***Forward/pA Physics at RHIC-II Whitepaper***

***January 26, 2006***

***Convenors:***

***Carl Gagliardi***

***Mike Leitch***

***and Kirill Tuchin***

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

[2 Gluon Saturation and Shadowing 4](#gluon-saturation-and-shadowing)

[3 Forward Hadron Suppression in d+Au Collisions
15](#forward-hadron-suppression-in-dau-collisions)

[4 Heavy Quarks at Forward Rapidity
16](#heavy-quarks-at-forward-rapidity)

[5 Forward Tagged Processes 26](#forward-tagged-processes)

[5.1 Tagged Drell-Yan Processes 26](#tagged-drell-yan-processes)

[5.2 Tagged Forward Protons 27](#tagged-forward-protons)

[6 Anti-quark distribution in nuclei at small x
27](#anti-quark-distribution-in-nuclei-at-small-x)

[7 Ultra-peripheral Processes 28](#ultra-peripheral-processes)

[8 Double Parton Correlations 30](#double-parton-correlations)

[9 Comparison of RHIC-II and LHC Heavy-ion programs
31](#comparison-of-rhic-ii-and-lhc-heavy-ion-programs)

[10 RHIC Detector Upgrades 31](#rhic-detector-upgrades)

[10.1 PHENIX Upgrades 31](#phenix-upgrades)

[10.1.1 Muon Trigger Upgrade 31](#muon-trigger-upgrade)

[10.1.2 Silicon Vertex Detector 33](#silicon-vertex-detector)

[10.1.3 Nose Cone Calorimeter 36](#nose-cone-calorimeter)

[10.2 STAR Upgrades 37](#star-upgrades)

[10.2.1 Forward Silicon Tracker 38](#forward-silicon-tracker)

[10.2.2 Forward Calorimeter? 38](#forward-calorimeter)

[11 Appendix: Rates for Forward and p(d)+A Processes
39](#appendix-rates-for-forward-and-pda-processes)

[12 Appendix: Top-down Physics Charts
40](#appendix-top-down-physics-charts)

**List of Figures**

[Figure 1 - Kinematic space of QCD. Arrow points out to the novel high
parton density regime of cold nuclear matter, the Color Glass
Condensate, which arises at small x and/or large nuclei.
5](#__RefHeading___Toc126071334)

[Figure 2 - Kinematic regions of high energy QCD.
8](#__RefHeading___Toc126071335)

[Figure 3 - Gluon production amplitude in p(d,γ^∗^) Α collisions in
terms of the fan-diagrams. 9](#__RefHeading___Toc126071336)

[Figure 4 - Prediction of CGC for the total charged particle
multiplicity in dAu collisions. 10](#__RefHeading___Toc126071337)

[Figure 5 - Calculations based on CGC versus RHIC experimental data. One
can see transition from the quasiclassical regime at midrapidity to the
quantum evolution regime at forward rapidities.
10](#__RefHeading___Toc126071338)

[Figure 6 - (see caption to Figure 5) 11](#__RefHeading___Toc126071339)

[Figure 7 - Depletion of two particle correlations due to gluon
saturation. 11](#__RefHeading___Toc126071340)

[Figure 8 - Enhancement of Cronin effect with rapidity as predicted by
the rescattering models. 12](#__RefHeading___Toc126071341)

[Figure 9 - Rapidity asymmetry ratio. 13](#__RefHeading___Toc126071342)

[Figure 10 - A parameterization of gluon shadowing.
13](#__RefHeading___Toc126071343)

[Figure 11 -- Preliminary measurement by PHENIX of prompt muons (from
charm and beauty decays) in the foward rapidity or small-x region (red)
and in the backward rapdity region (blue).
17](#__RefHeading___Toc126071344)

[Figure 12 - STAR $D \rightarrow K\pi$ signal in d+Au collisions at 200
GeV/c. 18](#__RefHeading___Toc126071345)

[Figure 13 - J/ψ and ψ\' suppression from E866/NuSea^,^ compared to
calculations from R. Vogt showing the many ingredients invoked to
explain the dramatic x~F~ dependence of the observed suppression.
20](#__RefHeading___Toc126071346)

[Figure 14 - J/ψ suppression at √S=200 GeV from PHENIX vs rapdity
compared to model calculations from R. Vogt for EKS shadowing and
different $c\overline{c}$absorption cross sections in the final state.
21](#__RefHeading___Toc126071347)

[Figure 15 -- Preliminary results for the nuclear modification factor in
AuAu and CuCu collisions from PHENIX vs centrality for forward and
central rapidity compared to CNM calculations consistent with those
shown in the previous figure (Figure 14).
22](#__RefHeading___Toc126071348)

[Figure 16 - Comparision of J/ψ nuclear suppression for three different
beam energies showing the lack of scaling vs x~2~ and approximate
scaling seen vs x~F~. 23](#__RefHeading___Toc126071349)

[Figure 17 - Ratio of central to peripheral yields per binary collision
for d+Au collisions comparison between J/ψ's (PHENIX) and light hadrons
from Brahms and PHENIX. A similar pattern is seen with a small
enhancement at negative rapidity (Au direction) and suppression at
postitive rapidity (d direction and small-x shadowing region).
24](#__RefHeading___Toc126071350)

[Figure 18 - Preliminary PHENIX ϒ results at forward and backward
rapidity (red) from 200 GeV p+p collisions compared to measurements at
other energies vs energy. 25](#__RefHeading___Toc126071351)

[Figure 19 -- Simulation of the neutron-tagged Drell-Yan process where
the muons are detected in the PHENIX muon arms and the neutron in a
small-angle calorimetet (e.g. the PHENIX ZDC).
26](#__RefHeading___Toc126071352)

[Figure 20 -- J/ψs produced in ultraperipheral Au+Au collisions at RHIC
from PHENIX. 30](#__RefHeading___Toc126071353)

[Figure 21 - PHENIX Muon Trigger upgrade (one arm shown) with its RPC
planes shown in black, existing muon tracking detectors in red. The
primary interaction region is at the right-center of the figure.
33](#__RefHeading___Toc126071354)

[Figure 22 - PHENIX Silicon Vertex Detector Upgrade including the
forward vertex detector (FVTX) and central barrel vertex detector (VTX).
34](#__RefHeading___Toc126071355)

[Figure 23 - The reconstructed Z-vertex distribution for J/ψ from B
decays (black line) and for prompt J/ψ (red line). Note that the J/ψ
yield has been scaled down by a factor of 100. The relative yield of J/ψ
from B decays versus prompt J/ψ is estimated to be about 1%.
35](#__RefHeading___Toc126071356)

[Figure 24 - Mass spectra for the J/ψ and ψ\', 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/ψ and ψ' in this plot represents our
expectation for a \~25 pb^-1^ p+p run. 36](#__RefHeading___Toc126071357)

[Figure 25 - PHENIX Nose Cone Calorimeter (NCC) upgrade (purple).
37](#__RefHeading___Toc126071358)

[Figure 26 - STAR Forward Silicon Tracker upgrade.
38](#__RefHeading___Toc126071359)

[Figure 27 - STAR ? upgrade. 38](#__RefHeading___Toc126071360)

[Figure 28 - Top-down physics chart for gluon saturation and shadowing
in nuclei. 40](#__RefHeading___Toc126071361)

[Figure 29 - Top-down physics chart for anti-quark distributions in the
nucleon sea (Jen-Chieh Peng). 41](#__RefHeading___Toc126071362)

**List of Tables**

[Table 1 - Rates for the PHENIX forward vertex detector (FVTX) in one
week of running. Integrated luminosities are 33 pb^-1^ for p+p, 62
nb^-1^ for d+Au, and 2.5 nb^-1^ for Au+Au (RHIC-II) and 9.9 pb^-1^ for
p+p, 2.8 nb^-1^ for d+Au and 0.33 nb^-1^ for Au+Au (RHIC-I, 2008). The
semileptonic decay rates are before application of a vertex cut.
19](#__RefHeading___Toc126071363)

[Table 2 - Beam energies, $E_{\text{beam}}$, Lorentz factors,
$\gamma_{L}$, photon cutoff energy in the center of mass frame,
$k_{\text{max}}$, and in the nuclear rest frame, $E_{\text{max}}$, and
equivalent nucleon-nucleon center of mass energy,
$\sqrt{S_{\text{max}}}$, for *AA* collisions at RHIC.
28](#__RefHeading___Toc126071364)

# Executive Summary

The suppression of various processes in p(d)+A collisions at forward
rapidity is usually thought to be caused by shadowing or saturation of
the gluons in nuclei for the small momentum fraction (x) region.
Shadowing is a depletion of the structure functions in the small-x
region thought to result from coherence effects on the process of
interest that depend on the momentum of the incoming parton or by
saturation of the population of the small-x gluons[^1] that may cause
two-to-one gluon diagrams to depopulate the smallest x gluons and
possibly enhance those at moderate x values (anti-shadowing). The
shadowing of quark distributions is well established from deep inelastic
scattering measurements, but that for the gluons largely comes from only
the Q^2^ evolution of these same measurements and so is poorly known
experimentally. Theoretical models for gluon shadowing are numerous and
differ both in their underlying physics and, by large factors, in the
predicted amount of gluon shadowing[^2]^,^[^3]^,^[^4]. Underlying
physics ideas include the coherence effects and gluon saturation
mentioned already, but also may involve energy conservation effects
(Sudakov suppression), energy loss in the initial state of the incoming
gluons or partons, or mass renormalization effects. These fundamental
physics ideas abound and overall leave a rather unsettled picture for
which processes are truly important and control the fundamental dynamics
of partons (gluons) in nuclei. In addition they are not well constrained
by present experimental measurements and there is a strong need for more
precise measurements that will isolate and constrain these fundamental
physic issues. Since these intrinsic properties of the gluons in nuclei
provide the initial state for nucleus-nucleus collisions, it is also
critical to understand them in order to obtain a clean baseline for the
study of hot-dense matter effects in nucleus-nucleus collisions, e.g. in
the study of the Quark Gluon Plasma.

It has also been observed that the production of many types of particles
at forward rapidity appear to follow a universal suppression pattern
with even hadrons at different energies following this trend (in the
rapidity gap from the kinematical limit), often called limiting
fragmentation[^5], although it is not clear what physics might be the
source of such a phenomena.

At RHIC our measurements explore the onset of this shadowing or
saturation, while at the LHC most measurements will lie deep in the
saturation region. We believe that studying the onset will be key to
understanding the saturation phenomena and that studies at RHIC and
RHIC-II will be complementary and supporting for those at the LHC. At
the LHC the p+A program is still considered an upgrade especially in
terms of running the accelerator for these collisions and we are not
likely to see such collisions until 2010 at the earliest. In addition,
it is likely to be quite difficult to run p+A collisions a the LHC given
that only approximately one month a year will be devoted to "heavy ion"
running and that the p+A running (along with all the heavy-ion running)
will have to come out of this time.

Some of the most compelling physics questions are:

-   Shadowing or saturation of the gluon densities at small-x and
    pinning down the underlying physics that controls these phenomena
    with precise measurements of a wide range of observables.

-   Power corrections in open charm production (Vitev and Qiu)[^6].

-   Study of limiting fragmentationError: Reference source not found,
    Sudakov suppression[^7] and other phenomena that may also be key
    ideas in the behavior of particle production in p(d)+A collisions at
    forward rapidity.

-   Parton recombination pictures that also provide an explanation for
    the forward-rapidity suppression[^8].

-   Quantifying the energy loss and multiple scattering of partons in
    cold nuclear matter.

-   Disentangling the complicated physics puzzle for J/ψ suppression in
    cold nuclear matter using accurate and robust measurements of both
    open- and closed-charm (J/ψ and ψ'); and similarly for beauty
    production and ϒ's.

-   Searching for mono-jets as a signature of gluon saturation[^9].

-   Double-parton correlations from 4-jet yields[^10] which can only be
    done with p+A collisions.

-   Processes tagged with forward neutrons or protons to isolate the
    structure of the nucleon's meson cloud or to explore gluon-rich
    states via Pomeron exchange

-   Ultra-peripheral collisions which provide a theoretically clean
    probe, e.g. of the gluon distributions in nuclei via J/ψ
    production[^11].

The most compelling measurements that will need RHIC-II luminosities
are:

-   Heavy-quark measurements are rare processes and require the highest
    luminosities to obtain the accuracy and reach needed to isolate the
    fundamental physics questions of interest. In particular J/ψ and ϒ
    measurements and also measurement of b-mesons via B → J/ψ X and
    d-mesons via D → Kπ

-   Ultra-peripheral collision measurements, which without much higher
    luminosities than presently available, will remain very low
    statistics measurements and of little value for quantitative
    studies.

-   Forward nucleon-tagged measurements which are inherently low-rate
    and need the highest luminosities possible. \[are these even
    possible at RHIC-II?\]

-   Double parton correlations via 4-jet events which clearly require
    the highest luminosites. \[what are the rates?\]

\[Most compelling physics that can benefit from RHIC-II luminosities
compared to RHIC-I with and w/o detector upgrades; and comparison to LHC
of these processes.\]

A number of critical detector upgrades to the large RHIC detectors will
also be necessary in order to effectively pull off these measurements
and provide the wide range of accuate and robust measurements necessary
to pin down the fundamental physics questions. These include:

-   The PHENIX Silicon Vertex detector, with the VTX at central rapidity
    (\|y\|\<1) and the FVTX at forward and backward rapidity
    (1\<\|y\|\<2.2), will enable precise measurements of open-charm and
    beauty and improve signal-to-noise and resolution for numerous other
    measurements.

-   The PHENIX Nose Cone Calorimeter (NCC) which will provide
    calorimetry in the forward and backward rapidity regions and allow
    measurements in the 1\<\|y\|\<3 rapidity region of direct photons to
    probe the gluons and χ~C~ → J/ψ γ to provide the χ~C~ part of the
    J/ψ puzzle.

-   The PHENIX Muon Trigger upgrade which will allow triggering at
    RHIC-II luminosities on very high momentum muons - in particular for
    those coming form the decay of W mesons, but also providing fast
    triggering momentum information that will allow the level-1 triggers
    necessary to capture many of the processes discussed here at RHIC-II
    luminosoties.

-   The STAR Forward Meson Spectrometer (FMS)

-   The STAR Forward Tracker (with GEM's)

-   Upgrades of the data-acquisition and triggering systems for both
    detectors to allow capture of all the processes of interest in the
    highest luminosity RHIC-II running.

-   Additional additions to our detector arsenal, e.g. to allow tagging
    with very forward protons using Roman pots.

The convenors of this working group are Carl Gagliardi, Mike Leitch and
Kirill Tuchin. A number of other people have been involved in the
meetings and discussions, these include: Tony Baltz, Les Bland, Ramiro
Debbe, Tony Frawley, Wlodek Guryn, Yuri Kovchegov, Pat McGaughey,
Jen-Chieh Peng, Peter Steinberg, and Ramona Vogt. Because of the highly
parallel nature of the various RHIC-II Science Physics working groups,
it was difficult to involve many members of the community who had
involvement in the other groups; and also for those involved in our
group, especially the convenors to fully participate in the discussion
of the other groups. We also note that many of the physics topics that
are important here were also discussed in other groups, most notably the
heavy-quark group which has a large overlap with ours.

In this document we include 1) this executive summary, 2) followed by
several sections discussing the most compelling physics areas in more
detail, then next 3) a discussion of the upgrades for the RHIC detectors
and their role in achieving the physics, 4) a comparision with the LHC
program, and then two appendices giving a) selected rate estimates for
RHIC-II measurements, and b) the "top-down" physics charts that were
formulated by our working group.

# Gluon Saturation and Shadowing

Perturbation theory plays the key role in establishing Quantum
Chromodynamics as the theory of strong interactions. It has been very
successful in describing particle production in processes with high
momentum transfer. It relies on the collinear factorization theorems
which allow separation of the short distance processes calculable using
the standard methods of perturbation theory and the non-perturbative
long distance processes. The basic idea is that the short and long
distance processes become incoherent when the momentum transfer becomes
sufficiently large. The long distances processes can be parameterized by
the universal distribution functions which depend on the momentum scale
Q^2^ and Bjorken variable x. Once a distribution is measured as a
function of x at a given value Q~0~^2^ its evolution at higher values of
Q^2^ is determined by the DGLAP evolution equations.

Despite its tremendous success at short distances, perturbation theory
describes only a small part of the full QCD. In fact, it does not allow
us study the beautiful non-linear structure of QCD. This structure
reveals itself at long distances where the coupling becomes strong not
allowing for systematic theoretical treatment. However, this structure
can be accessed also at small x where the fields become strong while the
coupling is weak. Alternatively, strong fields at weak coupling can be
created in processes with large nuclei.

The first signatures of the new regime of QCD came from the Deep
Inelastic Scattering experiment at HERA. It has been observed that the
gluon and sea quark distributions grow very fast with decreasing x. This
fast growth can be understood in pQCD as driven by radiation of gluons
with small Bjorken x via DGLAP evolution equations. Radiated gluons form
a *high parton density system* which cannot be described using the
collinear factorization scheme due to strong coherence effects. There is
a more fundamental reason to abandon the collinear factorization at
small x and/or large nuclei: the fast growth of parton distribution
functions cannot continue forever since it would lead to growth of
hadronic cross sections at a rate which would violate unitarity. This
necessitates extension of the pQCD framework to include the nonlinear
effects of parton recombination and saturation.

![](media/image1.wmf){width="4.629861111111111in"
height="3.9770833333333333in"}

[]{#__RefHeading___Toc126071334 .anchor}Figure 1 - Kinematic space of
QCD. Arrow points out to the novel high parton density regime of cold
nuclear matter, the Color Glass Condensate, which arises at small x
and/or large nuclei.

**Quasiclassial approximation**

Color Glass Condensate formalism is the natural generalization of pQCD
in order to make it applicable to dense partonic systems[^12]. It
provides a consistent way of systematic treatment of high energy parton
evolution and the nuclear coherence effects. Coherence effects start to
play a significant role in a scattering process at small x. When the
parton coherence length l~c~ in the projectile proton (deuteron) becomes
larger than the size of the target nucleus R

$l_{c} = \frac{1}{2m_{N}x} > R$ Equation 1

the projectile interacts coherently with all nucleons along its path
through the nucleus. Here m~N~ is a nucleon mass. In this situation the
total cross section is given by the sum over all possible interactions
of p(d) with any number of nucleons. Such interactions are suppressed in
the weak coupling regime. However, if the nucleus is sufficiently heavy
so that α~s~^2^A^1/3^\~1, then these interactions are large. They can be
resumed if we note that the parton distribution in the projectile does
not evolve during the interaction with the nucleus if l~c~\>\>R. In
particular, it is convenient to consider a projectile as a collection of
color dipoles with certain transverse sizes r~t~. The size of each such
dipole is fixed during the interaction. The forward scattering amplitude
of a (q anti-q) dipole on a nucleus is then given by the Glauber-Mueller
formula

$N(Y,r_{\hat{},b_{\hat{}) = 1 - \text{exp}}}$ Equation 2

where Y=ln(1/x) and we introduced the following notation

$Q_{s}^{2} = \frac{\alpha_{s}p^{2}}{2N_{c}}\rho T(b_{\hat{})\text{xG}_{N}(x,\frac{1}{r_{{\hat{}}^{2})}}}$
Equation 3

with T(b) being the nuclear profile function, and xG~N~ the gluon
distribution in a nucleon taken at some fixed value x. The momentum
scale Q~s~ is called the saturation scale since the scattering amplitude
reaches its unitarity limit (saturates) at N=1for dipoles r~t~\>1/Q~s~.
The ratio of N(x,r~t~,b) and the first term in its expansion at small
α~s~ is always smaller than 1. Therefore, Equation 2 effectively sums up
"shadowing corrections" due to multiple rescattering of the projectile
in the nucleus. Smallness of the coupling is ensured by the existence of
the hard scale Q~s~. Phenomenological analysis of the particle
production at RHIC gives Q~s~=1-2GeV which is large enough to keep the
coupling small α~s~(Q~s~)\<\<1. The total p(d)A cross section can be
calculated by convoluting Equation 2 with the parton distributions in a
proton (deuteron).

Equation 2 makes it possible to include the coherence effects in p(d)A
collisions at not very small x. Indeed, it is derived neglecting
possible emission of a gluons and quark--antiquark pairs in the high
energy projectile. It is this emission which leads to fast increase of
the gluon and sea quark distribution functions observed in γ^∗^p
collisions at HERA. Parametrically, each emitted gluon gives
contribution of the order of α~s~ln(1/x) to the scattering amplitude and
can be neglected if x\>exp(-α~s~). Therefore, one usually refers to
Equation 2 as the quasiclassical approximation to the scattering
amplitude valid for the following values of x:

$e^{- \alpha_{s}} < x < \frac{1}{2m_{N}R}$ Equation 4

Similarly, we can consider gluon or light quark production in p(d)A
collisions. Due to large coherence length of a low x gluon, its
radiation in a projectile wave function occurs way before (or after) the
interaction with the target. The radiation kernel is well-known in pQCD
and is given by (in the coordinate space)

$\frac{\alpha_{s}C_{F}}{p}\frac{r_{\text{01}}^{2}}{r_{\text{20}}^{2}r_{\text{21}}^{2}}$
Equation 5

where 0,1 are the coordinates of the initial quark and antiquark and 2
is the coordinate of the emitted gluon in the transverse plane.
Scattering of each dipole in a system of quark, antiquark, and gluon is
given by Equation 2. The cross section for the gluon production in p(d)A
collisions is

$\frac{ds}{d^{2}\text{kdy}} = \frac{1}{p}\int_{}^{}{d^{2}\text{bd}^{2}\text{rd}^{2}z\frac{1}{(2p)^{2}}\frac{\alpha_{s}C_{F}}{p}\frac{r \cdot z}{r^{2}z^{2}}}e^{- \text{ik}_{t} \cdot (r - z)}\left\lbrack N_{G}(0,r,b) + N_{G}(0,z,b) - N_{G}(0,r - z,b) \right\rbrack$
Equation 6

where N~G~ is the gluon dipole scattering amplitude taken at some
initial rapidity Y=0.

This formula can be cast in a more traditional form using the
unintegrated gluon distribution φ(x,q~t~) function

$\varphi(x,q_{t}) = \frac{C_{F}}{\alpha_{s}(2\pi)^{3}}\int_{}^{}{d^{2}\text{bd}^{2}\text{ze}^{- \text{iq}_{t} \cdot z}\nabla_{z}^{2}N_{G}(y = - \text{ln}x,z,b)}$
**Equation 7**

The inclusive cross section takes then the k~T~-factorized form

$\frac{d\sigma}{d^{2}\text{kdy}} = \frac{2\alpha_{s}}{C_{F}k^{2}}\int_{}^{}{d^{2}{q\varphi}_{p}(y = 0,q)\varphi_{A}(y = 0,k - q)}$
Equation 8

An important feature of the quasiclassical approximation is that the
transverse momentum of the projectile dipoles gets redistributed in
course of multiple rescattering in the nucleus. This property follows
from the following sum rule

$\int_{}^{}{d^{2}\text{kk}^{2}\frac{{d\sigma}^{\text{pA}}}{d^{2}\text{kdy}} = A}\int_{}^{}{d^{2}\text{kk}^{2}\frac{{d\sigma}^{\text{pp}}}{d^{2}\text{kdy}}}$
Equation 9

Multiple rescattering tends to increase the transverse momentum of the
projectile. Since the typical transverse momentum transfer is Q~s~^2^ ,
production of gluons with momentum k\~ Q~s~ is enhanced in pA collisions
as compared to pp ones. Equation 9 implies then suppression of soft
gluon production in pA collisions. In experimental data this
redistribution of particle momentum is known as the Cronin effect.
Therefore, appearance of the Cronin enhancement is a necessary feature
of the quasiclassical regime of CGC.

**High energy quantum evolution**

As the energy of the collision increases, the multiple gluon radiation
becomes parametrically large. A gluon radiated with the light-cone
momentum fraction x\<exp(-α~s~) contributes at the order α~s~y\~1 to the
scattering amplitude. Radiation of a gluon at rapidity Y+∆Y leads to
change in the amplitude ∆N(Y,r~t~,b). There are two physical processes
contributing to increase of the amplitude: multiplication of gluons
proportional to α~s~N and recombination proportional to -α~s~N^2^. The
Balitsky-Kovchegov evolution equation takes both processes into account

$\frac{\partial N(Y,r_{t})}{\partial Y} = \frac{\alpha_{s}C_{F}}{\pi^{2}}\int_{}^{}{\text{dx}_{2}\frac{x_{\text{01}}^{2}}{x_{\text{12}}^{2}x_{\text{20}}^{2}}\left\lbrack N(Y,x_{\text{02}}) + N(Y,x_{\text{12}}) - N(Y,x_{\text{01}}) - N(Y,x_{\text{02}})N(Y,x_{\text{12}}) \right\rbrack}$
Equation 10

This equation has been derived in the large Nc approximation and
neglecting target correlations. Together with the initial condition
Equation 2 it allows to calculate the forward amplitude of the
dipole-nucleus scattering at high energies.

As the result of the evolution of the amplitude N at high energies the
average gluon momentum acquires its energy and rapidity dependence

$Q_{s}^{2} = \Lambda^{2}A^{\frac{1}{3}}(\frac{s}{s_{0}})^{\frac{\lambda}{2}}e^{\lambda y}$
Equation 11

The line Q=Q~s~(s,y) divides the kinematic plane (Q^2^,y) into two
regions. The saturation region Q\<\<Q~s~(s,y) in which the scattering
amplitude is close to unity and the dilute region Q\>\>Q~s~(s,y) in
which the effect of multiple rescattering described by the nonlinear
term in the Equation 10 is small. Solution to Equation 10 exhibits a
remarkable property of 'geometric scaling': in the saturation regime the
amplitude N depends on x and Q only via one dimensionless parameter Q/
Q~s~ in agreement with the low x experimental data at HERA.

.

![](media/image2.wmf){width="4.372916666666667in"
height="3.3291666666666666in"}

[]{#__RefHeading___Toc126071335 .anchor}Figure 2 - Kinematic regions of
high energy QCD.

Condition N\<\<1 is necessary for the applicability of the collinear
factorization theorems. However, it is not sufficient since the low x
evolution in the vicinity of the saturation boundary is still driven by
the BFKL dynamics. Transition from BFKL to DGLAP dynamics happens when
α~s~y\~α~s~ln(Q~s~/ Q~s0~)\<α~s~ln(Q/Q~s~), i.e. Q\>Q~s~^2^/ Q~s0~.
Since the amplitude N geometrically scales along Q=Q~s~(s,y) and the LO
BFKL equation is conformally invariant, N also geometrically scales in
the wide kinematic region Q\<k~geom~ = Q~s~^2^/ Q~s0~. A more accurate
estimation yields for the boundary of the 'extended geometric region'

$k_{\text{geom}} = Q_{s}(Y)\left( \frac{Q_{s}(Y)}{Q_{s0}} \right)^{0\text{.}\text{34}}$
Equation 12

The kinematic plane of high energy QCD is shown in Figure 2.

Inclusive gluon production cross section can be written in a
k~T~-factorized form similar to Equation 8

$\frac{d\sigma}{d^{2}\text{kdy}} = \frac{2\alpha_{s}}{C_{F}k^{2}}\int_{}^{}{d^{2}{q\varphi}_{p}(Y - y,q)\varphi_{A}(y,k - q)}$
Equation 13

where φ now depend on energy and rapidity. The typical gluon production
amplitude (squared) is shown in Figure 3.

![](media/image3.wmf){width="3.2430555555555554in"
height="2.2534722222222223in"}

[]{#__RefHeading___Toc126071336 .anchor}Figure 3 - Gluon production
amplitude in p(d,γ^∗^) Α collisions in terms of the fan-diagrams.

While in the quasiclassical approximation (not very small x, see
Equation 4) the inclusive gluon cross section satisfies the sum rule
Equation 9, it breaks down at low x when the evolution effects become
important. It opens a possibility of suppression of nuclear modification
factor R~pA~ for gluon production in the extended geometric scaling
region. In the saturation region the main physics mechanism of R~pA~
suppression is multiple rescattering of a gluon in the nucleus. In the
extended geometric scaling region, higher twist terms (Q~s~/k)^2n^ are
small. However, the anomalous dimension of the unintegrated gluon
distribution function of nucleus near the saturation boundary is about
½. In the same kinematic region, gluon distribution in proton has the
anomalous dimension about 1. This reflects itself in the peculiar
dependence of the nuclear modification factor on A: R~pA~ \~A^-1/6^.

A detailed analysis yields

$R_{\text{pA}} \approx A^{- 0\text{.}\text{124}} < 1$ Equation 14

Suppression of the nuclear modification factor Equation 14 due to
dependence of the anomalous dimension of the gluon distribution function
on energy and rapidity can be refereed to as the 'leading twist
shadowing'.

One can think of the Color Glass Condensate approach as of a theory of
leading and higher twist shadowing based on pQCD (in the sense of weak
coupling). Phenomenological approaches based on CGC are successful in
describing the low x DIS data. In particular, we should mention
prediction of the geometric scaling, description of diffractive
processes and fit of the structure functions. In dA collisions the
experimental data on hadron production are in agreement with the CGC
predictions, see Figures 4,5,6

![](media/image4.wmf){width="2.6277777777777778in"
height="2.6041666666666665in"}

[]{#__RefHeading___Toc126071337 .anchor}Figure 4 - Prediction of CGC for
the total charged particle multiplicity in dAu collisions.

![](media/image5.wmf){width="6.131944444444445in"
height="1.6368055555555556in"}

[]{#__RefHeading___Toc126071338 .anchor}Figure 5 - Calculations based on
CGC versus RHIC experimental data. One can see transition from the
quasiclassical regime at midrapidity to the quantum evolution regime at
forward rapidities.

![](media/image6.wmf){width="6.131944444444445in"
height="1.7652777777777777in"}

[]{#__RefHeading___Toc126071339 .anchor}Figure 6 - (see caption to
Figure 5)

Equation 8 describes a single gluon production. This process is
kinematically permitted due to transverse momentum dependence of the
unintegrated gluon distributions φ. For gluons with transverse momentum
much larger then the typical transverse momentum transfer Q~s~ Equation
9 reduces to the familiar collinear factorized result. However, bulk of
gluons are produced as monojets. This implies depletion of the
back-to-back correlations which are inherent to the QCD processes at
very high momentum. This depletion is enhanced at higher
energies/forward rapidities as shown in Figure 7.

![](media/image7.png){width="2.379166666666667in"
height="2.2743055555555554in"}

[]{#__RefHeading___Toc126071340 .anchor}Figure 7 - Depletion of two
particle correlations due to gluon saturation.

Other inclusive channels such as heavy quark, quarkonium and dilepton
production can be calculated in the same framework provided that the
coherence length of the considered probe is much larger than the nucleus
size. Heavy quark production by a classical color fields is of special
theoretical interest. Large mass m of a quark justifies application of
perturbation theory regardless of the value of Q~s~ . Thus we can study
the onset of the classical regime of QCD as Q~s~ approaches m as well as
production of heavy quarks in saturated medium Q~s~ \>\>m. Production
pattern of light and heavy quarks in strong color fields is the same.
Therefore one expects similar suppression effect on heavy quarks at
Q~s~\>\>m.

**Alternative approaches**

As has been already discussed, there is a certain kinematic region,
Equation 4, where small x evolution effects are small and multiple
rescattering of a projectile in a nucleus accounts for the observed
particle spectra. One can try to extend this approach to higher
energies/rapidities. Momentum transfer in each individual
projectile-nucleon scattering is proportional to the parton density
which is increasing function of 1/x. Therefore, the average momentum
gained by the rescattering parton increases with energy/rapidity
implying enhancement of the Cronin effect: both the position and the
height of the maximum increase as shown in Figure 8.[^13]

![](media/image8.png){width="3.15625in" height="4.276388888888889in"}

[]{#__RefHeading___Toc126071341 .anchor}Figure 8 - Enhancement of Cronin
effect with rapidity as predicted by the rescattering models.

This model is suitable for description of the Cronin effect at
midrapidity. However, its failure at forward rapidities implies that
there must be an additional suppression in the parton distribution
function itself.

The forward-backward rapidity asymmetries of hadron production in dAu
collisions shown in Figure 9 (three lower curves) is another prediction
of a rescattering model improved by inclusion of a nuclear shadowing
effect[^14]. Again, it seems that the data favors the CGC shadowing
mechanism (upper two curves).

![](media/image9.png){width="4.416666666666667in"
height="3.348611111111111in"}
![](media/image10.png){width="3.0027777777777778in" height="2.275in"}

[]{#__RefHeading___Toc126071342 .anchor}Figure 9 - Rapidity asymmetry
ratio.

It has been suggested by Kopeliovich at. al.[^15] that the observed
suppression of the nuclear modification factor at midrapidity is a
consequence of the rapid decrease of the phase space available for gluon
production at x~F~→1. This fragmentation effect is energy independent.
On the contrary, the effect of gluon saturation increases with energy
which provides a clear experimental handle to distinguish between the
two physics mechanisms.

Another set of models uses traditional collinear factorization approach
to particle production in pA collisions. The shadowing effect is then
parameterized by the A-dependent parton distribution functions [^16], as
shown in Figure 10.

![](media/image11.png){width="3.7465277777777777in"
height="2.5861111111111112in"}

[]{#__RefHeading___Toc126071343 .anchor}Figure 10 - A parameterization
of gluon shadowing.

However, it was argued in [^17] that none of existing shadowing
parameterizations can describe the magnitude of experimentally observed
suppression.

In the case of ptoton-heavy nucleus collisions one can extend the pQCD
analysis of particle production in the framework of the collinear
factorization by summing up all higher twist terms of the type
(ξ^2^Α^1/3^/Q^2^)^N^ where ξ^2^ ∼α~s~ is a non-perturbative matrix
element proportional to xG[^18]. The resumation parameter in this
approach is α~s~A^1/3^\~1 (compared to α~s~^2^A^1/3^\~1 in CGC). The
result can be written in a collinear factorized form with the shift of
Bjorken variable x→x(1+ξ^2^(A^1/3^-1)/Q^2^) which leads to a net
suppression of the cross sections. Approach of Ref.7 fills the gap
between the leading twist collinear factorization picture and the CGC.

It was suggested in [^19] that parton recombination may play an
important role in particle production at RHIC. In particular, parton
recombination in the final state may be responsible for the suppression
of the nuclear modification factor at forward rapidity.

This idea deserves further investigation.

**Future experimental studies**

The RHIC experimental data from dA and AA collisions seems to favor the
discovery of

a new form of cold nuclear matter. RHICII offers a unique possibility to
confirm this discovery and study properties of the new form of nuclear
matter. The following experimental studies are of great importance:

-   Particle production at high transverse momentum. The higher
    transverse momentum, the better we know how to take into account the
    non-perturbative processes such as parton fragmentation.

-   Two particle correlations. Depletion of particle correlations is a
    very important signal of CGC, see Figure 6.

-   Charm and charmonium production at forward rapidities. The effect of
    quantum evolution in open charm production may be seen already at
    rapidity 2-3 at RHIC.

-   Electromagnetic signatures: photon and dilepton production offer a
    more precise tools to study the quantitative aspects of QCD matter
    at high energies.

# Forward Hadron Suppression in d+Au Collisions

![](media/image12.png){width="2.6666666666666665in"
height="2.5131944444444443in"}

![](media/image13.png){width="4.6194444444444445in"
height="2.579861111111111in"}

# Heavy Quarks at Forward Rapidity

Heavy quarks provide an important tool for accessing gluon distributions
since they are produced primarily through diagrams involving gluons,
mainly gluon fusion. In p(d)+A collisions they give a window into the
gluon distribution in "cold nuclear matter" (CNM) and thus can provide a
measure of the shadowing or saturation of the gluon distributions in
nuclei.

Heavy quarks are created early and therefore sample the entire evolution
of the collision. In heavy-ion collisions their momentum distributions
can then be used to measure their energy loss in the high-density matter
created in those collisions, while in p(d)+A collisions we can set a
baseline on this energy loss for CNM. In addition, the
multiple-scattering of the gluon in the initial state -- sometimes
called the Cronin effect, can be seen in the broadening of the p~T~
distributions of the heavy quark or of their bound states.

Another group in this study, the Heavy-Quark RHIC-II Science working
group, has concentrated on the complete heavy-quark picture for all
kinds of collisions, so here we will focus mainly on their study in
p(d)+A collisions.

Open charm and beauty, presently, are accessed primarily through their
decays to leptons (electrons or muons). These measurement rely on a
statistical subtraction of background sources, i.e. for electrons the
other sources of electrons including π^0^'s, photon conversions, etc are
subtracted in a so-called "cocktail" analysis; while for muons the
copious backgrounds from light hadrons decays and hadrons that "punch
through" the absorbers of the muon identifier are substracted. This
results in large systematics due to the knowledge of the subtracted
backgrounds. A preliminary measurement from PHENIX with muons in the
forward and backward rapidity regions is shown in Figure 11, where a
suppression for the forward rapidity is seen. Also shown, in Figure 12
is the $D \rightarrow K\pi$ signal seen in the STAR detector.

![](media/image14.png){width="4.627777777777778in"
height="4.164583333333334in"}

[]{#__RefHeading___Toc126071344 .anchor}Figure 11 -- Preliminary
measurement by PHENIX[^20] of prompt muons (from charm and beauty
decays) in the foward rapidity or small-x region (red) and in the
backward rapdity region (blue).

![](media/image15.png){width="4.722916666666666in"
height="5.616666666666666in"}

[]{#__RefHeading___Toc126071345 .anchor}Figure 12 - STAR
$D \rightarrow K\pi$ signal[^21] in d+Au collisions at 200 GeV/c.

Future detector upgrades to allow explicit observation on an
event-by-event basis of the small but finite decay distance of the charm
or beauty mesons are planned, but to reach large momenta and adequately
separate charm and beauty in these spectra will require higher
luminosity runs. In particular, explicit measurements of the process B →
J/ψ X will be important in measuring the B cross section independently
so that the then known B cross section can be used to separate out the
beauty and charm contribution to the single lepton spectra. As can be
seen in Table 1, large luminosities will be required to get substantial
numbers of B → J/ψ X events, and to extend the single-lepton
measurements to larger p~T~ values.

[]{#__RefHeading___Toc126071363 .anchor}Table 1 - Rates for the PHENIX
forward vertex detector (FVTX) in one week of running. Integrated
luminosities are 33 pb^-1^ for p+p, 62 nb^-1^ for d+Au, and 2.5 nb^-1^
for Au+Au (RHIC-II) and 9.9 pb^-1^ for p+p, 2.8 nb^-1^ for d+Au and 0.33
nb^-1^ for Au+Au (RHIC-I, 2008). The semileptonic decay rates are before
application of a vertex cut.

  -------------------------------------------------------------- --------------- ------------- --------------- ------------- --------------- -------------
                                                                 **p+p                         **d+Au                        **Au+Au         
                                                                 counts/week**                 counts/week**                 counts/week**   

  **Observable**                                                 **RHIC-I**      **RHIC-II**   **RHIC-I**      **RHIC-II**   **RHIC-I**      **RHIC-II**

  $$D \rightarrow \mu X$$                                        84M             21M           2.7M            60M           24M             180M

  $D \rightarrow \mu X$, 4\<p~T~\<5 GeV                          3.1k            10k           400             8.8k          3.5k            27k

  $$B \rightarrow \mu X$$                                        260k            880k          33k             740k          300k            2.3M

  $B \rightarrow \mu X$, 4\<p~T~\<5 GeV                          2.7k            9.1k          340             7.6k          3.1k            24k

  $B \rightarrow \frac{J}{\Psi X} \rightarrow \mu^{+}\mu^{-}$    200             650           25              550           220             1.7k
  -------------------------------------------------------------- --------------- ------------- --------------- ------------- --------------- -------------

The suppression in p(d)+A collisions remains a complicated physics
puzzle with a number of different effects that may contribute to the
complex pattern observed in fixed target measurements and at RHIC. The
x~F~ dependence of the suppression for J/ψ and ψ' from
E866/NuSea[^22]^,^[^23] is shown in Figure 13 along with model
calculations from R. Vogt[^24]. In this model a large number of physics
ingredients are included in order to explain the data. Alternative
explanations include modelsError: Reference source not found where
Sudakov suppression, an energy conservation effect, operates to force an
increasing suppression as one approaches x~F~ = 1.

![](media/image16.png){width="4.847222222222222in"
height="4.981944444444444in"}

[]{#__RefHeading___Toc126071346 .anchor}Figure 13 - J/ψ and ψ\'
suppression from E866/NuSeaError: Reference source not
found^,Error:\ Reference\ source\ not\ found^ compared to calculations
from R. VogtError: Reference source not found showing the many
ingredients invoked to explain the dramatic x~F~ dependence of the
observed suppression.

These measurements of J/ψ suppression have now been extended to RHIC
energies by PHENIXError: Reference source not found, as shown in Figure
14 compared to model calculations from R. VogtError: Reference source
not found using the EKSError: Reference source not found shadowing
prescription and different absorption cross sections for the final-state
$c\overline{c}$.

Clearly, with the statistics available so far, this data is not able to
constrain the absorption cross sections very well. The importance of
such constraints from d+Au collisions in establishing a baseline in A+A
collisions, where we look for effects beyond the cold nuclear matter
(CNM) effects seen in d+Au collisions from the QGP, can be seen in
Figure 15. Without a more accurate baseline from d+Au collisions one
cannot conclude that the A+A collisions show suppression beyond that
from CNM except at the highest centralities.

A higher luminosity d+Au (or p+Au) run will be necessary in the near
future in order to allow a clearer analysis of the A+A results, as well
as to pin down the physics of the fundamental processes (e.g. gluon
shadowing, intitial-state gluon energy loss, final-state $c\overline{c}$
absorption) that cause these CNM effects.

![](media/image17.jpeg){width="4.236805555555556in"
height="4.6305555555555555in"}

[]{#__RefHeading___Toc126071347 .anchor}Figure 14 - J/ψ suppression at
√S=200 GeV from PHENIX[^25] vs rapdity compared to model calculations
from R. Vogt[^26] for EKSError: Reference source not found shadowing and
different $c\overline{c}$absorption cross sections in the final state.

![](media/image18.jpeg){width="6.131944444444445in"
height="4.906944444444444in"}

[]{#__RefHeading___Toc126071348 .anchor}Figure 15 -- Preliminary results
for the nuclear modification factor in AuAu and CuCu collisions from
PHENIX[^27] vs centrality for forward and central rapidity compared to
CNM calculations consistent with those shown in the previous figure
(Figure 14).

Another outstanding part of the physics puzzle for J/ψ production in
p(d)+A collisions follows from the fact that the suppression pattern
does not scale with x~2~ as one would expect if the dominant physics
effect was nuclear shadowing or saturation. As shown in Figure 16 the
nuclear suppression from PHENIXError: Reference source not found at 200
GeV, E866/NuSeaError: Reference source not found at 39 GeV and NA3[^28]
at 19 GeV is not universal in x~2~ but, at least for the lower energy
results that span a large range in x~F~, show an approximate scaling in
x~F~. This suggests that the dominant physics behind the suppression
pattern is not shadowing or gluon saturation. As mentioned before, one
interpretation from Kopeliovich et al.Error: Reference source not found
is that instead the universal suppression at large x~F~ may be caused by
Sudakov suppression. Roughly speaking, this picture says that one must
exclude more inelastic processes as one approaches the kinematic limit
(x~F~ = 1) and that since these potential inelastic processes become
more copious in a nucleus this effect is stronger in a nucleus and
causes the observed increasing suppression as one approaches x~F~ = 1.

![](media/image19.png){width="5.252777777777778in"
height="3.7215277777777778in"}

[]{#__RefHeading___Toc126071349 .anchor}Figure 16 - Comparision of J/ψ
nuclear suppression for three different beam energies showing the lack
of scaling vs x~2~ and approximate scaling seen vs x~F~.

It is also interesting to note that the trends vs rapidity seen in J/ψ
suppression are similar to those seen for light hadrons, as shown in
Figure 17. This suggests a common underlying physics effect such as the
Sudakov suppression mentioned above, or the phenomena discussed in the
interpretation of PHOBOS data called "limiting fragmentation"Error:
Reference source not found.

![](media/image20.jpeg){width="5.5in" height="4.729861111111111in"}

[]{#__RefHeading___Toc126071350 .anchor}Figure 17 - Ratio of central to
peripheral yields per binary collision for d+Au collisions comparison
between J/ψ's (PHENIX) and light hadrons from Brahms and PHENIX. A
similar pattern is seen with a small enhancement at negative rapidity
(Au direction) and suppression at postitive rapidity (d direction and
small-x shadowing region).

Finally, in Figure 18, we show preliminary results for ϒ production from
PHENIX in the forward and backward rapidity regionsError: Reference
source not found. These measurements are severely limited by the small
cross section for ϒ's and clearly need the higher luminosity of RHIC-II
to both improve the statistics of the signal and to allow better
determination of the background including that from Drell-Yan pairs.

![](media/image21.png){width="5.052777777777778in"
height="5.245833333333334in"}

[]{#__RefHeading___Toc126071351 .anchor}Figure 18 - Preliminary PHENIX ϒ
results[^29] at forward and backward rapidity (red) from 200 GeV p+p
collisions compared to measurements at other energies vs energy.

# Forward Tagged Processes

## Tagged Drell-Yan Processes

An interesting possibility at RHIC-II is the study of the tagged
Drell-Yan process in which Drell-Yan di-leptons are accompanied by an
energetic neutron or proton carrying a large fraction of the incident
proton beam momentum. Such a process is the hadronic analog of the
diffractive DIS process observed recently at HERA[^30]. In the HERA
experiment, the DIS was tagged by a forward-going neutron or proton.
These tagged DIS events can be interpreted as virtual photons scattering
off the pion cloud (or pomeron) of the proton beam. The pion stricture
function can be extracted from such measurements.

It is natural to extend the HERA measurement to other hard-processes
tagged by forward-going nucleons. Of particular interest is the tagged
Drell-Yan, which could provide new insight on the origin of the flavor
asymmetry of the nucleon sea. The large
$\frac{\overline{d}}{\overline{u}}$ asymmetry observed in Drell-Yan
measurements[^31] was attributed to the presence of meson cloud in the
nucleon. A tagged Drell-Yan measurement would allow a direct
determination of the meson cloud. A simulation for the p + p → μ^+^μ^-^
X for the PHENIX detector, where the muon pairs are detected in the muon
arms and the neutrons are detected by a small-angle calorimeter (such as
the Zero Degree Calorimeter), has been carried out and the result is
shown in Figure 19.

![](media/image22.png){width="3.501388888888889in"
height="3.501388888888889in"}

[]{#__RefHeading___Toc126071352 .anchor}Figure 19 -- Simulation of the
neutron-tagged Drell-Yan process where the muons are detected in the
PHENIX muon arms and the neutron in a small-angle calorimetet (e.g. the
PHENIX ZDC).

The forward tagging capability could lead to many other measurements not
feasible in the fixed-target experiments. For example, one could
consider tagging the forward-going ∆ or λ. The λ-tagging is of special
interest since it can shed light on the strange-quark contents of the
proton. Another possibility is the measurement of the double-helicity
asymmetry, A~LL~, in tagged the $\overrightarrow{p}\overrightarrow{p}$
Drell-Yan process. Since the underlying process involves the proton-pion
interaction, A~LL~ is expected to be zero. The doubly-tagged Drell-Yan
process, which involves the pion-pion interaction, can also be
contemplated. Finally, it is natural to extend tagged Drell-Yan
measurement to tagged J/ψ production.

## Tagged Forward Protons

Wlodek Guryn?

# Anti-quark distribution in nuclei at small x

In the past decade, quark shadowing at small *x* has been very well
characterized experimentally in DIS[^32]. The experimental signature is
that the DIS cross section ratio falls below unity for
$x \leq 0\text{.}\text{08}$. Theoretically, shadowing has been studied
extensively in the past 10 years[^33].

Quark shadowing is also expected in hadronic processes. To date, the
only experimental evidence for shadowing in hadronic reactions is the
reduction in the nuclear dependence seen in the Drell-Yan experiments
E772[^34] and E866[^35]. The lowest *x* covered in these experiments is
*x* = 0.04, just below the onset of shadowing effect.

Shadowing in the *p+A* Drell-Yan process is largely due to antiquarks in
the nucleus, unlike in DIS where both quarks and antiquarks can
contribute. Although shadowing effects are expected for antiquarks,
there is no known requirement that they be identical[^36] to those for
quarks. There exists no experimental information on the antiquark
shadowing at small *x* (*x* \< 0.04). The coverage in *x~2~* will be
significantly extended at RHIC. In particular, the lowest *x~2~*
reachable at RHIC is around 10^-3^, a factor of 40 lower than in E772.
Therefore, nuclear shadowing effect of antiquarks can be well studied at
PHENIX using the muon arms and possibly the Nose Cone Calorimeter (NCC)
which could detect Drell-Yan events via the μ^+^μ^-^ and e^+^e^-^
channels, respectively.

An important role of the NCC and the forward silicon vertex detectors in
the Drell-Yan measurement is that it will allow a realistic
determination of the contribution of open-charm background to the dimuon
(or di-electron) events. The eμ pair events from the NCC and muon arm
would lead to a direct measurement of the charm background. This would
enable a reliable Drell-Yan measurement down to the smallest possible
*x* values.

# Ultra-peripheral Processes

In addition to studies of strong interactions of dense matter, RHIC also
has an electromagnetic interaction program focusing on ultraperipheral
collisions (UPCs) with large impact parameters, $b > 2R_{A}$ in
symmetric A+A collisions. It is possible to study electromagnetic
interactions through photoproduction (a photon from one nucleus
interacts with a quark or gluon from the opposite nucleus) and
two-photon processes (two photons, one from the field of each nucleus)
using UPCs because highly accelerated ions are surrounded by photon
fields. These photons are almost real since their virtuality is less
than $(\hslash\frac{c}{R_{A}})^{2}$.

The photon flux is calculated using the Weiszacker-Williams method. The
flux is typically greater for large *Z* nuclei since a distance *b* away
from the nucleus, the flux is

$\frac{d^{3}N_{\gamma}}{\text{dkd}^{2}b}\  = \ \frac{Z^{2}{\alpha w}^{2}}{\pi^{2}\text{kb}^{2}}\left\lbrack K_{1}^{2}(w)\  + \ \frac{1}{\gamma_{L}^{2}}K_{0}^{2}(w) \right\rbrack$
\[Equation 12\]

where$w = \frac{\text{kb}}{\gamma_{L}}$, *k* is the photon energy,
$\gamma_{L}$ is the Lorentz boost in the center-of-mass frame of the
collision and $K_{0}(w)$, $K_{1}(w)$are modified Bessel functions. The
photon flux decreases exponentially above a cutoff energy determined by
the size of the nucleus. In the lab frame, the cutoff is
$k_{\text{max}} \approx \gamma_{L}\hslash\frac{c}{R_{A}}$. In the rest
frame of the target nucleus, the cutoff is boosted to
$E_{\text{max}} = \ (2\gamma_{L}^{2} - 1)\hslash\frac{c}{R_{A}}$. Table
2 shows the beam energies, $E_{\text{beam}}$, Lorentz factors,
$\gamma_{L}$, $k_{\text{max}}$, and $E_{\text{max}}$, as well as the
corresponding maximum center of mass energy,
$\sqrt{S_{\text{max}}} = \sqrt{2E_{\text{max}}m_{p}}$, for single photon
interactions with protons.

[]{#__RefHeading___Toc126071364 .anchor}Table 2 - Beam energies,
$E_{\text{beam}}$, Lorentz factors, $\gamma_{L}$, photon cutoff energy
in the center of mass frame, $k_{\text{max}}$, and in the nuclear rest
frame, $E_{\text{max}}$, and equivalent nucleon-nucleon center of mass
energy, $\sqrt{S_{\text{max}}}$, for *AA* collisions at RHIC.

  ----------- ---------------------------- ---------------- --------------------------- --------------------------- ----------------------------------
  ***A***     $E_{\text{beam}}$**(GeV)**   $$\gamma_{L}$$   $k_{\text{max}}$**(GeV)**   $E_{\text{max}}$**(TeV)**   $\sqrt{S_{\text{max}}}$**(GeV)**

  **O**       125                          133              8.7                         2.31                        66

  **Si**      125                          133              7.2                         1.92                        60

  **I**       104                          111              3.6                         0.81                        39

  **Au**      100                          106              3.0                         0.66                        35
  ----------- ---------------------------- ---------------- --------------------------- --------------------------- ----------------------------------

The total photon flux striking the target nucleus is the integral of
\[Equation 12 over the transverse area of the target for all impact
parameters subject to the constraint that the two nuclei do not interact
hadronically. A reasonable analytic approximation for *A+A* collisions
is given by the photon flux integrated over distances $b > 2R_{A}$. The
analytic photon flux is

$\frac{\text{dN}_{\gamma}}{\text{dk}}\  = \ \frac{2Z^{2}\alpha}{\pi k}\ \left\lbrack \ w_{R}^{\text{AA}}K_{0}(w_{R}^{\text{AA}})\ K_{1}(w_{R}^{\text{AA}})\  - \ \frac{(w_{R}^{\text{AA}})^{2}}{2}\ \left( K_{1}^{2}(w_{R}^{\text{AA}})\  - \ K_{0}^{2}(w_{R}^{\text{AA}}) \right) \right\rbrack$
\[Equation 13\]

where $w_{R}^{\text{AA}}\  = \ 2\frac{\text{kR}_{A}}{\gamma_{L}}$.

Calculations of interactions such as heavy quark production by
photon-gluon fusion, $\gamma + g\  \rightarrow \ Q\overline{Q}$, can be
treated similarly to parton-parton interactions in the initial
nucleon-nucleon interactions in central collisions since *k* is a
continuum up to $E_{\text{beam}} = \ \gamma_{L}m_{p}$. Predictions for
charm production in UPCs at RHIC can be found in Ref. [^37]. Since the
photoproduction cross section is proportional to a single power of the
nuclear gluon distribution, UPCs are an alternative method of measuring
the gluon distributions albeit at higher *x* than in central collisions.

Presently the UPC photoproduction data at RHIC are from ρ and J/ψ
measurements at STAR[^38] and PHENIX[^39] respectively. These vector
mesons are typically produced when a photon in the field surrounding the
nucleus fluctuates into $q\overline{q}$ pairs with the same quantum
numbers as the photon and then materialize through elastic scattering
with the nucleus, known as vector meson dominance. Since vector mesons
are produced coherently by this mechanism at rather low *p~T~*,
$p_{T}\  = \ \hslash\frac{c}{R_{A}}\  \approx \ \text{100}$ MeV, such
measurements are better done at RHIC than at LHC. The STAR ρ event
samples in *AA* collisions are large enough to study quantum
interference effects. (The ρ production cross section in Au+Au
collisions at STAR is about 10% of the total hadronic cross
section[^40].) Interference arises because either nucleus can emit the
photon, so that the processes are indistinguishable[^41].

Photoproduction events are relatively clean since they are typically low
multiplicity. Only one nucleus breaks up, leaving a rapidity gap between
the vector meson and the nucleus that emitted the photon. The PHENIX J/ψ
measurement shown in Figure 20 was based on an electromagnetic
excitation trigger (a neutron in one of the ZDCs) and detection of a
single electromagnetic cluster with energy greater than 800 MeV. The
observed e^+^e^-^ pairs are at *p~T~ \<* 50 MeV, indicating coherent
production.

![](media/image23.png){width="4.079861111111111in"
height="3.6527777777777777in"}

[]{#__RefHeading___Toc126071353 .anchor}Figure 20 -- J/ψs produced in
ultraperipheral Au+Au collisions at RHIC from PHENIX.

# Double Parton Correlations

Mark Strikman

![](media/image24.png){width="3.326388888888889in"
height="3.2263888888888888in"}

# Comparison of RHIC-II and LHC Heavy-ion programs

# RHIC Detector Upgrades

An active upgrade program of the major RHIC detectors is planned in
order to extend their capability to more complete and robust
measurements, especially in the era of RHIC-II luminosities. We will
discuss each planned upgrade briefly here with an emphasis on what each
brings to the forward/pA physics being discussed in this working group.

## PHENIX Upgrades

### Muon Trigger Upgrade

The PHENIX forward muon trigger upgrade is primarily intended to allow
fast selection of very high momentum (p \> 25 GeV/c) muons from W decays
for spin measurements that will access the spin dependence of the
nucleon sea. However, it will also be able to help with other triggers,
in conjunction with the FVTX and NCC (see below) to allow capture of
many of the more rare processes in the high-luminosity era of RHIC-II.
It will also help with pattern recognition in high-occupancy events such
as those from central Au-Au collisions, where present muon triggering
and reconstruction is not very clean or efficient.

Resistive plate (RPC) detectors located in front of the muon arm, in
between the muon tracker and muon identifier, and behind the muon
identifier will be used to make a fast rough determination of the
momentum which then allows rejection of lower momentum muons. The will
also provide a coarse time-of-flight measurement which can be used to
reject particles that do not originate at the interaction region, in
particular rejecting backgrounds that come into PHENIX from the rear of
the muon identifiers that are associated with the incoming beam halo. A
schematic of the planned RPC arrangement (RPC's in black) is shown in
Figure 21.

The project is funded by NSF; see the MRI proposal at,

https://www.phenix.bnl.gov/WWW/trigger/forwardupgrade/NSF_MRI/MRIfiles/NSF_MRI_Wboson_Final.pdf

For p(d)+A collisions, will allow level-1 triggers based on high
momentum muons (p\>??) that will aid in capture to tape of the more rare
higher momentum events, e.g. from semi-leptonic decays of b mesons. It
may also help in triggering for ϒ events by requiring the higher
momentum muons from these decays at the fast trigger level.

![](media/image25.png){width="3.5861111111111112in"
height="2.946527777777778in"}

[]{#__RefHeading___Toc126071354 .anchor}Figure 21 - PHENIX Muon Trigger
upgrade (one arm shown) with its RPC planes shown in black, existing
muon tracking detectors in red. The primary interaction region is at the
right-center of the figure.

### Silicon Vertex Detector

The PHENIX silicon vertex detector upgrade includes both a central
rapidity barrel silicon detector (VTX) and a forward (and backward)
rapidity silicon detector (FVTX). Between them they cover a rapidity
range, -2.2 \< y \< 2.2, and can identify detached vertices on an
event-by-event basis to isolate short and long-lived decays. This will
allow the identification of open charm and beauty decays and the
rejection of the longer-lived decays of light hadrons which presently
contribute large backgrounds for measurements at forward and backward
rapidity. The precise measurement of the tracks near the primary vertex
will also improve the resolution for a number of signals including the
J/ψ and ϒ mass resolutions.

![](media/image26.png){width="4.127777777777778in"
height="2.2840277777777778in"}

[]{#__RefHeading___Toc126071355 .anchor}Figure 22 - PHENIX Silicon
Vertex Detector Upgrade including the forward vertex detector (FVTX) and
central barrel vertex detector (VTX).

More details than will be discussed here can be found in the CDR's for
these upgrades at,

<http://www.phenix.bnl.gov/phenix/WWW/publish/akiba/2004/VTX_rev2/PHENIX-VTX-PROPOSAL.pdf>
(VTX CDR)

and

<https://www.phenix.bnl.gov/phenix/WWW/publish/leitch/fvtx/> (draft FVTX
CDR)

As was discussed in Section 4 with rates in Table 1, RHIC-II
luminosities will be needed for many of the heavy-quark measurements
since these are rare processes and rates are low for many and a large
reach in p~T~ is important. In addition to the luminosity need, most of
these measurements also need the detached vertex discrimination provided
by the PHENIX silicon vertex detector upgrade. The systematics of
measurements of charm and beauty via their decays to muons in forward
and backward directions would remain large without the event-by-event
rejection of light hadron decays which the FVTX provides. Explicit
identification of beauty via the B → J/ψ X only becomes possible with
this upgrade.

![](media/image27.jpeg){width="4.0055555555555555in"
height="3.877083333333333in"}

[]{#__RefHeading___Toc126071356 .anchor}Figure 23 - The reconstructed
Z-vertex distribution for J/ψ from B decays (black line) and for prompt
J/ψ (red line). Note that the J/ψ yield has been scaled down by a factor
of 100. The relative yield of J/ψ from B decays versus prompt J/ψ is
estimated to be about 1%.

So far the mass resolution and signal-to-background in the muon
spectrometers in PHENIX has not been good enough to allow a clear
separation of the ψ' from the J/ψ and from the underlying background
largely composed of random muon pairs from decays of light hadrons. The
FVTX will both improve the mass resolution and strongly suppress the
background from random pairs and will open up the study of the ψ'. The
ψ' is a cleaner physics process to study since, unlike the J/ψ, it does
not have a large contribution from decays of higher-mass resonances and
thus all the ψ' one studies are primary.

![](media/image28.png){width="4.117361111111111in"
height="2.7729166666666667in"}

[]{#__RefHeading___Toc126071357 .anchor}Figure 24 - Mass spectra for the
J/ψ and ψ\', 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/ψ
and ψ' in this plot represents our expectation for a \~25 pb^-1^ p+p
run.

### Nose Cone Calorimeter

The PHENIX Nose Cone Calorimeter (NCC) upgrade (Figure 25) will replace
the present copper nose cone hadron absorbers in the forward and
backward rapidity regions in front of the muon arms with electromagnetic
calorimeters. The calorimeters are tungsten layers with active silicon
pads in many layers and would cover a rapidity range of 1 \< \|y\| \< 3,
providing an increase in coverage compared to the central arm
calorimeters of over a factor of ten.

![](media/image29.png){width="4.501388888888889in"
height="3.3777777777777778in"}

[]{#__RefHeading___Toc126071358 .anchor}Figure 25 - PHENIX Nose Cone
Calorimeter (NCC) upgrade (purple).

The NCC will add to PHENIX the capability to measure χ~C~ → J/ψ γ and
direct photons in the forward and backward directions. Both provide
access to modifications of the gluon structure functions in these
rapidity ranges which correspond to small-x of the gluon distributions
where shadowing or gluon saturation effects are thought to be strong.

The χ~C~ is important because:

-   Approximately 30% of the detected J/ψs come from its decay, and to
    unravel the complex puzzle of J/ψ suppression definitively will
    require knowing the nuclear dependence of χ~C~ production.

-   Like the ψ', in terms of physics the χ~C~ is a cleaner probe of the
    gluons since, unlike the J/ψ, it does not suffer from feeddown from
    higher mass resonances.

Direct photons also provide a probe of the gluon distribution in nuclei.

A draft CDR for the NCC can be found at,

https://www.phenix.bnl.gov/WWW/publish/seto/NCC/ncccdr.pdf

## STAR Upgrades

### Forward Silicon Tracker

![](media/image30.png){width="2.10625in" height="2.8333333333333335in"}

[]{#__RefHeading___Toc126071359 .anchor}Figure 26 - STAR Forward Silicon
Tracker upgrade.

### Forward Calorimeter?

![](media/image31.png){width="2.2666666666666666in"
height="2.3333333333333335in"}

[]{#__RefHeading___Toc126071360 .anchor}Figure 27 - STAR ? upgrade.

# Appendix: Rates for Forward and p(d)+A Processes

![](media/image32.png){width="6.873611111111111in"
height="3.3604166666666666in"}

# Appendix: Top-down Physics Charts

![](media/image33.wmf){width="5.947916666666667in" height="4.4375in"}

[]{#__RefHeading___Toc126071361 .anchor}Figure 28 - Top-down physics
chart for gluon saturation and shadowing in nuclei.

![](media/image34.wmf){width="6.1375in" height="4.5256944444444445in"}

[]{#__RefHeading___Toc126071362 .anchor}Figure 29 - Top-down physics
chart for anti-quark distributions in the nucleon sea (Jen-Chieh Peng).

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