"}

[]{#__RefHeading___Toc124816757 .anchor}Figure 7 - 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 FVTX combined with the muon spectrometers will allow measurement of
charm and beauty over a much broader range in *p*~T~. This will extend
the single muon measurement to the *p*~T~ region near 0.5 GeV/c, which
is essential for an accurate determination of the *p*~T~ integrated
charm yield at forward and backward rapidities, since more than half of
the yield from charm decays is in this *p*~T~ region. 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 8. 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 beauty) enhancement.

![](media/image9.jpeg){width="4.376388888888889in"
height="3.3583333333333334in"}

[]{#__RefHeading___Toc124816758 .anchor}Figure 8 - Rapidity distribution
from Vogt[^10] 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/ Suppression and Comparisons with Open charm, ' and 

J/ production in heavy ion collisions is a complicated process that can
be both difficult to dissect but also allows the possibility to
understand several features of heavy ion collisions at the same time, if
the measurement is precise enough and it is used in conjunction with
other relevant measurements, such as open charm production. J/
production can be modified in AuAu collisions with respect to pp
collisions by modification of the gluon distribution functions in a
nucleus, energy loss of the composite charm quarks in the medium,
contributions to the production from both prompt production and
recombination (if the charm density is high enough), as well as the
historical prediction of suppression due to Debye screening in a plasma.
To quantitatively understand this suppression/enhancement requires
knowledge of the initial production of $c\overline{c}$pairs and the
effect of cold nuclear matter on production. The effectiveness of a
deconfined medium in preventing the formation of J/ can be quantified
using the ratio J//(open charm) with the open charm in the same
acceptance as PHENIX measures the J/The FVTX upgrade provides for the
detection of open charm over about the same rapidity interval as for J/
decays to dimuons. In addition, the J/ measurement uncertainties in AuAu
interactions are currently dominated by the amount of background that
must be subtracted from the J/ peak, even with a limited detector
acceptance chosen to reduce the backgrounds. The addition of the FVTX
will greatly enhance the J/ measurement in the forward region by
eliminating most of the combinatorial background that comes from pion
and kaon decay muons and by improving the mass resolution (see Figure 9)
which results from a more accurate measurement of the dimuon opening
angle.

The measurement of the production of ' and will also greatly improve the
understanding of J/ production as they have larger and smaller Debye
screening lengths, respectively. The provides a comparison of beauty
production to charm production, while the ' shares much of the same
production issues as the J/ but does not suffer from feed-down from
other states. These, combined with open charm measurements, should allow
for separation of initial state and final state modifications to J/
production.

![](media/image10.png){width="4.117361111111111in"
height="2.7729166666666667in"}

[]{#__RefHeading___Toc124816759 .anchor}Figure 9 - Mass spectra for the
J/ and \', showing the substantial improvement in separation expected
with a vertex detector (yellow, 100 MeV resolution) compared to that
without a vertex detector (black, 150 MeV resolution). The number of J/
and ' in this plot represents our expectation for a \~25 pb^-1^ p+p run.

### Reaction Plane and Azimuthal Asymmetries

The large increase in the overall solid angle for observing charge
particles provided by the FVTX (plus a more optimal rapidity coverage)
will result in a substantial improvement in the reaction plane
resolution, 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 this is a critical
improvement 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 function of path length
in the medium. It is generally agreed upon 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. Alas, Figure 10, which shows a measurement
with the MVD pad detectors for minimum bias Au-Au collisions from run4,
demonstrates that the elliptic flow at the magenta 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/image11.png){width="5.008333333333334in"
height="3.529166666666667in"}

[]{#__RefHeading___Toc124816760 .anchor}Figure 10 - 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 to reaction plane resolution
and confidence levels for providing \'reaction plane bins\' and will be
discussed in the following. The simulation has been validated with the
MVD pad detector measurements from run4.

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. For this is a rather complex variable
we choose to first represent it in Figure 11 and then translate it into
a more intuitive variable in Figure 12 namely a confidence level of
having made the right determination.

![](media/image12.jpeg){width="5.995138888888889in"
height="4.063888888888889in"}

[]{#__RefHeading___Toc124816761 .anchor}Figure 11 - 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 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 11 shows in color the square root of the mean cosine of the
reaction plane difference between north and south detector as function
of the track multiplicity (here called Nhit), 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 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
with yields the best resolution.

Studies from Hijing (presented in section xxx) 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/image13.png){width="4.78125in" height="3.3673611111111112in"}

[]{#__RefHeading___Toc124816762 .anchor}Figure 12 - 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 i.e. v2, shown in Figure 12 as 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 11 is therefore about
0.75.

Figure 13 shows in color the expected confidence levels (measured from 0
to 100 percent or as on the z-axis label from 0 to 1.) as function of
the reaction plane bin size (see above), i.e. delta phi on the ordinate
and the reaction plane resolution on the abscissa. For a given 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 13 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 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/image14.png){width="4.685416666666667in"
height="3.0965277777777778in"}

[]{#__RefHeading___Toc124816763 .anchor}Figure 13 - 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 reactionplane
resolution. The reaction plane resolution of 0.75 estimated in figure 4
would result is a 65 precent confidence level if binning the reaction
plane into 3 bins. Two bins (delta phi = 90 degrees) will give a
confidence level of 85 precent 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, being of increase importance for PHOBOS will be
decommissioned. In the following we discuss the measurements obtained
with the MVD pad detectors in run4 which covered about the same rapidity
range and where already shown above in the context of the reaction plane
measurements.

Figure 10 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. In
the future running of RHIC PHOBOS, which provided valuable flow
measurements in the past, will no longer be taking data so it is
important that asymmetry measurement in the intermediate rapidity range
will be provided by PHENX. 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 12 and Figure 14 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
alas with better statistical and systematic error bars. Simulations on
the FVTX performance have begun.

![](media/image15.png){width="4.464583333333334in"
height="3.1395833333333334in"}

[]{#__RefHeading___Toc124816764 .anchor}Figure 14 - 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 Gluons in Nuclei

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 of 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[^11]. These modifications 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.

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

Of particular interest is the depletion of low momentum partons (gluons
or quarks) in nuclei, called shadowing, which results from the large
density of low momentum partons. For gluons at very low momentum
fraction, *x* \< 10^-2^, one can associate with them, 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 small values of *x*. 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 above that is
enhanced. In recent years a model for gluon saturation at small *x* has
been discussed extensively by McLerran and collaborators[^12]. Gluon
saturation affects both the asymptotic behavior of the nucleon's gluon
distribution as *x* approaches zero and causes shadowing.

![](media/image16.png){width="4.079861111111111in"
height="2.6381944444444443in"}

[]{#__RefHeading___Toc124816765 .anchor}Figure 15 - Gluon shadowing from
Eskola[^13] 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.

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)Error: Reference source not
found (Figure 15) predict only a 30% reduction due to gluon shadowing,
while those of Frankfurt & Strikman[^14] (shown in Figure 16) or
Kopeliovich[^15] predict up to a factor of three reduction.

![](media/image17.jpeg){width="4.372916666666667in"
height="3.1534722222222222in"}

[]{#__RefHeading___Toc124816766 .anchor}Figure 16 - Gluon shadowing
prediction from Frankfurt and StrikmanError: Reference source not found,
which shows substantially larger gluon shadowing than that of EKSError:
Reference source not found.

The coverage in *x* for the FVTX is indicated in Figure 17, 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 PHENIX. 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 is not accessible
with the VTX barrel-only upgrade. While the *x*-range for J/ψproduction
also extends into the shadowing range, final state effects, such as
dissociation, complicate the extraction of the gluon structure function.
Open charm and beauty measurements are unaffected by these final state
effects.

![](media/image18.jpeg){width="5.504166666666666in"
height="4.261805555555555in"}

[]{#__RefHeading___Toc124816767 .anchor}Figure 17 - 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 EKSError: Reference source not found and FGSError: Reference source
not found for different Q values.

### Disentangling the Physics of J/ and Quarkonium Production in Nuclei

Recent measurements by PHENIX of the J/ψ nuclear dependence for d+Au
collisions[^16] are shown in Figure 18 and indicate weaker absorption
and shadowing than expected. The large rapidity region corresponds to
small momentum fraction 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 either
initial-state energy loss of the gluon from the projectile[^17] or from
Sudakov suppression effects on the final-state $c\overline{c}$[^18].
Increased statistics from higher luminosity runs and more definitive
measurements via observables that are sensitive to gluon structure
functions in several different channels will be necessary to test the
theory with sufficient power to constrain the underlying QCD processes.

![](media/image19.jpeg){width="4.853472222222222in"
height="4.997916666666667in"}

[]{#__RefHeading___Toc124816768 .anchor}Figure 18 - J/ψ nuclear
dependence versus rapidity compared to theoretical predictions with
several types of gluon shadowingError: Reference source not found.

![](media/image20.jpeg){width="5.376388888888889in"
height="3.8256944444444443in"}

[]{#__RefHeading___Toc124816769 .anchor}Figure 19 - Alpha versus x~2~
and x~F~ from measurements at three different energies 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)Error: Reference source not found, E866/NuSea (s = 39 GeV)[^19]
and NA3 (s = 19 GeV)[^20].

Earlier data from lower-energy fixed-target p+A measurements at Fermilab
(E866) are shown in Figure 19, compared to data from PHENIX and NA3.
They show much 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 of the gluon from the
proton projectile). A stronger absorption at mid-rapidity is seen in the
lower energy experiments than with the PHENIX experiment. The 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 and other nuclear effects are playing important roles in
modifying J/ production, at least at lower energies.

It is clear that precise knowledge of the shadowed gluon structure
functions in nuclei is essential towards understanding several of the
important signatures for QGP in heavy-ion collisions at RHIC, including
modification of open and closed heavy-quark production with respect to
p-p collisions. Recombination models for J/ production, which might
cause an enhancement of that production in heavy-ion collisions due to
the large density of charm quarks created in a collision, must be
constrained by an accurate measurement of the amount of charm produced,
given the shadowing of the gluon densities in the colliding nuclei.

In the J/ψ studies done at CERN by NA38/50[^21] the J/ψ yields were
usually divided by the Drell-Yan dimuon yields, since the latter should
have little nuclear dependence. But this is actually an unnatural
procedure since the Drell-Yan process involves quarks (q-qbar
annihilation) while J/ψ production involves gluons (gluon fusion). The
nuclear effects on the initial parton distributions for quarks and
gluons are likely different and their energy loss in the initial state
before the hard interaction is also likely different. Additionally the
yields of Drell-Yan dimuon pairs were quite small at CERN and dominated
the statistical uncertainties in this ratio. The relative rates for
Drell-Yan at PHENIX are even smaller and making such a ratio makes even
less sense here. It is much more natural to compare J/ψ production to
open-charm production, where the initial-state effects are probably the
same. Therefore a robust measurement of open-charm is quite important
for the physics of the J/ψ. Of course, it has also been suggested by
some theoretical groups[^22] that the effective gluon distributions are
process dependent, and different for open- versus closed-charm
production. These models suggest that such a difference, if seen by
comparisons of open and closed charm, would indicate that higher-twist
contributions to closed charm production are substantial.

Another area of importance, especially to the J/ψ measurements, is the
production of beauty quarks. The decay of B-mesons will produce J/ψs (BR
\~ 1.14%) that tend to have somewhat higher p~T~ than for prompt J/ψ. In
a scenario where color-screening in a QGP created in heavy-ion
collisions destroys most of the J/ψs it is conceivable that,
particularly at higher p~T~, the remaining J/ψs are dominated by those
that come from B decays. An estimate of this from Lourenco[^23] several
years ago indicated that for central collisions the fraction of J/ψs
from B decays might be as large as 20% overall, with even larger
fractions at high p~T~. Clearly one would like to measure the B cross
sections at RHIC energies so that a more reliable estimate of their
contribution to J/ψ production can be made, an issue which would be
particularly important should a large suppression of J/ψs be seen in
central Au-Au collisions at RHIC. How much suppression is actually
occurring in the plasma would be difficult to determine without
establishing what fraction of the remaining J/ψs do come from B decays.

In addition, given sufficient RHIC luminosity, it would be quite
instructive to measure for beauty the same observables already discussed
for charm, and to compare these results. As RHIC luminosity increases we
will also be able to measure the , a
![](media/image21.png){width="0.20277777777777778in"
height="0.17569444444444443in"} bound state; and for it, a comparison
with open-beauty will obviously be important.

The FVTX can also enable measurements of at mid-rapidity for decays that
give one muon in each of the two muon arms. The study of s provides an
important comparison to J/ψs for a system composed of beauty instead of
charm quarks that is smaller and more tightly bound. Previous
measurements at lower energies showed weaker absorption in the
final-state than that observed for the J/ψA solid baseline for
production is also, of course, critical for comparisons with the J/ψ in
nucleus-nucleus collisions where the heavier should not be screened by
the QGP and also should not have large contributions to its production
from recombination of beauty quarks, since their production (at RHIC) is
too small to give substantial recombination.

While PHENIX has recently observed an signal for decays with both muons
detected in a single arm, the s with one muon in each arm are swamped by
copious background from random pairs of muons. This background (shown
for dAu collisions in Figure 20) turns on at pair masses of about 5 GeV,
corresponding to the sum of the single muon momentum thresholds in the
two muon arms, and makes it impossible to see the small signals from
mid-rapidity s and Drell-Yan. With the FVTX we can remove, on an
event-by-event basis, the light hadron decays which cause most of these
random pairs and should be able to observe a clean Upsilon and high-mass
Drell-Yan signal at mid-rapidity.

![](media/image22.jpeg){width="5.993055555555555in"
height="2.270138888888889in"}

[]{#__RefHeading___Toc124816770 .anchor}Figure 20 - Dimuon mass spectrum
in dAu collisions for one muon at positive and one muon at negative
rapidity, showing the large combinatoric background from random muon
pairs (black) that dominates the μ^+^μ^-^ spectrum (red points with
error bars) starting a little below 5 GeV in mass. The (unobserved)
would appear as a peak at 9.46 GeV.

Finally, the ψ' is also an important signal in dAu collisions. Although
it has a smaller yield (\~few %) compared with the J/ψ and is therefore
harder to measure, its physics is cleaner since it does not suffer from
the large feed-down from higher mass resonance decays that the J/ψ does
(\~40% of J/ψ s come from decays of higher mass resonances). Its physics
should also be different from the J/ψ since it is a larger and more
weakly bound object, and so should see larger absorption, at least after
it has hadronized.

In current measurements of the dimuon mass spectra, the large
combinatoric backgrounds from hadron decays also make it very difficult
to identify and extract the ψ' yield, as shown in Figure 21. Here again,
the elimination of these muons from hadron decay can reduce the
background and the improved J/ψ and ψ' mass resolutions should make it
much easier to extract a clear ψ' signal.

![](media/image23.jpeg){width="4.877083333333333in"
height="3.6458333333333335in"}

[]{#__RefHeading___Toc124816771 .anchor}Figure 21 - The PHENIX 2003 dAu
dimuon mass spectrum (top panel) with the combinatoric background shown
in black and the total μ^+^μ^-^ pairs in red; and (bottom panel) the
spectrum with the background subtracted where a hint of the ψ' peak (at
3.7 GeV) has been fit. The ψ' is not well determined, due to the
statistical uncertainty contributed by the subtraction and the poor mass
resolution (\~170 MeV).

### Heavy-quarks: Charm and Beauty Mesons

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

-   Gluon shadowing or saturation effects for single heavy quarks. To be
    contrasted with similar studies of quarkonia where initial state
    effects are the same but final state effects are different and more
    important.

-   Energy loss of heavy versus light quarks in cold nuclear matter and
    multiple scattering (Cronin effect), the latter especially at
    backward rapidity where the heavy quarks are nearer the nucleus in
    rapidity.

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

As already discussed above, measurements of single heavy quarks (charm
and beauty) 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 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 is thought to have a small
effect at RHIC, since the energy loss per unit length (fm) in most
models is thought to be approximately constant and small compared to the
initial-state parton momenta at RHIC. On the other hand, partons in the
final state could show some effects of energy loss since their momentum
are lower, while heavy-quarks are expected to lose less energy than
light quarks due to the dead-cone effect[^24]. 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.

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 broaden the transverse
momenta.

A recent result for the p~T~ dependence of the nuclear modification
factor for prompt muons is shown in Figure 22 from PHENIX[^25]. Data for
prompt muons at forward ("North") and backward ("South") rapidities in
dAu collisions show a suppression at forward rapidities (small *x*
values) in Au where one would expect shadowing effects. At backward
rapidities 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 occur.

![](media/image24.png){width="5.374305555555556in"
height="4.810416666666667in"}

[]{#__RefHeading___Toc124816772 .anchor}Figure 22 - Nuclear modification
factor in dAu collisions, RdAu, for prompt muons in the forward and
backward rapdity regions versus p~T~. The prompt muons are primarily
from the decays of charm and beauty mesons although perhaps 10% are from
other processes such as light meson decays.

These results are obtained through a statistical method where the vertex
distribution for the events contributing to the single muons is studied
and a component that matches the raw vertex distribution is determined
after subtracting another component that follows the decay distribution
expected for light meson decays. For example, the light mesons which
originate from a vertex that is farther from the spectrometer in z will
have more probability of decay and therefore will be more numerous. This
statistical method suffers from substantial systematic effects that are
probably limited to 20-30% even at much larger integrated luminosity.
With the FVTX upgrade these events can be separated 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
smaller p~T~ values by substantially reducing the low-mass meson decay
backgrounds.

### 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 the muon
identifier at the rear of the muon arms. These punch-through hadrons
contribute roughly 10% of the 2 GeV particles that are seen several
layers deep in the muon identifier. Using the same statistical
techniques described previously in section 2.2.3, the yield of decay
muons is determined. 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 23. Similar to the prompt
results shown earlier, these particles also exhibit suppression at
forward rapidities and enhancement at backward rapidities.

Hadron production at forward rapidity, like the heavy-quarks discussed
earlier, is also 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 well into
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 to see
shadowing[^26]. In any case, the clean measurements possible with the
FVTX could help resolve this question.

It is also important to study the modification of jets in the forward
and backward directions for dAu, 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.

![](media/image25.png){width="5.747222222222222in" height="3.90625in"}

[]{#__RefHeading___Toc124816773 .anchor}Figure 23 - Nuclear modification
factor in dAu collisions (RdAu) 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. 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 in central versus peripheral dAu collisions is shown
versus rapidity in Figure 24. Data for light hadrons and J/ show a
surprisingly similar trend, with suppression at forward rapidity and
enhancement at backward rapidity. The FVTX will provide reduced
systematic errors for all of the measurements at \|y\|0.

![](media/image26.jpeg){width="5.5in" height="4.715277777777778in"}

[]{#__RefHeading___Toc124816774 .anchor}Figure 24 -- Nuclear
modification in dAu 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/.

### 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/ mass from copious pairs due to
open-charm decays. For example, as shown in Figure 25, the FNAL E866
Drell-Yan data was limited to masses above 4 GeV, due to a large
contribution of randoms (charm decays) at lower masses.

![](media/image27.png){width="4.843055555555556in"
height="2.3361111111111112in"}

[]{#__RefHeading___Toc124816775 .anchor}Figure 25 - Dimuon mass spectrum
from E866/NuSea, showing the Drell-Yan mass region used in their
analysis, which excluded masses below 4 GeV. Lower masses were excluded
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 which are present at RHIC energies. This should
allow Drell-Yan measurements over a broad mass range including values
below the J/, 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 at much smaller values of *x* then 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

In summary, the silicon forward vertex micro-vertex detector, which
covers the PHENIX central arm mid-rapidity range (1.2 \< \|*y*\| \<
2.2), addresses the following physics in dA reactions:

-   Probing the small-x shadowing or gluon saturation region in nuclei
    through the production of single heavy quarks (c and b) and of bound
    states of heavy quarks (J/ψ, ψ' and ), and providing a gluon
    structure function measurement in the small-x region for cold
    nuclear matter.

-   Disentangling various nuclear effects on J/ψ production by
    contrasting it with open charm production at large positive and
    negative rapidity. These should share the same initial-state effects
    and have similar production mechanisms; but will have different
    final-state effects.

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

-   Measurements of light hadrons via their decays to muons or when they
    punch through the muon absorbers, in contrast with heavy quarks in
    the same kinematical regions.

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

-   Robust measurements of the energy loss and flow of charm (and
    beauty) quarks in cold nuclear matter using high-p~T~ single muons.

-   Accurate measurement of the nuclear dependence of the charm cross
    section to provide a solid cold nuclear matter baseline for
    recombination effects in J/production from nucleus-nucleus
    collisions.

-   Improved separation of the ' from the J/, leading to the first '
    data from RHIC.

-   Low-mass muon pairs and Drell-Yan measurements of anti-quark
    shadowing at small *x* values.

-   and Drell-Yan measurements at mid-rapidity using one muon in each
    arm after removing the copious random pair backgrounds from light
    hadron decays.

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

Understanding the substructure of the nucleon (protons and neutrons) 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 26 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 and gluon polarization is
virtually unknown, with the present set of data.

![](media/image28.png){width="4.041666666666667in"
height="3.6770833333333335in"}

[]{#__RefHeading___Toc124816776 .anchor}Figure 26 - 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
parametrizations of these distributions.

The PHENIX spin program aims to measure the gluon spin structure
function in the proton. The existing PHENIX capability to do so is shown
in Figure 27 as the blue bars. However, precision measurements for heavy
quarks with the separation of charm and beauty are only possible with
the addition of a precision vertex tracking detector. The green bars in
Figure 27 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 Si Endcap
Vertex Detector (FVTX) proposed here extends the coverage (red bars in
Figure 27) 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/image29.jpeg){width="5.497916666666667in"
height="4.240972222222222in"}

[]{#__RefHeading___Toc124816777 .anchor}Figure 27 - 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 \[T.
Gehrmann and W. J. Stirling, Z. Phys. C65, 461 (1995)\].

### The Role of the Silicon Vertex Detector

The Endcap Vertex Detector provides tremendous improvements in *x*-range
over a Barrel-only detector, as shown in Figure 27. It also provides a
model independent clean separation of light hadron, charm and beauty
production. The following detailed list of improvements has been
produced by simulating *pp* 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. The *x*-range is
    extended considerably down to *x* = 0.001,
    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*/ from $B \rightarrow \frac{J}{y}$ decay. This
    provides coverage for 0.005 *x* 0.3. The selection of semi-leptonic
    decays $b\overline{b} \rightarrow e\mu X$ at high momentum is
    improved using displaced vertices. This extends the *x*~gluon~
    coverage for these semi-leptonic decays to 0.010.3. Measurement of
    $B \rightarrow \mu X$ is also possible by placing a cut on the
    *p*~T~ of the muon.

-   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; in general, a muon from a *W* decay is isolated from
    jet activity, while a light hadron normally has associated jet
    particles around it. 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

Most of our current knowledge of the nucleon spin comes from Deep
Inelastic Scattering (DIS) experiments. To first order in DIS, however,
an incoming lepton only couples to the charged quarks or anti-quarks,
and not to the neutral gluons. To get around this difficulty, one may
use measured (polarized) quark and anti-quark distributions to derive
the (polarized) gluon distribution via QCD-evolution equations over a
sufficiently large range of *x* and *Q*^2^ -- but these data are not
available. On the experimental side, semi-inclusive DIS experiments
(SMC, HERMES, COMPASS) explore higher order processes, such as di-hadron
production, to measure the polarized gluon distributions, as is
illustrated in Figure 28. However, current results are limited by
statistics and theoretical uncertainties.

![](media/image30.png){width="4.041666666666667in" height="2.34375in"}

[]{#__RefHeading___Toc124816778 .anchor}Figure 28 - Higher order
semi-inclusive DIS is used to explore gluon distribution.

The RHIC-SPIN program provides a new tool to directly collide
(polarized) quarks and gluons at leading order at high energy (see
Figure 29) and as such PHENIX has a major goal of measuring the gluon
spin-structure function in protons. In the PHENIX experiment, we will
measure the polarized gluon distribution $\frac{\Delta G(x)}{G(x)}$
using many different processes. Experimentally we measure the double
spin asymmetry:

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

where $\frac{\Delta f(x_{1})}{f(x_{1})}$ and
$\frac{\Delta f(x_{2})}{f(x_{3})}$ are the polarized parton
distributions for parton (*x*~1~) and (*x*~2~), and H is the final state
particle detected by the PHENIX detector. The polarized parton
distributions can be derived from the experimentally measured asymmetry
once we know the partonic asymmetry
$a_{\text{LL}}(x_{1} + x_{2} \rightarrow H + X)$ which is normally
calculated within the framework of pQCD.

![](media/image31.png){width="4.385416666666667in"
height="2.6041666666666665in"}

[]{#__RefHeading___Toc124816779 .anchor}Figure 29 - At RHIC-SPIN, quarks
and gluons interact directly at leading order.

A partial list of basic partonic processes relevant to this proposal:

1.  Inclusive open charm and open beauty production (into heavy mesons
    "*Q*") followed by decay to single muons;

$$\begin{array}{r}
\text{gg},\text{gq},\text{qq} \rightarrow \underset{¯}{Q} + X \\
\text{                    }Q \rightarrow m^{+ -} + X
\end{array}$$

2.  Open beauty production (into heavy mesons, usually *B*) followed by
    decay to *J/*, resulting in a displaced muon pair from *J*/ decay;

$$\begin{array}{r}
\text{gg},\text{gq},\text{qq} \rightarrow \underset{¯}{B} + X \\
\text{                    }B \rightarrow \underset{¯}{\frac{J}{y}} + X \\
\text{                            }\frac{J}{y} \rightarrow m^{+}m^{-}
\end{array}$$

3.  Inclusive light hadron production (pions and kaons) followed by a
    continuous distribution of in-flight decay, resulting in either
    displaced single muons (one extreme) or hadron punch-through to the
    muon identifier (the other extreme);

> $$\begin{array}{r}
> \text{gg},\text{gq},\text{qq} \rightarrow \underset{¯}{\frac{p^{+ -}}{K^{+ -}}} + X \\
> \text{                    }\frac{p^{+ -}}{K^{+ -}} \rightarrow m^{+ -} + X\text{   }(\text{maybe})
> \end{array}$$

4.  Heavy quarkonium production, producing muon pairs at the original
    event vertex.

$$\begin{array}{r}
\text{gg},\text{qq} \rightarrow \underset{¯}{\frac{J}{y}} + X \\
\text{               }\frac{J}{y} \rightarrow m^{+}m^{-}
\end{array}$$

It is important to note that at RHIC energy, heavy flavor production is
dominated by gluon-gluon interactions, thus we have,

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

However, in reality, one always faces various backgrounds in the
measurement, so the measured signal asymmetry is diluted,

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

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

Figure 30 shows the preliminary result of open heavy flavor production
with muons from 2002 *pp* data at RHIC. The prompt muons are mostly from
open charm decay in the measured *p*~T~ range. It is clear from Figure
30 that non-prompt muon backgrounds dominate at most of the low *p*~T~
region where we have the maximum statistics in the experiment. Without
the proposed vertex detector, it is very hard to do precision
measurements of asymmetries with prompt muons from open heavy quark
(charm and beauty) decay.

As discussed above, we plan to observe open charm production though
semi-leptonic decay to muons. The proposed FVTX will allow us to reject
muons from light hadron decays as well as misidentified prompt
punch-through hadrons based on the secondary vertex distributions.
However, at high *p*~T~, the open charm production measurement is
limited by beauty production contamination.

![](media/image32.png){width="5.129166666666666in"
height="3.704861111111111in"}

[]{#__RefHeading___Toc124816780 .anchor}Figure 30 - PHENIX preliminary
results (blue points) for prompt single muons (mostly from open charm
decay) measurement from run2 pp data. Two sources of background are
shown.

Measurements of beauty production can be performed in the present PHENIX
detector using electron-muon coincidence with central and forward
spectrometers. However, such measurements are limited to a narrow
kinematics range. This limitation can be overcome by direct measurements
of open beauty production with the vertex detectors. As discussed in an
earlier chapter (2.2.2), by identifying displaced *J*/ dimuons from open
beauty decay, we can achieve a very pure open beauty event sample with a
good acceptance. This will provide a very important cross check for the
gluon polarization measurement with open charm.

Another important physics topic is to study the beauty production
mechanism. Beauty production was measured at the Tevatron at 1.8 TeV,
and the next-to-leading order pQCD calculation underestimated the data
by a factor of 2 or greater. The discrepancy between the experimental
data and the theory has sparked much debate and excitement recently,
including possible hints of new physics beyond the standard model. New
data from polarized *pp* collisions at RHIC will provide crucial
information on the beauty production mechanism, and also possibly point
to new physics.

Figure 31 shows projected experimental sensitivities of double spin
asymmetry measurements if we can identify prompt muons from open charm
and open beauty decay.

![](media/image33.png){width="4.666666666666667in"
height="3.4166666666666665in"}

[]{#__RefHeading___Toc124816781 .anchor}Figure 31 -- Expected size of
double-spin asymmetries (lines) in the observation of single muons from
open charm and bottom production. The projected uncertainties (points
with error bars) are shown for a few values of *p*~T~.

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

There is copious production of light hadrons at RHIC. Figure 32 shows
the muon *p*~T~ spectra with different origins in 200 GeV *pp*
collisions, where it is seen that muons from light charged hadron decay
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 33. Such samples can be used to explore gluon
polarization since they have good statistics and also cover a wide range
of momentum fraction *x*. Figure 34 shows the double spin asymmetry with
charged pions in the PHENIX muon spectrometer acceptance.

![](media/image34.png){width="4.245138888888889in"
height="3.3541666666666665in"}

[]{#__RefHeading___Toc124816782 .anchor}Figure 32 - 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 beauty (red).

![](media/image35.png){width="3.3333333333333335in" height="2.46875in"}

[]{#__RefHeading___Toc124816783 .anchor}Figure 33 - Partonic origin of
charged pions produced within the acceptance of muon spectrometer in pp
collisions at sqrt(s) = 200 GeV.

![](media/image36.png){width="3.5527777777777776in"
height="2.3069444444444445in"}

[]{#__RefHeading___Toc124816784 .anchor}Figure 34 - Model calculation of
double spin asymmetry for charged pions within the muon spectrometer
acceptance.

#### 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 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.

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 35 shows the opposite charge dimuon pair mass spectrum from
run5 *pp* data. The J/ signal clearly stands out from the background.
There were about 7300 J/ candidates from which the double spin asymmetry
was measured, see Figure 36.

![](media/image37.png){width="3.6493055555555554in"
height="2.497916666666667in"}

[]{#__RefHeading___Toc124816785 .anchor}Figure 35 - J/ measurement from
run5 pp run. The J/ peak clearly stands out from the background. The
background fraction is about 25% under the J/ mass peak.

![](media/image38.png){width="3.875in" height="2.7291666666666665in"}

[]{#__RefHeading___Toc124816786 .anchor}Figure 36 - The first
measurement of double spin asymmetry from polarized *pp* collisions at
RHIC.

The majority of the background under the J/ 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/ sample will be
contaminated by J/'s from *B* decay. The proposed forward silicon vertex
detector will help us to improve the prompt J/ signal purity by
rejecting background muon pairs through a cut on displaced vertices
since muons from prompt J/ decay point back to the original collision
vertex. Figure 37 shows the expected asymmetry measurements for prompt
J/ (not from *B* decay) with projected luminosities at RHIC.

![](media/image39.png){width="4.322916666666667in" height="3.3125in"}

[]{#__RefHeading___Toc124816787 .anchor}Figure 37 - Expected
experimental sensitivities of double spin asymmetry measurements with
prompt J/ (not from *B* decay).

### 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 38):

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

Similarly, for *W*, the process is:

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

![](media/image40.png){width="3.3875in" height="3.453472222222222in"}

[]{#__RefHeading___Toc124816788 .anchor}Figure 38 -- W production and
decay to a muon plus a neutrino.

![](media/image41.png){width="5.958333333333333in" height="4.5in"}

[]{#__RefHeading___Toc124816789 .anchor}Figure 39 - Inclusive muon
production showing punch-through hadrons in red.

The main background for a *W* measurement is muons from heavy flavor and
light hadron decay and/or punch-through (Figure 39). The background from
heavy flavor decays 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. This 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 40 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.

![](media/image42.png){width="3.90625in" height="4.583333333333333in"}

[]{#__RefHeading___Toc124816790 .anchor}Figure 40 - Expected flavor
dependent polarized quark distribution functions measured by the PHENIX
muon spectrometers.

### 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 the experiment. The fact that the
nucleon spin composition can be measured directly from 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 led 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 41 shows an NRQCD
prediction for the double spin asymmetry of the J/ in two different
helicity states. Experimentally we can identify the helicity state by
examining the dimuon angular distribution from the J/ decay.

Before using charm and beauty 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 beauty 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 *QQ*
pair[^27]. Present data on charm and bottom production is scarce and of
limited statistics. Data from polarized *pp* collisions at RHIC will
provide critical information about our understanding of heavy quark
production mechanisms.

![](media/image43.png){width="4.719444444444444in"
height="3.839583333333333in"}

[]{#__RefHeading___Toc124816791 .anchor}Figure 41 -- Predicted double
spin asymmetry for charmonium at RHIC. The asymmetry value depends on
the final state charmonium polarization, which can be tested
experimentally.

###  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 beauty 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.

# Simulations and Required Performance for the FVTX Upgrade

The performance requirements for the Si Endcap detector are:

-   Ability to match tracks from a muon arm to hits in multiple layers
    of the Si detector.

-   Sufficient position accuracy in the r-z plane so that the
    displacement resolution of the track with respect to the collision
    point is less than the c of charm and beauty decays, i.e. a
    resolution less than 100m, preferably at the level of \~50 m for
    high momentum muons.

-   Good resolution in both r- and z are required.

-   Sufficient segmentation to operate well in Au-Au and high luminosity
    p+p collisions.

For the simulations we have used a nominal thickness of 1% of a
radiation length for each layer. This includes detector, readout and
cooling in a simplified one-volume effective layer. 1% is achievable
because we are implementing a design that has incorporated a readout bus
in the silicon chips and sensors and we are able to thin the chips. We
are striving to minimize this thickness, in particular for the critical
first disk.

![](media/image44.png){width="4.236805555555556in"
height="2.9458333333333333in"}

[]{#__RefHeading___Toc124816792 .anchor}Figure 42 - Principle of
operation of the 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 42 shows the basic principle of operation of the endcap silicon
detector. A D meson is created at the point 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 50
micron radial pitch. The reconstructed muon track has a small but
non-zero *distance of closest approach* (dca), unlike particles from
pion and kaon decays, which have a much larger average dca.

![](media/image45.png){width="5.961805555555555in"
height="2.8118055555555554in"}

![](media/image46.png){width="5.961805555555555in" height="2.825in"}

[]{#__RefHeading___Toc124816793 .anchor}Figure 43 - Top panels:
Simulated z-vertex resolution (microns) versus muon momentum (in GeV)
and strip width (microns.) For example, with 50 micron strip spacing, a
5 GeV muon provides a z-vertex resolution of \~200 microns. Bottom
panels: The corresponding resolution in terms of distance of closest
approach is about three times smaller. The dca resolution for the 5 GeV
muon is \~ 70 microns.

A simulation of the z-vertex resolution for single muons, as a function
of transverse momentum and strip width is shown in Figure 43. The
simulation includes the beam pipe, the central silicon barrels and the
forward silicon tracker, with \~1% of a radiation length per silicon
layer. The resolution is dominated by multiple scattering at low momenta
and by the silicon strip width at high momenta. Also shown in the figure
are the dca resolutions, which are about a factor of 3 smaller than the
corresponding z-vertex resolutions. These resolution studies do not
include the effects of charge sharing, which could significantly improve
the track resolution.

The endcap mini-strips vary in size from 50m width by 2mm length to 50m
by 13.5mm as the radius increases. The simulated hit density at the
first silicon layer for central collisions is shown in Figure 44. For
50μ×2mm strips at the smallest radii, a density of 7/cm^2^ translates
into occupancy = 0.7%. Accounting for charge sharing and a possible
under-prediction of the total yield of soft charged particles, the
maximum occupancy is expected to be \~1.5% for Au-Au central collisions.

![](media/image47.png){width="4.000694444444444in"
height="3.4145833333333333in"}

[]{#__RefHeading___Toc124816794 .anchor}Figure 44 - 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.

## Charm Measurements

> **Si Endcaps:** $D \rightarrow \mu X$**,**
> $D\overline{D} \rightarrow \mu\text{eX}$**,**
> $D\overline{D} \rightarrow \mu^{+}\mu^{-}X$**,** *J/ ^+^, ' ^+-^*

### Single muons from semi-leptonic D meson decays: $D \rightarrow \mu X$

Each silicon endcap detector has four layers of pixel detectors, which
measure the trajectory of particles within the nominal rapidity
acceptance of the muon arms. The impact parameter of each track is
determined accurately along the Z (beam) direction. For each detected
muon, the impact parameter is used to eliminate muons that come from
pion and kaon decays. These long-lived decays are the primary source of
background muons with transverse momenta below 3 GeV/c. At higher
momenta, hadrons which punch through the nosecone and central magnet
steel are the primary background. These include hadrons which decay in
the muon tracking volume and those that punch through even the steel
layers of the muon identifiers.

Contrasted with these background muons are \"prompt\" single muons,
which come from more short-lived decays, e.g. open charm and beauty. For
transverse momenta below \~5 GeV/c the prompt muons are primarily from
semi-leptonic charm decay. Other processes that produce prompt muons,
such as J/or Drell-Yan decays to muon pairs, have much smaller
cross-sections times branching ratios. Muons from *B* decays become
important only at larger transverse momenta.

The PYTHIA event generator was used to simulate semi-leptonic charm
decays to muons. The total charm pair cross-section of 920 µb is taken
from the PHENIX at 200 GeV[^28]. The decay muons were tracked through
the proposed silicon vertex detector and then through the muon
spectrometer using the PHENIX simulation package PISA. See Appendix C.

The mean vertex of the detected muons from charm decay is 785m from the
interaction vertex. This is \~2.5 times larger than the proper decay
length of semi-leptonic charm decays (m), due to the Lorentz boost. The
impact parameter resolution for these muons ranges from 92 to 115 m,
depending on how many layers of silicon are traversed. By requiring that
the muon vertex is within 1cm of the collision point we remove many of
the muons from pion and kaon decay while retaining prompt muons from
charm and beauty.

Figure 45 shows a simulated muon *p*~T~ spectrum, including charm,
beauty and light quark decays, before the application of a vertex cut.
The background from light quark decays dominates the spectrum below 4
GeV/c. The *p*~T~ distribution of muons that survive a 1 cm vertex cut
is shown in Figure 46. This vertex cut reduces the muon background from
light mesons by about an order of magnitude over what the muon arm alone
can achieve, making a charm measurement possible even at low *p*~T~.
Note that the removal of the muon background from pion and kaon decays
could be achieved with a detector with less spatial resolution. The
resolution requirement is mainly driven by the physics program of
measuring open beauty and rejecting punch-through hadrons (see next
sections).

![](media/image48.png){width="3.8916666666666666in" height="2.79375in"}

[]{#__RefHeading___Toc124816795 .anchor}Figure 45 - Single muon p~T~
distributions for charm, beauty and backgrounds from low-mass meson
decays, as expected for the 2003 d+Au run. Note that the light-meson
decays are above charm up to near 4 GeV/c. The black curve is for pion
and kaon decays, green is charm and red is beauty.

![](media/image49.jpeg){width="3.2715277777777776in"
height="3.2715277777777776in"}

[]{#__RefHeading___Toc124816796 .anchor}Figure 46 - The p~T~
distribution of muons that decay within 1 cm of the collision vertex.
The red histogram is for charm decays while the black is for pion and
kaon decays.

Note that the punch-through hadrons are not shown in the preceding
figures. Estimates of the relative amount of these hadrons versus the
hadron decays and prompt muons are shown in Figure 47. The
punch-throughs can be removed by applying an impact parameter cut to
eliminate tracks originating within one or two sigma of the prompt
vertex. Unlike the loose cut used to eliminate hadron decays in Figure
46, this cut requires good spatial resolution for high momentum tracks.

![](media/image50.jpeg){width="4.575694444444444in"
height="3.0430555555555556in"}

[]{#__RefHeading___Toc124816797 .anchor}Figure 47 - The p~T~
distribution of negative prompt muons, decay muons and punch-through
hadrons at pseudorapidity () = -1.65. The punch-throughs become the
dominant background for p~T~ values above 3 GeV. The curves are
simulations, while the data are PHENIX measurements.

To calculate the yield of charm, we assume a 920 µb D pair cross-section
and an integrated RHIC-II *p+p* luminosity of 33 pb^-1^per week. A total
of \~7x10^7^ semi-leptonic charm decays would be reconstructed. This
rate is before application of a vertex or impact parameter cut.

See details of the rate calculations in Appendix C. Even if a large
pre-scale is required for single muon triggers, the yield is still very
large.

The momentum vector of the charm decay muon is correlated with the
Bjorken-x variables of the two gluons that fused to create the charm
quark pair. x~1~ is primarily correlated with p~Z~ and x~2~ with p~T~ of
the muon. The fitted correlations from PYTHIA are shown in Figure 48.
These can be used to extract model dependent measurements of the gluon
momenta.

Since charm is produced in pairs, coincidence measurements of
opposite-sign lepton pairs may serve to further enhance the signal to
noise in *p+p* and *p+A* reactions. One could use vertex identified
muon-electron coincidences to obtain a clean charm pair signal in the
rapidity interval midway between the PHENIX central and muon arms.

![](media/image51.jpeg){width="3.2715277777777776in"
height="2.4791666666666665in"}

[]{#__RefHeading___Toc124816798 .anchor}Figure 48 - Left panel:
Correlation between x~1~ and p~Z~ of muons from D meson decays (PYTHIA
simulation.) Right panel: Correlation between x~2~ and p~T~.

### Muon Pairs from J/ and ' Decays: J/ ^+^, ' ^+-^

The PHENIX muon spectrometers provide large acceptance for dimuon
events. On the order of 10,000 J/ decays have been reconstructed from
data taken so far. Unfortunately, the precision of the J/ data from
Au-Au interactions is currently limited by the uncertainty in the
background underneath the J/. This background is due to a combination of
decay muons and punch-thru hadrons.

shows the estimated composition of the background in the J/ mass region.
The vertical axis is the ratio of background events containing a decay
muon to the total background. The FVTX detector can eliminate about 60%
of the total background, by rejecting these decay muons. The
punch-through hadrons cannot be easily eliminated by a vertex cut, since
they are prompt. Figure 50 shows a preliminary dimuon mass spectrum for
the most central collisions from Au-Au. The J/ peak is only visible
after background subtraction. A factor of two reduction in the
background under the J/ peak, coupled with an improved mass resolution
described below, would significantly increase the accuracy of the J/
measurement.

Identification of the ' in PHENIX has been hampered by the dimuon mass
resolution and the large backgrounds. Both of these will be improved by
the FVTX. The mass resolution can be improved by measuring the opening
angle of the muon pair before multiple scattering occurs in the nosecone
and central magnet. The resulting improvement in the mass resolution was
shown previously in Figure 9.

![](media/image53.png){width="4.899305555555555in"
height="3.066666666666667in"}

[]{#__RefHeading___Toc124816799 .anchor}Figure 49 -- Fraction of dimuon
pair background containing decay muons versus dimuon mass. At the J/
mass (3.1 GeV), about 60% of the total background contains at least one
decay muon, which can be rejected using the FVTX.

![](media/image54.png){width="4.790277777777778in"
height="3.6118055555555557in"}

[]{#__RefHeading___Toc124816800 .anchor}Figure 50 - PHENIX preliminary
dimuon mass spectrum from 2004 for the most central Au-Au collisions.
Top panel: The red histogram is for opposite sign muon pairs, while the
black histogram is for smoothed like sign pairs. Bottom panel: The
opposite sign spectrum after background subtraction. The peak at 3.1 GeV
is the J/. Note that the signal to background ration is less than 1:10.

### Charm Pair Decays to Dimuons and Electron-muon Pairs: $D\overline{D} \rightarrow \mu^{+}\mu^{-}X$**,** $D\overline{D} \rightarrow \mu\text{eX}$

PHENIX has good acceptance for semi-leptonic charm pair decays. However,
a direct measurement is difficult, due to large numbers of muons from
pion and kaon decays, together with the large backgrounds in the
electron spectra. The FVTX, in combination with the proposed VTX
(central barrel Si tracker), will eliminate most of these backgrounds.
Electron-muon pairs are especially interesting, as they provide unique
rapidity coverage in between the nominal muon and central arm
acceptances.

## Open Beauty Measurement

B meson production, while much less frequent than *D* production, is
somewhat simpler to measure. The challenge is the relatively low rate.
There seem to be at least two possible methods:

-   Since beauty mesons have a larger lifetime than charm mesons,
    especially the D^0^, it is possible to extract the beauty yield from
    the distribution of decay distances of single muons from
    semi-leptonic decays. Figure 51 shows the B meson decay vertex
    distribution, together with a fit to the D meson distribution. In
    addition, at large transverse momentum (above about 5 GeV/c) beauty
    decays are expected to dominate the total muon yield, as shown
    previously in Figure 45.

-   The decay channel *B* J/+X produces J/s that are displaced from the
    collision point by about one mm in Z. The FVTX can separate these
    from the prompt J/

![](media/image55.png){width="3.129166666666667in"
height="3.1395833333333334in"}

[]{#__RefHeading___Toc124816801 .anchor}Figure 51 - The Z-decay length
for semi-leptonic B decays (black histogram). The black line is an
exponential fit to the beauty decays, with an average lifetime of 970
microns. The red line is a fit to the charm decays, with an average
lifetime of 785 microns.

Si Endcaps: $B \rightarrow \frac{J}{\psi} \rightarrow \mu^{+}\mu^{-}$,
$B \rightarrow \mu X$, ^+-^

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

Applying a vertex cut on each reconstructed J/ has been used
successfully to identify B-production in experiments at lower
energies[^29]. Since the B cross-section is larger at RHIC energies, the
measurement should be easier. As the average p~T~ of J/ from beauty
decays is larger than for prompt J/, a p~T~ cut could also be used to
enrich the beauty sample.

Pythia was used to simulate
$B \rightarrow \frac{J}{\psi} \rightarrow \mu^{+}\mu^{-}$ decays. The
resulting muons are tracked through the silicon and muon spectrometers
using PISA. These muons have an impact resolution of \~55 m,
significantly better than muons from D decays, due to their larger
average momentum. The muon pair z-vertex resolution is \~133 m, while
the mean decay length is \~1.1mm. With a downstream pair z-vertex cut of
1 mm, 39% of the B decays are retained, while the prompt J/ are
attenuated by a factor of 2x10^-4^. Figure 52 shows the reconstructed
Z-vertex distribution for the J/ from B decays as well as prompt J/.

The momentum vector of the J/resulting from beauty decay is correlated
with the Bjorken-x variables of the two gluons that fused to create the
beauty pair, just as was shown earlier for the muons from charm decays.
The fitted correlations from PYTHIA are shown in Figure 53. Note that
the x~2~ values are much larger than for charm decays.

We have assumed a total$b\overline{b}$cross-section of 2 microbarns and
4 microbarns for J/production. The branching ratio (BR) of 1.09% for BJ/
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 BJ/ 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. See rate details in Appendix C. Thus, an excellent *B*
measurement is possible.

### Muon Pairs from Upsilon Decays: ^+-^

PHENIX has recently reported the first Upsilon (b-bbar resonance) decay
to dimuons seen at RHIC. These high mass events are at forward
rapidities and have both muons detected in the same muon arm, where the
backgrounds are low. PHENIX can also detect upsilon decays at central
rapidity where one muon goes into the north muon arm and one into the
south. At present these upsilons are not observable due to large
backgrounds from pion and kaon decays. The FVTX will eliminate \~60% of
this background, providing a significant increase in the effective
acceptance for upsilon decays. PHENIX already has a limited acceptance
for upsilon decays to electron pairs, but the yields are presently too
low to be useful.

![](media/image56.jpeg){width="3.5145833333333334in"
height="3.3930555555555557in"}

[]{#__RefHeading___Toc124816802 .anchor}Figure 52 - The reconstructed
Z-vertex distribution for J/ from B decays (black line) and for prompt
J/ (red line). Note that the J/ yield has been scaled down by a factor
of 100. The relative yield of J/ from B decays versus prompt J/is
estimated to be about 1%.

![](media/image57.jpeg){width="3.1in" height="2.3805555555555555in"}

![](media/image58.jpeg){width="3.1in" height="2.38125in"}

[]{#__RefHeading___Toc124816803 .anchor}Figure 53 - Left panel:
Correlation between gluon x1 and p~Z~ of J/ from B meson decays (PYTHIA
simulation.) Right panel: Correlation between x2 and p~T~.

## Heavy Quark Energy Loss and Flow

To be written.

## Trigger Plans

We plan to use the level 1 single and di-muon triggers as the main
physics triggers for the Si Endcaps. For p-p running we envision a level
1 trigger that is based on stand-alone hit information from the endcaps
to select events with a displaced track or vertex. Studies are underway
and the necessary hardware is being developed under the framework of an
SBIR grant recently obtained by Iowa State University. A higher-level
trigger could be based on displace muon tracks, possibly similar to the
triggers used by CDF and E789. These triggers were implemented in
hardware to optimize them for speed. For PHENIX, they could be ported to
trigger level 2.

The algorithm for the Si Endcaps / muon spectrometers could be very
similar to that done previously by E789, described in the following
three steps (translated into PHENIX language):

1\) Muon tracks are found from stubs in the Muon ID and Muon Tracker.
The momentum and angle of each track are determined.

2\) These tracks are then matched to hits in the Si Endcap using a
pre-computed lookup table.

3\) Si hits within the matching window are formed into a Si track stub.
The stub is then fitted with a straight line to determine the momentum,
angle and impact parameter of the track.

The reconstructed events would then be passed to the level 2 triggers of
displaced vertexes and/or high-momentum tracks. For pair triggers,
tracks could be combined and fitted to determine a pair vertex.

## Si Endcap Event Rates

The event yields in the previous sections are summarized below in
Table 1. They assume an integrated p+p luminosity on tape (for Run 10)
of 50 pb^-1^. Yields from a comparable Au-Au run would be about a factor
of 3X lower. The yields for semileptonic heavy quark decays are about an
order of magnitude larger than for the Si Barrel, due to the larger
acceptance of the Si Endcap. The *B* decay rates could benefit from the
increased luminosity in the RHIC II proposal.

[]{#__RefHeading___Toc124816837 .anchor}Table 1 -- 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 semileptonic decay
rates are before application of a vertex cut.

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

  $$D \rightarrow \mu X$$                                       \~ 71M                 \~180M

  $$B \rightarrow \mu X$$                                       \~880k                 \~2.3M

  $B \rightarrow \frac{J}{\Psi X} \rightarrow \mu^{+}\mu^{-}$   \~650                  \~1.7k
  ------------------------------------------------------------- ---------------------- ---------------------

## Matching to Muon Spectrometers 

Track matching between the Si Endcaps and the Muon Spectrometers was
studied by using Hijing Au-Au central collisions in a PISA simulation. A
muon track was embedded in a Hijing event. The muon track was found in
station 1 from the muon tracker by demanding that the muon reached the
middle of the MUID, i.e. the muon energy was \> 2.5 GeV. The
distribution of the muon hits in station 1 was found to be +- 2 cm from
the projection of the Si Endcap track, due to multiple scattering in the
central magnet steel. No other track in the tracker was found to be in a
+- 2cm cut around the muon hit in station 1. We then looked for all
tracks in the Si Endcaps that had their projection fall into the 2 cm
cut about the muon track. In addition to the muon, typically 3 other
tracks fell into this cut. Of these candidate tracks all except the muon
came from the primary interaction vertex. The background would be the
fraction of primary tracks that fall outside of a 1 mm cut in the
z-direction.

## Integration with PHENIX

The proposed Endcap vertex detector matches and extends the capability
of the existing muon spectrometer arms. A central vertex detector for
PHENIX has also been proposed and is currently being reviewed by the
DOE. We are actively investigating the integration of the two detectors,
both in terms of mechanical design and simulated performance. Figure 54
shows the various layers of active silicon 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. Most of those tracks first traverse
one or both of the central barrel silicon pixel layers (areas above the
two blue 'pix hit' lines). Those additional hits will provide useful
track confirmation for the pattern recognition, an improved impact
parameter plus a precise measure of the azimuthal angle of the track,
which the FVTX would otherwise only roughly reconstruct.

In addition a TPC is being proposed to sit outside the vertex detector.
The Detector Advisory Committee recommended studies exploring the impact
of the FVTX on the TPC with the possibility of standalone running for
either detector. Because the Endcaps are outside of the acceptance of
the HBD/TPC we believe that both detectors can operate simultaneously.
(Comment on integration studies already done with the TPC and central
barrel).

![](media/image59.png){width="4.178472222222222in"
height="3.995138888888889in"}

[]{#__RefHeading___Toc124816804 .anchor}Figure 54 - 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 pix hits) 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.

# 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 55 (and Figure 1) show a three
dimensional model of the two detectors, the geometrical parameters are
shown in Table 2. The VTX detector consists of a barrel region and the
two endcap regions enclosed in an environmental enclosure. The
environmental enclosure is needed because the barrel detector must be
operated at 0 deg C. The enclosure radius is 20 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. Generally, the barrel uses 240 deg in phi of the surface
area at the ends while the endcaps use 40 deg at the top and bottom. The
four endcap lampshades contain 48 individual wedge shaped towers mounted
on a carbon composite cooling substrate. Each wedge supports silicon
sensors with readout chips flip chip assembled to the sensors, one on
each side of the cooling substrate so that the acceptance is hermetic in
the radial direction. In addition, adjacent wedges overlap by about one
millimeter to give hermetic coverage in the phi direction. The
technology for the sensors is identical to the patented p-spray ATLAS
detectors with the strips oriented so that the strips nearest the beam
pipe at a radius of 3.5 cm are short, \~2.0mm long in the phi
coordinate, and at the largest radius of 18 cm they are about 13.5 mm
long, i.e. individual strips fan out on from the center of the 7.5 deg
wedge. The maximum occupancy at the inner strip is 1.5%. The total
number of readout strips in each endcap is \~ 860,000. The PHX chips on
each sensor are connected to a flexible kapton bus that takes the data
outside of the enclosure.

![](media/image60.png){width="6.166666666666667in"
height="3.6979166666666665in"}

[]{#__RefHeading___Toc124816805 .anchor}Figure 55 - 3-D model of the
full vertex detector showing the barrel portion and the endcaps on left
and on the right. Also shown is the VTX mounting fixture in the bottom
of the picture.

[]{#__RefHeading___Toc124816838 .anchor}Table 2 - Summary of the
parameters of the FVTX disks.

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

  Geometrical     z (cm)              20.0    26.0      32.0      38.0

  Dimensions      R (cm) inner        3.5     3.5       3.5       3.5

                  R (cm) outer        10.6    14.0      18.0      18.0

  Unit Counts     \# of wedges        48      48        48        48

                  sensors/wedge       2       2         2         2

                  readout chips       6       8         11        11

                  Readout Channels            197k      270k      270k
                  147k                                            

  Radiation       Sensor (300 m)      0.3     0.3       0.3       0.3
  Length                                                          

                  Readout (150 m)     0.2     0.2       0.2       0.2

                  Bus                 0.2     0.2       0.2       0.2

                  Ladder&cooling      0.5     0.5       0.5       0.5

                  total               1.2     1.2       1.2       1.2
  --------------- ------------------- ------- --------- --------- ---------

## Silicon Readout Chip - PHX

A number of candidate chips for the readout of the endcaps were
investigated, most were developed by the Fermi National Lab Electrical
Engineering Department. The ASIC development group is lead by Ray
Yarema. Initially we looked at the LHCb pixel chip developed for the
LHCb experiment (a faster version of the ALICE chip). However, to cover
the acceptance of the muon arms would have taken \~33 x 10^6^ channels.
FNAL Electrical Engineering Department had developed in parallel the
FPIX 2.1 chip, a low-noise programmable Si pixel readout chip for the
recently discontinued BTeV experiment. The chip is an advanced mixed
analog/digital DC-coupled design optimized for a p-sprayed silicon
detector with 50 m by 400 m pixels. The device has very low noise (60
electrons RMS at zero input capacitance) and high-speed readout, up to
840Mbits/. The BTeV data-push technology enables the interfacing to a
level 1 type trigger with order micro second latency. Each channel has
90 uW power. Approximately 3000 FPIX2 chips have been produced in an
engineering run, with a very high yield of fully functional devices.
Test results are very encouraging, with the prototypes demonstrating
excellent performance and minimal crosstalk. The FPIX2 and
specifications are shown in Figure 56.

![](media/image61.png){width="6.135416666666667in"
height="2.7395833333333335in"}

[]{#__RefHeading___Toc124816806 .anchor}Figure 56 - The FNAL FPIX2 pixel
readout chip

The electrical design of the FPIX2 chip is similar to that needed for
the Si Endcap pixels. The main change required is to adapt the physical
chip geometry to accommodate the Endcap sensors larger mini-strips. Ray
Yarema has offered the services of his engineers and facilities to
perform this work. They have already completed a conceptual layout of
the modified PHX readout chip, which is shown in Figure 57.

![](media/image62.png){width="2.1875in" height="2.7916666666666665in"}

[]{#__RefHeading___Toc124816807 .anchor}Figure 57 - Conceptual layout of
the PHX pixel readout chip. The left side graphic depicts the general
layout of the chip. Green is the area for bonding, blue the programming
interface, red the discriminator, orange the pipeline and yellow the
digital interface. The left side graphic shows the bonding layout, the
bump spacing is 200 micron. The signal and power bus will be routed on
the surface on the chip and bonded via the bump bonds on the ends of the
chip.

The proposed conceptual design has the readout and power bus structure
integrated onto the chip itself, simplifying the sensor-readout assembly
process. This has never been done before since detailed simulations are
needed to validate this idea. Preliminary calculations indicate that it
should work. The PHX chip will be bump-bonded to the sensor, with 200 m
bump spacing. This relatively large spacing was chosen to ensure high
yields during the assembly process. Yarema's team has also simulated the
FPIX2 response with input capacitances corresponding to our larger
mini-strips and found it to be acceptable. Design studies of the
equivalent noise charge of the FPIX2 cell including the expected
capacitance of our ministrips have already been done. The results are
shown in . With a nominal capacitance of the mini strips of about 1.5
pf, we would expect an ENC of 300 electrons. For a 300 um sensor (24,000
electrons for a minimum ionizing particle) this would correspond to a
signal to noise of about 75 to 1. The more meaningful ratio is the
signal to threshold ratio because it impacts the noise occupancy. BTeV
was designed to run at a threshold of about 1500 electrons, i.e. a
signal to threshold of about 10 to 1. Optimization of the PHX chip could
improve these figures. The PHX chips have LVDS outputs that are designed
to drive the data cables up to 30 feet.

![](media/image63.png){width="5.373611111111111in"
height="4.083333333333333in"}

[]{#__RefHeading___Toc124816808 .anchor}Figure 58 - The equivalent noise
charge (ENC) versus capacitance.

## Silicon Mini-strip Sensors

We plan on using existing technology for the silicon sensor. Pixel
Sensor technology from the ATLAS and BTeV efforts will have the pixel
layout (masks) modified to match the longer mini-strips that we need.
The sensor technology needed for the modified PHX chip is the n^+^ on n
concept. The pixels consist of n^+^ - implantations in high resistivity
n type silicon while the pn-junction is located on the sensor's backside
surrounded by a multi guard ring structure. An advantage of this type of
sensor compared to the standard p^+^n -- sensors is that it can be
operated partially depleted - if full depletion cannot be reached
anymore due to radiation damage. Also, it keeps the side close to the
pixel chip to be held at ground potential thereby eliminating
potentially disruptive discharges between the sensor and chip.
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 BTeV
sensors are listed below.

**MATERIAL SPECIFICATION:**

Wafer diameter 4 inches (100mm**)**

Crystal orientation \<100\>

Thickness 250 m +10 m --20 m

Uniformity (across wafer) \< 10 m

Wafer bowing after processing \< 50 m (sagitta)

Doping of starting material: n-type

Resistivity: 1.5 -2.5 K cm

Uniformity of resistivity (wafer to wafer) 25%

> Oxygenation: The wafers need to undergo an oxygen thermal diffusion
> process for 24 hours at 1150C

Polishing: Double sided

> Passivation: Covering both sides except for bond pads (both bump and
> wire bond pads) and reference marks. It can either be silicon oxide or
> silicon nitride.

**DESIGN PARAMETERS**

-   Devices shall be n^+^ pixels on n substrate using "moderated
    p-spray" as the n-isolation technology. Note: *This is covered by a
    Non-Disclosure Agreement with six institutes in the ATLAS
    collaboration and three patents held by Garching Innovation.*

-   The full design for the masks will be provided by us in electronic
    form (GDS-2 file)

-   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. Any proposed change to the design must be approved by
    the BTeV pixel group.

-   Mask alignment precision within the same side : 2um

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

-   Processing parameters shall be the same as for the ATLAS production
    moderated p-spray detectors (as covered by the Non-Disclosure
    Agreement and patents mentioned above):

> Front Side (n-side)

1.  N-implantation:

    -   minimum width 5 m

    -   minimum spacing 5 m

2.  P-implantation "moderated p-spray":

    -   minimum width 5 m

    -   minimum spacing 5 m

3.  Contact holes in oxide:

    -   minimum diameter 5 m

    -   minimum spacing 20 m

4.  Metal:

    -   minimum width 8 m

    -   minimum spacing 5 m

5.  Contact holes in passivation:

> \- Minimum diameter 12 m

-   minimum spacing 40 m

-   

Back Side (p-side):

1.  p-implantation:

    a.  minimum width 5 m

    b.  minimum spacing 5 m

2.  Contact via in oxide (or nitride):

    a.  minimum diameter 5 m

    b.  minimum spacing 10 m

3.  Metal:

    a.  minimum width 8 m

    b.  minimum spacing 5 m

4.  Contact via in passivation:

> \- minimum width 50 m
>
> \- minimum spacing 100 m

Three different silicon sensors of trapezoidal shape are used to tile
the active areas of the Si Endcap, as shown in Figure 59. Also shown is
the arrangement of the readout chips on each of the sensors. The largest
sensor is 79 mm high and 27 mm wide at its large end. Six PHX chips are
used to readout the 3072 mini-strips. The smaller sensors contain 2560
and 1536 strips, respectively.

The Si Endcap detector layers are assembled as shown in Figure 60
through Figure 62. First, the sensors are tiled on carbon wedges that
serve as the support and cooling structure for each of the sector
assemblies (Figure 60). Next, 24 sectors are joined to form each of the
four stations (Figure 61). Finally, the four stations are assembled for
each Si Endcap detector (Figure 62). Each Endcap contains approximately
860,000 strips.

![](media/image64.png){width="5.010416666666667in" height="3.6875in"}

[]{#__RefHeading___Toc124816809 .anchor}Figure 59 - Three silicon
detector sizes will be used. The largest will have 6 chips reading out
two rows of 1536 strips, the intermediate silicon will have 5 chips
reading out two rows of 1280 strips and the smallest silicon is half the
size of the largest with 3 chips reading out two rows of 768 strips.
(All dimensions are in millimeter)

![](media/image65.png){width="5.83125in" height="3.3916666666666666in"}

[]{#__RefHeading___Toc124816810 .anchor}Figure 60 - A wedge assembly
will have 24 carbon panels (one shown here in brown) in azimuth, each of
them carrying 4 silicon detectors (blue), two in the front and two in
the back. They overlap on the edges by a few millimeters to avoid dead
areas. The bus on a silicon assembly is routed on the chips as described
above, the connection of the inner silicon detectors is realized via a
kapton bus (golden).

![](media/image66.png){width="6.0in" height="3.3666666666666667in"}

[]{#__RefHeading___Toc124816811 .anchor}Figure 61. Each station carries
24 wedges, i.e. 96 silicon detectors. The stations are placed at \~20,
26, 32 and 38 cm from the interaction point.

![](media/image67.png){width="5.997916666666667in"
height="4.013888888888889in"}

[]{#__RefHeading___Toc124816812 .anchor}Figure 62. Each endcap will have
4 stations of silicon detectors. The inner station has a reduced size in
order to not interfere with other PHENIX detectors.

## Electronics Transition Module

The electronics transition module will take the continuously streaming
data (data-push) from the PHX via flexible cables, 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
Lvl-1 trigger and reformat the data before it is sent to the PHENIX
DCMs. A possible data buffering concept proposed by Dr. C.Y.Chi,
Columbia University, and M.L. Brooks, LANL is shown in Figure 63. The
PHX data with the beam clock counter is routed by an FPGA chip to one of
64 buffers corresponding to the beam clock number. The FPGA than allows
the data from the appropriate beam clock to be sent to a Level 1 trigger
(currently under development by Iowa State University) or to the DCM if
a LV1 trigger accept is received. The existing PHENIX DCMs can be used
without modification. The time to pass all of the data to the Level 1
trigger is expected to be less than 1 us.

![](media/image68.png){width="6.0in" height="3.6166666666666667in"}

[]{#__RefHeading___Toc124816813 .anchor}Figure 63 - The transition
module concept proposed by Columbia.

The buffering requirements of the transition module are expected to be
quite modest with \<50 kbits of data expected in Central AuAu events for
up to 44 chips serviced by the same FPGA. The tracks in the central
region are approximately straight, i.e. a track typically intersects 4
wedges that are located behind each other. Thus 4 stations with 11 chips
each is a natural choice of segmentation. Noise hits are expected to
take even less space. The readout time is expected to be less than 4
beam clocks for Central AuAu events, as we plan to use at least two
readout lines per chip. Some calculations of data sizes and readout
times can be found in Table 3, 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.

<table style="width:100%;">
<colgroup>
<col style="width: 7%" />
<col style="width: 8%" />
<col style="width: 6%" />
<col style="width: 8%" />
<col style="width: 6%" />
<col style="width: 6%" />
<col style="width: 6%" />
<col style="width: 6%" />
<col style="width: 6%" />
<col style="width: 6%" />
<col style="width: 6%" />
<col style="width: 7%" />
<col style="width: 7%" />
<col style="width: 7%" />
</colgroup>
<tbody>
<tr class="odd">
<td>Layers Ganged</td>
<td><p>channels/</p>
<p>chip</p></td>
<td><p>chips/</p>
<p>board</p></td>
<td>channels/ board</td>
<td><p>Occup</p>
<p>ancy</p></td>
<td>Real Hits/ 64 Clocks</td>
<td><p>Real data size</p>
<p>/64 clocks (kbits)</p></td>
<td>Noise</td>
<td>Clocks</td>
<td>Noise Hits/ 64 Clocks</td>
<td>Noise data size/64 clocks (kbits)</td>
<td>Buffer needed for 64 clocks (kbits)</td>
<td>Number of Readout Lines</td>
<td><p>Readout</p>
<p>Time (ns)</p></td>
</tr>
<tr class="even">
<td>1</td>
<td>512</td>
<td>11</td>
<td>5632</td>
<td>0.015</td>
<td>84.48</td>
<td>2.03</td>
<td>0.001</td>
<td>64</td>
<td>360.4</td>
<td>8.7</td>
<td>10.7</td>
<td>1</td>
<td>212.4</td>
</tr>
<tr class="odd">
<td>4</td>
<td>512</td>
<td>44</td>
<td>22528</td>
<td>0.015</td>
<td>337.92</td>
<td>8.11</td>
<td>0.001</td>
<td>64</td>
<td>1441.8</td>
<td>34.6</td>
<td>42.7</td>
<td>1</td>
<td>212.4</td>
</tr>
<tr class="even">
<td>1</td>
<td>512</td>
<td>11</td>
<td>5632</td>
<td>0.015</td>
<td>84.48</td>
<td>2.03</td>
<td>0.001</td>
<td>64</td>
<td>360.4</td>
<td>8.7</td>
<td>10.7</td>
<td>2</td>
<td>106.2</td>
</tr>
<tr class="odd">
<td>4</td>
<td>512</td>
<td>44</td>
<td>22528</td>
<td>0.015</td>
<td>337.92</td>
<td>8.11</td>
<td>0.001</td>
<td>64</td>
<td>1441.8</td>
<td>34.6</td>
<td>42.7</td>
<td>2</td>
<td>106.2</td>
</tr>
<tr class="even">
<td>1</td>
<td>512</td>
<td>11</td>
<td>5632</td>
<td>0.015</td>
<td>84.48</td>
<td>2.03</td>
<td>0.001</td>
<td>64</td>
<td>360.4</td>
<td>8.7</td>
<td>10.7</td>
<td>4</td>
<td>35.3</td>
</tr>
<tr class="odd">
<td>4</td>
<td>512</td>
<td>44</td>
<td>22528</td>
<td>0.015</td>
<td>337.92</td>
<td>8.11</td>
<td>0.001</td>
<td>64</td>
<td>1441.8</td>
<td>34.6</td>
<td>42.7</td>
<td>4</td>
<td>35.3</td>
</tr>
<tr class="even">
<td>1</td>
<td>512</td>
<td>11</td>
<td>5632</td>
<td>0.015</td>
<td>84.48</td>
<td>2.03</td>
<td>0.001</td>
<td>64</td>
<td>360.4</td>
<td>8.7</td>
<td>10.7</td>
<td>6</td>
<td>35.4</td>
</tr>
<tr class="odd">
<td>4</td>
<td>512</td>
<td>44</td>
<td>22528</td>
<td>0.015</td>
<td>337.92</td>
<td>8.11</td>
<td>0.001</td>
<td>64</td>
<td>1441.8</td>
<td>34.6</td>
<td>42.7</td>
<td>6</td>
<td>35.4</td>
</tr>
</tbody>
</table>

[]{#__RefHeading___Toc124816839 .anchor}Table 3 - 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.

## 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 will be
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 provides the mechanical designer 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 mechanical conceptual design
was completed and a report written. Recently, in September 2005, the
original concept was reanalyzed to incorporate changes that have
occurred over the past 2-½ years, a report was issued in October 2005.
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.

### The Enclosure and Environmental Envelope

The original conceptual design was for room temperature operation.
Because of the requirement for 0 deg operation, we now need to include
an environmental enclosure. Shown in Figure 64 is an isometric view of
this new design. The original concept was for an octagonal structural
enclosure uniform in outside radius and this is retained. Added is the
new environmental enclosure to contain the dry gas.

![](media/image69.wmf){width="3.084722222222222in"
height="3.2284722222222224in"}![](media/image70.wmf){width="2.8645833333333335in"
height="3.376388888888889in"}

[]{#__RefHeading___Toc124816814 .anchor}Figure 64 - An isometric view of
the VTX showing all of the internal features coaxial with the beam tube:
(moving out from the beam tube), two cylinders of pixel detectors, two
cylinders of strip detectors, the GRFP structure (gray in color), and
finally, the cylindrical enclosure wall.

### Endcap Ladder Structure

The forward regions consist of 4 conical arrays of ladder modules tilted
from the normal to the beam pipe by 22 deg. Conceptually, we have chosen
a flat octagonal panel structure with sensors and electronics mounted on
either side of the panel so that we can achieve hermetic coverage.
Figure 65 shows this arrangement on the left and an octagon panel
structure on Figure 66.

![](media/image71.jpeg){width="2.501388888888889in"
height="2.220833333333333in"}

[]{#__RefHeading___Toc124816815 .anchor}Figure 65 - 3D model of
octagonal disk like structures for the endcap ministrips. Cooling tubes
are to demonstrate both the number and routing.

![](media/image72.jpeg){width="2.2118055555555554in"
height="2.7527777777777778in"}

[]{#__RefHeading___Toc124816816 .anchor}Figure 66 - The octagon panel
structure is on the right with the cooling channel shown. A heat load of
0.1 W/cm\*\*2 is assumed.

The original concept was designed for a modified LHCb chip with a total
heat load on each endcap of approximately 450 W, or about 15W per octant
panel. The new PHX chip has a heat load of 90 uW per channel so the
total for each end cap now is \~70 W or 2.2 W per octant panel. This
much lower number indicates that convective cooling might be possible.
In comparison to the barrel this is a very small heat load and greatly
simplifies the removal of heat. The octant panel structure consists of a
composite sandwich of C_C facings on either side of a carbon foam in
which is embedded an aluminum cooling tube (Figure 67). Thermal and
gravity sag calculations were performed in a manner similar to those
discussed in chapter 4 and no serious distortions were observed. For the
case of 0 deg Celsius operation, more work is necessary.

![](media/image73.png){width="3.9319444444444445in"
height="2.2104166666666667in"}

[]{#__RefHeading___Toc124816817 .anchor}Figure 67 - Illustration of an
embedded cooling passage arrangement in the composite sandwich used in
the endcap thermal and static calculations. The upper panel depicts a
circular tube with supports and the bottom panel shows a flattened tube
that enhances heat transfer and provides a thinner sandwich.

### Radiation Length

The thermal and static design studies produced a range of solutions for
the endcaps. Figure 68 shows the radiation length estimate for different
cooling tube dimensions. The parameters used in the calculations are:

-   Al tube, 200 micron.

-   4 mm carbon foam separator.

-   Tube support 2 mm wider than tube diameter.

-   Sandwich facings of 400 micron.

![](media/image74.png){width="3.9972222222222222in"
height="2.1840277777777777in"}

[]{#__RefHeading___Toc124816818 .anchor}Figure 68 - Estimated normal
radiation length for the endcap octant panel for different tube
diameters.

## 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. 

-   Two adjacent octant panels can be cooled in series thus reducing
    service connections.

-   2mm cooling tubes and panel thickness are adequate.

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

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

# R+D Schedule, Responsibilities and Budget

## R+D Areas

The R&D associated with the endcaps involves modifying the topology of
the PHX chip, developing the interface between the PHX chip and the
existing PHENIX DCMs, modifying the design of an existing sensor,
developing the wedge structure, and developing the bus and flex cable.
The date 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 PHX
design and modification. All activities will begin in FY2006.

### PHX 

The PHX chip is a modification of the FPIX 2.1 pixel chip used for the
BTeV experiment. The modifications take it from a 22 column x 128 row
structure to a 2 column x 256 channel structure. The R&D issues involve
optimizing the front-end for the mini-strips, designing the built-in bus
structure and incorporating the redesign of the digital section to be
identical to that in the FSSR chip. The novel R&D issue is the integral
bus and will be addressed first.

### Sensor

The sensor will be identical technology that is used in the BTeV sensor
design, which is the same as that used in the ATLAS pixel detector. We
have obtained the design specifications for this sensor. We will produce
new drawings for the 2 column, ministrip layout. The significant R&D
will be to design into the sensor the small bus extension for the daisy
chain from one chip to another.

### Interface

The interface board that will connect between the PHX chip and PHENIX
DCMs will need to provide the following functions:

-   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 AuAu 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 design to be not too much different from a number of
other PHENIX interface boards, containing one or more FPGA to handle the
data buffering and packaging and I/O lines to PHENIX T+FC, DCM, ARCnet
(or equivalent) and to the PHX chip readout lines. The FPGA code
development will take several months, as has been standard for PHENIX.
We are hoping that we can begin development on the code even in the
absence of the final PHENIX interface board as we already have an
FNAL-designed Xilinx FPGA board which can nominally provide all the I/O
lines needed to develop the code that has the needed functions. We have
organized a team with members from Columbia, Iowa State and LANL to
address this portion of the project.

## Schedule

The schedule for the FTVX project is shown in Figure 69. 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 first 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/image75.png){width="5.997916666666667in"
height="4.272916666666666in"}

![](media/image76.png){width="5.997916666666667in"
height="4.272916666666666in"}

[]{#__RefHeading___Toc124816819 .anchor}Figure 69 -- 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 4 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 PHX chip came from the
FNAL engineers who designed the FPIX2 chip. The HYTEC engineering team
previously designed the ATLAS pixel mechanical structures 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 Nov. 2005 and on drawings of
the wafers with the FVTX wedges (Figure 70) The contingency analysis
method is listed in Appendix A.

![](media/image77.wmf)

[]{#__RefHeading___Toc124816840 .anchor}Table 4 -- Cost estimate for the
FVTX endcaps with contingency. The methodology used for contingency is
in Appendix A.

![](media/image78.jpeg){width="6.0in" height="3.3in"}

[]{#__RefHeading___Toc124816820 .anchor}Figure 70 - Silicon wafer layout
used for wedge sensor cost estimate.

### 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 in Figure 71.

![](media/image79.wmf)

[]{#__RefHeading___Toc124816821 .anchor}Figure 71 -- Organizational
Chart for the FVTX project.

Institutional Responsibilities

Los Alamos National Laboratory

LANL coordinate work to procure the silicon sensors, work with FNAL on
the development of the PHX chip, with Columbia on 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.

Columbia University

Columbia University is an acknowledged expert on the PHENIX DAQ system.
They will work on the interface between the PHX chip and the PHENIX DAQ.

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.

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.

Ecole Polytechnique, Saclay

Ecole Polytech has contributed to the electronics and software for the
muon system has expressed interest in doing the same for the FVTX.
Saclay will work on software. 

Yonsei University, Seoul, Korea

The Yonsei group has worked on electronics and software for the muon
system and will do the same for the FVTX.

Argonne National Laboratory

Argonne National Laboratory is not a member of PHENIX, but is
considering joining to work on the spin physics program and the FVTX. We
will want them to manage and coordinate all activities at FNAL.

# Appendix A

## Contingency Analysis

The average contingency for the FVTX is 27 %.

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 from  No schedule    Not used
             modifications to   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 experience non-critical   done; some
                                                   subsystem item analysis done

  6          New design;        In-house estimate  Not used       Not used
             different from     for item with                     
             established        minimal experience                
             designs or         but related to                    
             existing           existing                          
             technology         capabilities                      

  8          New design;        In-house estimate  Delays         Conceptual
             requires some R&D  for item with      completion of  design phase;
             but does not       minimal experience critical path  some drawings;
             advance the\       and minimal        subsystem item many sketches
             state-of-the-art   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___Toc124816841 .anchor}Table 5 - 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___Toc124816842 .anchor}Table 6 - Technical, cost,
schedule and design weighting factors.

# Appendix B. Level 1 Trigger {#appendix-b.-level-1-trigger .unnumbered}

Iowa State University (ISU) is developing hardware for a level 1 trigger
to be used with the FVTX. This hardware is not included in the cost and
schedule of the FVTX proposal.

-   []{#__RefHeading___Toc124816735 .anchor}Estimate of the Level 1
    Trigger Rejection Factor

We set the trigger such that the z-coordinate of the decay is displaced
from the z-coordinate of the collision vertex by 0.015cm \<
Zdecay-Zvertex \< 0.2cm. The lower limit is chosen to be several times
the position resolution so that few tracks from the collision vertex are
misidentified as decaying particles, while the upper limit is chosen to
be several times the lifetime of charmed particles with typical momenta
at RHIC. The resulting estimated rejection factor is 25 for Au+Au
collisions simulated into the acceptance of one endcap.

-   []{#__RefHeading___Toc124816736 .anchor}Summary of Level 1 Prototype
    Trigger Hardware

ISU is developing a prototype level-1 trigger board in conjunction with
Northern Microdesign Inc via the STTR program. In the Phase I STTR, they
developed a proof-of-principle FPGA-board that tracked particles in
hardware using input signals from a simulated collision between two Au
nuclei at RHIC. The simulated data was preloaded into the RAM of the
device. A collision vertex was calculated from these tracks as well as
the distance of closest approach (DCA) from each track to the collision
vertex. This DCA could be used to trigger the experiment, e.g., if an
event contains a track with a large DCA, then that event could contain
the decay of a rare charm or beauty particle. In hardware, this
proof-of-principle FPGA-board calculated the DCAs from a full Au+Au
event within 1.5 microseconds, within the time budget allowed for the
first-level trigger in the PHENIX experiment at RHIC. ISU and Northern
Microdesign have since been awarded a Phase II STTR and are planning to
produce a prototype trigger board with multiple FPGAs that would receive
data from the FVTX DAQ interface board.

-   []{#__RefHeading___Toc124816737 .anchor}Estimated Cost of Level I
    Trigger

450k\$

#  {#section-1 .unnumbered}

#  {#section-2 .unnumbered}

# Appendix C. Estimates for Rates and Triggers for the PHENIX FVTX {#appendix-c.-estimates-for-rates-and-triggers-for-the-phenix-fvtx .unnumbered}

## Cross sections, branching ratios and acceptances:

### D μ 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 μ 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/image80.wmf){width="5.996527777777778in"
height="3.640972222222222in"}

[]{#__RefHeading___Toc124816822 .anchor}Figure 72 - Cross section
calculatations for beauty with FONNL for various parameters from Ramona
Vogt.

Which gives a single-beauty 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/ X

We use the 4 μb cross section for B given above.

For the combined branching ratio we use 1.094% (B J/X) and 5.9% (J/ 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/X of 39%.

## Luminosities

We use the RHIC-II luminosities from T. Roser as given at,

<http://www.phenix.bnl.gov/phenix/WWW/publish/leitch/rhicii-forward/RHIC_II_Luminosity_Roser.xls>

[]{#__RefHeading___Toc124816843 .anchor}Table 7 - 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       ...           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                                

                     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___Toc124816844 .anchor}Table 8 - 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

## 

## 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 Roser luminosities

-   Lowering the single-muon momentum threshold to 2.6 GeV from 2.5 GeV.

[]{#__RefHeading___Toc124816845 .anchor}Table 9 - Comparison of new and
old values for variouse parameters used in these rate calculations.

  ------------ -------- --------- --------- --------- ------------- -----------
               D μ X              B μ X               B J/ 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% • 5.9% 1.2% • 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

[]{#__RefHeading___Toc124816846 .anchor}Table 10 - Estimated rates per
week for p+p collisions.

  --------------------------- ------------------------ ----------------------- ---------------------- ------------------------ -------------------------- -------------------------- --------------------------- ----------------------------- -------------------------
  **pp**                      **ccbar**                                                                                                                                                                                                        

                              **sigma**                **1-arm**                                      **Lumi**                 **Lumi**                                              **with**                                                  **with**

  **[process]{.underline}**   **[(ub)]{.underline}**   **[Acc]{.underline}**   **[BR]{.underline}**   **[Type]{.underline}**   **[(pb-1)]{.underline}**   **[counts]{.underline}**   **[reality]{.underline}**   **[eff_dzvtx]{.underline}**   **[dzvtx]{.underline}**

  D -\> mu                    920                      0.0232                  0.119                  RHIC-II                  33                         3.4E+08                    7.1E+07                     1                             7.1E+07

                              920                      0.0232                  0.119                  2008                     9.9                        1.0E+08                    2.1E+07                     1                             2.1E+07

  B -\> mu                    2                        0.145                   0.1087                 RHIC-II                  33                         4.2E+06                    8.8E+05                     1                             8.8E+05

                              2                        0.145                   0.1087                 2008                     9.9                        1.2E+06                    2.6E+05                     1                             2.6E+05

  B -\> J/Psi                 2                        0.046                   0.00065                RHIC-II                  33                         7.9E+03                    1.7E+03                     0.39                          6.5E+02

                              2                        0.046                   0.00065                2008                     9.9                        2.4E+03                    5.0E+02                     0.39                          2.0E+02
  --------------------------- ------------------------ ----------------------- ---------------------- ------------------------ -------------------------- -------------------------- --------------------------- ----------------------------- -------------------------

[]{#__RefHeading___Toc124816847 .anchor}Table 11 - Estimated rates per
week for d+Au collisions.

  --------------------------- ------------------------ ----------------------- ---------------------- ------------------------ -------------------------- -------------------------- --------------------------- ----------------------------- -------------------------
  **dAu**                     **ccbar**                                                                                                                                                                                                        

                              **sigma**                **1-arm**                                      **Lumi**                 **Lumi**                                              **with**                                                  **with**

  **[process]{.underline}**   **[(ub)]{.underline}**   **[Acc]{.underline}**   **[BR]{.underline}**   **[type]{.underline}**   **[(nb-1)]{.underline}**   **[counts]{.underline}**   **[reality]{.underline}**   **[eff_dzvtx]{.underline}**   **[dzvtx]{.underline}**

  D -\> mu                    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 -\> mu                    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/Psi                 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___Toc124816848 .anchor}Table 12 - Estimated rates per
week for Au+Au collisions.

  --------------------------- ------------------------ ----------------------- ---------------------- ------------------------ -------------------------- -------------------------- --------------------------- ----------------------------- -------------------------
  **AuAu**                    **ccbar**                                                                                                                                                                                                        

                              **sigma**                **1-arm**                                      **Lumi**                 **Lumi**                                              **with**                                                  **with**

  **[process]{.underline}**   **[(ub)]{.underline}**   **[Acc]{.underline}**   **[BR]{.underline}**   **[type]{.underline}**   **[(nb-1)]{.underline}**   **[counts]{.underline}**   **[reality]{.underline}**   **[eff_dzvtx]{.underline}**   **[dzvtx]{.underline}**

  D -\> mu                    920                      0.0232                  0.119                  RHIC-II                  2.5                        9.9E+08                    1.8E+08                     1                             1.8E+08

                              920                      0.0232                  0.119                  2008                     0.327                      1.3E+08                    2.4E+07                     1                             2.4E+07

  B -\> mu                    2                        0.145                   0.1087                 RHIC-II                  2.5                        1.2E+07                    2.3E+06                     1                             2.3E+06

                              2                        0.145                   0.1087                 2008                     0.327                      1.6E+06                    3.0E+05                     1                             3.0E+05

  B -\> J/Psi                 2                        0.046                   0.00065                RHIC-II                  2.5                        2.3E+04                    4.3E+03                     0.39                          1.7E+03

                              2                        0.046                   0.00065                2008                     0.327                      3.0E+03                    5.7E+02                     0.39                          2.2E+02
  --------------------------- ------------------------ ----------------------- ---------------------- ------------------------ -------------------------- -------------------------- --------------------------- ----------------------------- -------------------------

## Trigger considerations

### Rejection factors

For pp triggers we use Lajoie's estimate from run5 data and simulations
of of 478 (1-deep), 23500 (1-deep & 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
10^4^ rejection for 1d1s dimuons (south arm).

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.

These are all 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.

[]{#__RefHeading___Toc124816849 .anchor}Table 13 - Level-1 muon trigger
rejection factors for pp and AuAu based on previous data and simulations
of the level -1 triggers.

  ------------- ---------- ---------------- ------------------- ----------------
  **Species**   **Arm**    **Source**       **Trigger**         **Rejection
                                                                factor**

  **pp**        N          Run5 & sims      1-deep              580

                           "                1-deep & 1-shallow  28700

                           "                2-deep              20000

                S          "                1-deep              376

                           "                1-deep & 1-shallow  18300

                           "                2-deep              67000

                N&S avg    "                1-deep              478

                           "                1-deep & 1-shallow  23500

                           "                2-deep              133500

  **AuAu**      N          Sim on run4 prdf 1-deep              5.1

                           "                1-deep & 1-shallow  5.3

                           "                2-deep              15.3

                S          "                1-deep              4.8

                           "                1-deep & 1-shallow  5.3

                           "                2-deep              16.1

                N&S avg    "                1-deep              5

                           "                1-deep & 1-shallow  5

                           "                2-deep              15.7
  ------------- ---------- ---------------- ------------------- ----------------

### Trigger rates and needed rejection factors

For these estimates we will use a 2d dimuon trigger in AuAu and a 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.
\[We need an estimate of how much the event size will increase given
various upgrades including the FVTX.\]

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 arm 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___Toc124816850 .anchor}Table 14 -- Estimated trigger
rates and addition rejection factors needed for p+p and Au+Au collisions
in PHENIX.

  ------ ----------------------- -------------------------- ------------------------------ ---------------------------- ----------------------- ------------------------ ------------------------- ------------------------ -------------------------- ------------------------ ------------------------ --------------------------
                                                                                                                                                                         **1d**                                             **1d**                     **1d1s**                                          **1d1s**

                                 **lumi/wk**                                               **lumi pk**                  **MB pk rate**          **evt size**             **pk rate**               **1d**                   **prescale**               **pk rate**              **1d1s**                 **prescale**

         **[era]{.underline}**   **[(pb-1)]{.underline}**   **[zvtx\<10cm]{.underline}**   **[(10\^32)]{.underline}**   **[Mhz]{.underline}**   **[(kb)]{.underline}**   **[(khz)]{.underline}**   **[Mb/s]{.underline}**   **[needed]{.underline}**   **[(hz)]{.underline}**   **[Mb/s]{.underline}**   **[needed]{.underline}**

  pp     RHIC-II                 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

                                                                                                                                                                                                                                                                                                         

                                                                                                                                                                         1d                                                 **1d**                     **2d**                                            **2d**

                                 **lumi/wk**                                               **lumi pk**                  **MB pk rate**          **evt size**             **1d pk rate**            **1d**                   **prescale**               **pk rate**              **μμ**                   **prescale**

         **[era]{.underline}**   **(nb-1)**                 **[zvtx\<10cm]{.underline}**   **[(10\^26)]{.underline}**   **[khz]{.underline}**   **[(kb)]{.underline}**   **[(khz)]{.underline}**   **[Mb/s]{.underline}**   **[needed]{.underline}**   **[(hz)]{.underline}**   **[Mb/s]{.underline}**   **[needed]{.underline}**

  AuAu   RHIC-II                 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
  ------ ----------------------- -------------------------- ------------------------------ ---------------------------- ----------------------- ------------------------ ------------------------- ------------------------ -------------------------- ------------------------ ------------------------ --------------------------

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