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# The RHIC Cold QCD Program

Elke-Caroline Aschenauer  Brookhaven National Laboratory, Upton, New York
11973 Kenneth Barish  University of California, Riverside, California 92521
Alexander Bazilevsky  Brookhaven National Laboratory, Upton, New York 11973
Xiaoxuan Chu  Brookhaven National Laboratory, Upton, New York 11973 James
Drachenberg  Abilene Christian University, Abilene, Texas 79699 Oleg Eyser
Brookhaven National Laboratory, Upton, New York 11973 Renee Fatemi  University
of Kentucky, Lexington, Kentucky 40506-0055 Carl Gagliardi  Texas A&M
University, College Station, Texas 77843 Sanghwa Park  Mississippi State
University, Mississippi State, Mississippi 39762 Vincent Schoefer  Brookhaven
National Laboratory, Upton, New York 11973 Ralf Seidl  RIKEN Nishina Center
for Accelerator-Based Science, Wako, Saitama 351-0198 Scott Wissink  Indiana
University, Bloomington, Indiana 47408 Qinghua Xu  Shandong University,
Qingdao, Shandong 266237 Maria Zurek  Argonne National Laboratory, Lemont,
Illinois 60439

###### Contents

  1. 1 Executive Summary
    1. 1.1 Recommendations and Initiatives
  2. 2 Polarized High-Energy Proton Beams
    1. 2.1 Preparation and Preservation of Hadron Beam Polarization
    2. 2.2 Polarimetry of High-Energy Hadron Beams
  3. 3 Collinear Proton Structure
    1. 3.1 $W$ $A_{L}$ and sea quark polarization
    2. 3.2 Double helicity asymmetries $A_{LL}$ and gluon polarization
    3. 3.3 Nonlinear QCD effects
  4. 4 Three-dimensional Structure
    1. 4.1 Studies of initial and final state TMD effects with jets
    2. 4.2 Transversity from di-hadron interference fragmentation functions
    3. 4.3 Transverse single-spin asymmetry in the forward region
    4. 4.4 Transverse single-spin asymmetry of weak bosons
    5. 4.5 Transverse single-spin asymmetries of direct photons and heavy flavor decay leptons
    6. 4.6 Nuclear dependence of single spin asymmetries
    7. 4.7 Ultra-peripheral collisions
  5. 5 Appendix
    1. 5.1 STAR Forward Upgrade
    2. 5.2 sPHENIX Detector

##  1 Executive Summary

RHIC has produced a remarkable breadth of physics results over the years, with
compelling discoveries in both Hot and Cold QCD. It is critical to utilize the
last three years of operations to complete the extraordinarily rich program
that is uniquely possible with the $pp$, $pA$ and $AA$ collisions provided by
RHIC.

A significant piece of the RHIC legacy is the 25 years of innovation in
accelerator science and experimental techniques necessary to collide highly
polarized, high-energy proton beams. These achievements, discussed in detail
in Section 2, include the design and construction of the the world’s highest
luminosity polarized proton source, the use of Siberian snakes to reduce the
depolarizing effects of the resonance field harmonics, the implementation of
spin rotators to provide proton beams polarized in the longitudinal,
transverse or radial direction and the development of techniques to maintain
orbit and emittance stability from injection to full energy in order to
maximize polarization lifetimes. In parallel, new techniques and tools were
developed to monitor and evaluate the quality of the beams. As a result it is
now possible to make precision measurements of the beam spin tune, to extract
the transverse/radial polarization component in a longitudinally polarized
beam and precisely measure the spin-dependent relative luminosities. These
advances, along with the design, construction, and operation of absolute and
relative high precision hadron polarimetry have played an essential role in
the success of the RHIC experimental Cold QCD program and have laid the
foundation for the design of the future Electron-Ion Collider’s (EIC) highly
polarized high energy hadron beams.

RHIC has driven the exploration of the fundamental structure of strongly
interacting matter into new territory and will continue to enable advances in
the field for years to come. These explorations have always thrived on the
complementary nature of lepton scattering and purely hadronic probes. This is
demonstrated clearly in the flagship measurements of the gluon and sea-quark
helicity distributions that are discussed in detail in Section 3. The sea-
quark program exploited the advantages afforded by high energy hadron beams,
using $W^{+/-}$ production to reveal the flavor asymmetry of the
$\Delta\bar{u}$ and $\Delta\bar{d}$ distributions without the complications of
fragmentation effects. Similarly, reconstructed jet and pion asymmetries were
used for the first time to directly probe gluon interactions in proton-proton
collisions, discovering a sizable gluon helicity distribution in the region
$x>0.05$, as shown in the left panel of Fig. 1.

The RHIC Cold QCD program leverages the techniques and tools developed in the
high profile helicity program to open new frontiers in the rapidly evolving
field of transverse spin physics. For example, the reconstruction of $W$
bosons in transversely polarized proton collisions is used to test the
predicted sign change of the Sivers’ function and to provide the first
constraints on the sea-quark Sivers functions. Hadron-in-jet asymmetries,
measured for the first time at RHIC, and di-hadron asymmetries provide access
to the collinear quark transversity distributions, as well as the transverse
momentum dependent (TMD) Collins Fragmentation Function (hadron-in-jet) and
collinear Interference Fragmentation Functions (di-hadron) in the final state.
These new channels, and many more, are discussed in detail in Section 4.
Again, the transverse spin program exploits the complementarity of the high
energy hadron collider configuration by accessing distributions originally
measured in lepton scattering experiments, but in a different kinematic
regime, allowing for new insights into universality, factorization and TMD
evolution.

Figure 1:  Left: The impact of RHIC data to constrain gluon helicity [1, 2].
Right: The $x$-$Q^{2}$ probed with data from the future EIC and Jlab-12 GeV as
well as the current semi-inclusive deep inelastic scattering (SIDIS) data and
the jet and $W$-boson data from RHIC. All data are sensitive to the Sivers
function and transversity times the Collins fragmentation function (FF) in the
TMD formalism.

As the realization of a future EIC draws closer, there is a growing scientific
imperative to complete a set of “must-do” measurements in $pp$ and $pA$
collisions in the remaining RHIC runs. The ongoing RHIC Cold QCD program will
build on the accelerator’s unique ability to collide a variety of ion beams in
addition to polarized protons, and a detector with wide kinematic coverage
that has been further enhanced through an upgrade at forward rapidities
consisting of electromagnetic and hadronic calorimetry as well as tracking.
The new detectors will enable $e/h$ discrimination with charge-sign
determination and full jet reconstruction in the forward direction for the
first time, allowing RHIC to extend the full complement of the existing
transverse spin program into new kinematic regimes! This will expand the
existing transverse spin program into both lower and higher $x$ domains, as
illustrated in the right panel of Fig. 1. In addition to the expanded
transverse spin program, RHIC will be able to further explore exciting new
signatures of gluon saturation and non-linear gluon dynamics (see Section 3).
The ratios of forward Drell-Yan and photon-jet yields in $pp$ and $pA/AA$
collisions are clean probes of nuclear modifications to initial state parton
distributions as well as gluon saturation effects. All of these measurements
rely critically on the successful completion of scheduled RHIC operations
before the shutdown in 2025.

While the remaining RHIC Cold QCD program is unique and offers discovery
potential on its own, it is also essential to fully realize the scientific
promise of the EIC. These data will provide a comprehensive set of
measurements in hadronic collisions that, when combined with EIC data, will
establish the validity and limits of factorization and universality. The
separation between the intrinsic properties of hadrons and interaction
dependent dynamics, formalized by the concept of factorization, is a
cornerstone of QCD and largely responsible for the predictive power of the
theory in many contexts. While this concept and the associated notion of
universality of the quantities that describe hadron structure has been
successfully tested for unpolarized and - to a lesser extent - longitudinally
polarized parton densities, its experimental validation remains an unfinished
task for much of what the EIC is designed to study, namely the three-
dimensional structure of the proton and the physics of dense partonic systems
in heavy nuclei. To establish the validity and the limits of factorization and
universality, it is essential to have data from both lepton-ion and proton-ion
collisions, with an experimental accuracy that makes quantitative comparisons
meaningful. The final experimental accuracy achieved with the data collected
during this final RHIC campaign will enable quantitative tests of process
dependence, factorization and universality by comparing lepton-proton with
proton-proton collisions. When combined with data from the EIC, it will
provide a broad foundation to a deeper understanding of Quantum
Chromodynamics.

###  1.1 Recommendations and Initiatives

The RHIC Cold QCD community proposes the following recommendations. These
proposals were presented, discussed and received strong support at the QCD
Town Hall Meeting in September of 2022.

  1. 1.

Continued funding of RHIC operations to enable collection of the last $pp$,
$pA$ and $AA$ datasets that are required for completion of the RHIC Hot and
Cold QCD missions.

  2. 2.

Continued strong funding of the RHIC Hot and Cold QCD experimental analysis
groups well beyond the final operation of RHIC. This will enable effective and
timely analysis and publication of the wealth of data collected, and to be
collected. The unprecedented originality of the RHIC data sets have discovery
potential on their own and are critical to fully accomplish the scientific
mission of the EIC. Continued support of the experimental groups is also
critical to ensure the continued effective training of the next generation of
experimentalists in preparation for EIC operations.

  3. 3.

Continued strong funding of the RHIC Hot and Cold QCD theoretical groups and
collaborations well beyond the final RHIC operations to ensure that the
knowledge generated by analyses of the RHIC data are fully incorporated into
the next-generation of theoretical interpretations.

##  2 Polarized High-Energy Proton Beams

The Relativistic Heavy Ion Collider, RHIC, has the unique capability to
collide polarized protons at center-of-mass energies up to 510 GeV. High beam
polarizations are an important prerequisite for the efficient and timely
execution of the physics program at RHIC, since the figure of merit for any
spin-dependent observable is directly proportional to the square of the
polarization of the beam and the number of events. For double-spin
observables, it is the product of the two beam polarizations which enters into
the figure of merit, so losses that affect both beams similarly are
potentially even more severe.

The BNL collider complex is using a set of accelerators between the proton
(ion) source and the main RHIC collider. The proton beams are injected in up
to 120 bunches which can collide in several different interaction points.
Proton-proton collisions can reach center-of-mass energies up to 510 GeV.
Other collision energies in the past have included 64 and 200 GeV with
longitudinal or transverse beam polarizations. Proton bunch intensities reach
$2.7\cdot 10^{11}$, resulting in peak luminosities of about $5\cdot
10^{32}\leavevmode\nobreak\ \mathrm{cm}^{-2}\mathrm{s}^{-1}$ with average beam
polarizations of $\left<P\right>\approx 55\%$. The recent RHIC Run-22
delivered about $800\leavevmode\nobreak\ \mathrm{pb}^{-1}$ with an average
$68\leavevmode\nobreak\ \mathrm{pb}^{-1}$ per week (the luminosity was limited
to $1.27\cdot 10^{32}\leavevmode\nobreak\ \mathrm{cm}^{-2}\mathrm{s}^{-1}$ by
request from the experiment).

###  2.1 Preparation and Preservation of Hadron Beam Polarization

Unlike electron beams, hadron beams at the RHIC energy scale lack any
significant synchrotron radiation mechanism for self-polarizing or natural
emittance damping. This means that the production of high-energy, high-
brightness, highly polarized beams consists largely of creating intense, low
emittance polarized beams at the source and carefully preserving the beam
quality through all stages of acceleration. Developments in source technology
and accelerator physics are therefore both of key importance in supporting the
RHIC spin physics program.

The RHIC polarized proton beams are created in an optically pumped polarized
ion source (OPPIS [3]). The source has undergone continuous development during
the RHIC era, including a major upgrade in 2013. Source technology upgrades
include changing from an electron cyclotron resonance source to a fast atomic
beam source (ABS), addition of a superconducting solenoid for enhanced
polarization preservation, and installation of a novel pulsed electromagnetic
vacuum valve. The output beam of the source is actually an $H^{-}$ beam where
the protons have been polarized. The upgraded source reliably produces beams
of up to $10^{12}$ particles in a 300 $\mu$s pulse. Proton polarizations of
82-84% have been achieved out of the source as measured by a high precision
carbon target polarimeter at the end of the 200 MeV Linac. The source can
change the spin orientation (vertically up and down) between consecutive
pulses, allowing for an arbitrary pattern of spin directions along the RHIC
bunch train. The high pulse intensity 111The pulse intensity is a factor of 3
higher than what is required in RHIC. enables various scraping schemes in the
downstream accelerators which reduce the intensity by scraping away high
amplitude particles (transversely and longitudinally) but preserve a high
brightness core with an intensity and emittance optimized for RHIC operations.

After creation in the source and acceleration in the 200 MeV Linac (to a total
energy of 1.1 GeV), the $H^{-}$-beam is injected into the Booster synchrotron
via a charge-exchange injection process which strips the electrons with a
carbon foil and produces the proton beam. From there the beam is accelerated
in three successive synchrotrons. First the protons are accelerated in the
Booster to 2.3 GeV, then in the Alternating Gradient Synchrotron (AGS) to 23
GeV and finally in the RHIC rings themselves to a top energy of up to 255 GeV.
The magnetic fields that produce the steering and focusing necessary to
confine the beam during acceleration will also induce motion of the spin
vectors of the particles as they precess about the local field lines. This
combination of particle motion and spin motion in a periodic system like a
synchroton ring introduces resonance conditions which can cause rapid
polarization losses. Resonances occur whenever the natural frequency of the
spin motion (characterized as the number of spin precessions per turn, or spin
tune) is equal to some frequency with which the spin perturbing magnetic
fields are sampled. A magnetic field that deflects a proton by an angle
$\theta$ will precess the spin vector by an angle $G\gamma\theta$, where $G$
is the anomalous gyromagnetic ratio ($G=1.79$ for protons) and $\gamma$ is the
relativistic factor. The spin motion in magnetic fields is therefore highly
energy dependent and during acceleration to top energy in RHIC these resonance
conditions are met very often.

In order to reduce polarization losses, the spin motion of particles can be
manipulated such that some resonances are completely avoided. In RHIC this is
accomplished with helical dipoles (so-called Siberian snakes). Two helical
dipoles magnets, located diametrically opposite one another, each provide a
full spin-flip (from up to down or vice versa) in a single passage (for each
of the two rings). The result is that the spin tune is made energy-independent
(fixed at 1/2) and there is complete cancellation of all first order
depolarizing resonance terms [4]. Even in the presence of full snakes,
however, depolarization is still possible due to higher order resonances
called snake resonances. Minimizing the effects of these resonances requires
careful control of the betatron tune (the natural frequency of the transverse
particle oscillations) during acceleration. In RHIC this is done using a fast
phase-locked loop tune feedback system, in operations since 2006 [5] which
enables acceleration very close to a low-order betatron resonance without loss
of intensity or emittance dilution, and which maximizes the distance to the
nearest depolarizing snake resonance. This is an excellent example of
developments in accelerator physics and beam control being driven by the
stringent demands of a polarized collider physics program.

In the AGS, resonance avoidance is somewhat more complicated because there is
not sufficient space in the magnetic lattice for snakes that provide a full
spin-flip. Instead, the AGS uses two weaker partial snakes, which rotate the
spin through an angle less than $180^{\circ}$ ($18^{\circ}$ and $10^{\circ}$,
respectively). In this case the spin tune is still energy dependent, but is
prevented from taking a small range of values [6]. By careful control of the
betatron tune, this allows the strongest resonance to be avoided. A fast tune
jump minimizes the polarization loss from the many weak residual resonances
that are driven by the partial snakes themselves. The Booster, by contrast,
only has two resonance crossings, which are each handled by an orbit harmonic
correction scheme, rather than specialized snake magnets.

The strongest resonances encountered during acceleration are dependent on the
beam emittance, with the larger amplitude particles experiencing greater
depolarization. This makes emittance control for a polarized beam particularly
important since it affects two components of the collider performance:
luminosity and polarization. A variety of techniques are employed in the RHIC
accelerator complex to prevent emittance growth. Bunch lengthening
manipulations, like dual harmonic RF schemes (in AGS and Booster) and the
addition of the low frequency 9 MHz RF system in RHIC lower the peak current
of the bunches and prevent emittance increases due to space charge forces and
electron cloud buildup. A strong driver of emittance growth during RHIC
polarized proton stores is the nonlinear defocusing force of each beam upon
the other (the beam-beam effect) at the point of collision, which can cause
fast emittance blowup immediately upon steering the beams into one another.
Starting in Run-15, this fast blowup was suppressed by a pair of electron
lenses, which provide an equal but opposite nonlinear force [7].

In addition to preserving the beam polarization, the spin physics program
requires specialized instrumentation and methods to measure aspects of the
spin dynamics like the spin tune and the spin direction at key locations in
the ring. RHIC is the first polarized beam facility to measure the spin tune
non-destructively using coherent excitation of the spin motion. An interleaved
sequence of 5 RF dipoles and 4 DC dipoles produces a driven coherent
precession of the particle spin vectors. The pC polarimeters deliver a
measurement of the asymmetry synchronized to the phase of the driving field.
The spin tune is then calculated from the relationship between the driven and
measured amplitudes. Since this is an adiabatic excitation, it can be reversed
without loss of polarization, which allows scans and repeated measurements at
top energy without costly refill times [8]. This integration of accelerator
physics methods with polarimetry allowed optimization of the accelerator
lattice to optimize the spin tune and its spread.

These efforts will continue to be important in the EIC era, and a host of
further developments will continue through the end of the RHIC program. The
hadron spin dynamics and equipment in the EIC are more complicated than those
of RHIC. The altered IP geometry produces additional complications for the
spin rotation manipulation, including change of spin direction in the arcs,
which will have to be measured, controlled and verified. A more complete
partial snake resonance compensation for the AGS is planned for commissioning
in Run-24. Furthermore, the production and acceleration of polarized Helium-3
requires extensive source development and use of the full toolkit of resonance
avoidance including re-introduction of methods previously used for polarized
protons, like use of an AC dipole resonance crossing, currently under
development in the Booster.

###  2.2 Polarimetry of High-Energy Hadron Beams

The experiments at RHIC require that the beam polarizations are known with
good accuracy. Double helicity asymmetries are typically small ($O(10^{-3})$)
and knowledge of the relative luminosity is the leading uncertainty for these
observables. Early estimates have set a requirement of less than
$\sigma(P)/P=4\%$ for the relative polarization uncertainty. With increased
interest in large transverse single-spin asymmetries and high luminosity data
sets, the achieved benchmark has been lowered to $1.4\%$ in recent years [9].

The beam polarizations at RHIC are measured through a combination of absolute
and fast polarimeters. Both are based on the detection of recoil particles
from elastic scattering at low energies, where a spin-dependent asymmetry is
introduced through a spin-flip in the Coulomb-Nuclear interference region. The
determination of the absolute beam polarization makes use of a polarized
atomic hydrogen gas jet target, HJET, resulting in an uncertainty of a $3-4\%$
over the course a typical RHIC fill (8 hours long). The target polarization is
prepared from a state-of-art atomic beam source in a sextupole magnet system
in combination with an RF-transition unit, which optimizes the atomic target
density and polarization, $P\approx 96\%$. The remaining molecular fraction of
$H_{2}$ in the target has been the major source of uncertainty in the
determination of the beam polarization. The recent significant improvement is
a major step towards the applicability of the existing system at the EIC,
where a polarization uncertainty of 1% or better is required.

The HJET is complemented by fast measurements with Carbon fiber targets every
few hours which allow for the tracking of polarization decay from injection to
the end of each RHIC fill. The time-dependent knowledge of the beam
polarization is important for the correct use in the experiments, where the
luminosity-weighted polarization can be significantly different from the time-
average value.

The ultra-thin Carbon targets scan transversely through the beam bunches
during each set of measurements, thereby providing a picture of the transverse
beam polarization profile itself. While it was originally assumed that the
transverse polarization profile is flat, the measurements show that the
polarization indeed peaks in the center of the bunches, in both the horizontal
and vertical directions. This information, again, is essential for the proper
determination of the beam polarizations in collision at the experiments. The
convolution of bunch intensities with the polarization profile results in a
higher polarization value than that measured with the HJET. Maybe even more
surprising, a longitudinal polarization profile of the proton bunches has been
measured with the HJET and the Carbon polarimeters independently. The
longitudinal polarization dependence is smaller than the transverse profile;
in addition, the polarization is lower towards the center of the bunch.

Polarimetry at RHIC relies on a good understanding of the spin dynamics and
the stable spin direction of the accelerator. The transverse direction of the
polarization vector (with respect to the beam momentum) at the collision
points in the experiments is confirmed and monitored through local
polarimetry. The concept is based on neutron production at very forward
directions, measured in the Zero Degree Calorimeters. This method was
discovered in the first polarized proton collisions at RHIC, and it was
essential for the successful commissioning of the spin rotators for
longitudinally polarized experiments.

Control and verification of the spin direction is important at the
experimental collision points as well as at the location of the polarimeters.
In a lattice like RHIC with full snakes, the design stable spin direction (the
direction about which misaligned spin vectors will precess from turn to turn),
is vertical. Pairs of additional helical dipoles, called spin rotators, that
flank the interaction points of the large experiments in the RHIC ring can
rotate the spin locally, providing longitudinally or radially directed
polarization at those specific locations, while leaving the polarization in
the rest of the ring unperturbed. The spin direction can deviate from the
intended orientations for a number of reasons, including errors in the helical
dipole fields and misalignment of quadrupoles in the lattice. Over the years,
systematic scans of the helical dipole settings and the beam energy have
helped to understand and characterize the source of these deviations. These
efforts were particularly vital in shaping the response to a failure of two of
the four magnets that make up one of the snakes in the Blue ring in Run-22.
Meeting the physics requirements with only the remaining two magnets required
compensation with the other functioning snake, a change in the store energy to
minimize the resulting (and now strongly energy dependent) deviation of the
spin direction, and development of new methods of spin direction measurement.
Since the local polarimetry at STAR and the pC polarimeters are only sensitive
to the transverse components of the stable spin direcion, measurements were
developed using the spin rotators (at STAR) and a horizontal orbit angle (at
the pC) to rotate the hidden longitudinal direction into the transverse plane
[10].

Proton polarimetry at RHIC does not only provide vital input for the
experiments and fast feedback to the collider during beam development and
regular operations. It has also delivered surprising results, which further
our general understanding of spin-dynamics in particle accelerators and
storage rings. The intricate correlation of the spin tune, stable spin-
direction, and the polarization lifetime has been studied over many years, but
it proved to be of special importance during RHIC Run-22 when one of the
Siberian snakes had a partial failure. Based on past experiences and through
ingenious combination of the remaining snake parts with spin rotators and the
polarimeters, it was possible to determine a setup that showed no significant
loss of beam polarization at flattop energy. All of this information will
directly benefit the future Electron-Ion Collider and any other polarized
accelerator for medical or other applications.

##  3 Collinear Proton Structure

  * •

RHIC high precision longitudinally polarized proton-proton data for a variety
of probes and center of mass energies have played a decisive role in
constraining the sea-quark and gluon helicity distributions in the proton.

  * •

$W$ production in longitudinally polarized $pp$ collisions revealed the
existence of a flavor asymmetry in the polarization in the sea of light anti-
quarks with $\Delta\bar{u}$ being positive, while $\Delta\bar{d}$ is negative.

  * •

Collisions at center of mass energies of 200 GeV provided the first evidence
that the gluons inside a proton are polarized. Data from the RHIC run in 2009,
when included in global analysis, showed that gluons carry approximately 40%
of the proton spin in the region where the gluon carries more than 5% of the
proton momentum ($x>0.05$) at $Q^{2}=10\,\mathrm{GeV}^{2}$.

  * •

The published and preliminary results based on data collected in 2012, 2013
and 2015 at center of mass energies of 200 and 510 GeV reduce the present
uncertainties on gluon helicity $\Delta g$ even further, providing more
insights in the region of momentum fraction $x$ between about 0.01 to 0.5 of
the momentum of a polarized proton.

  * •

STAR $pp$ and $pA$ forward di-hadron correlation results pioneered the
observation of nonlinear gluon dynamics dependence on the nuclear mass number
$A$. Higher-precision measurements will be performed with the STAR forward
upgrade to further explore nonlinear gluon dynamics. All the studies provide
the baseline for searching for gluon saturation at the future EIC.

###  3.1 $W$ $A_{L}$ and sea quark polarization

The STAR and PHENIX Collaborations have concluded the measurements of the
parity-violating spin asymmetry in the production of weak bosons from
collisions with one of the proton beams polarized longitudinally [11, 12, 13,
14, 15, 16]. In 510 GeV center-of-mass proton-proton collisions at RHIC,
$W^{+}$ bosons are produced primarily in the interactions of $u$ quarks and
$\bar{d}$ antiquarks, whereas $W^{-}$ bosons originate from $d$ quarks and
$\bar{u}$ antiquarks. The longitudinal single spin-asymmetry ($A_{L}$)
measurements of the decay positrons provide sensitivity to the $u$ quark and
$\bar{d}$ helicities in the proton, whereas the decay electrons do so for the
$d$ and $\bar{u}$ helicities. Combined, they make it possible to delineate the
light quark and antiquark polarizations in the proton by flavor.

Figure 2: Longitudinal single-spin asymmetries, $A_{L}$, for $W$ production as
a function of the lepton pseudorapidity, $\eta_{\mathrm{lepton}}$, for the
combined STAR and PHENIX data samples [13, 14, 15, 16]. Figure 3: The impact
of the RHIC $W$ $A_{L}$ results on $\bar{u}$ (top) and $\bar{d}$ (bottom)
polarizations as a function of $x$ at a scale of $Q^{2}$= 10 GeV2. The black
curves with the $1\sigma$ uncertainty bands marked in light blue show the
results from the DSSV14 global fit [17] and the blue curves with $1\sigma$
uncertainty bands in dark blue show the results for the new preliminary DSSV
fit [2] including the RHIC $W$ data [13, 14, 16].

These measurements shed light on understanding of the light quark
polarizations $-$ one of the two initial motivations for the spin-physics
program at RHIC. The data, shown in Fig. 2, are the final results from STAR
and PHENIX on this topic [13, 14, 15, 16] that combine all the published data
obtained in 2011, 2012, and 2013. The impact of the RHIC $W$ data on the sea
quark helicity distributions $\Delta\bar{u}$ and $\Delta\bar{d}$ is presented
in Fig. 3. The plot shows the impact of the RHIC $W$ data [13, 14, 16] from
the new global fit by the DSSV group including also the recent jet, dijet, and
pion data [18, 19, 20, 21, 22, 23, 24] (that constrain mostly the gluon
helicity). The sea quark $\bar{u}$ helicity $\Delta\bar{u}$ is now known to be
positive and $\Delta\bar{d}$ is negative. The STAR 2013 data [16] were also
used in the reweighting procedure with the publicly available NNPDFpol1.1 PDFs
[25]. The results from this reweighting, taking into account the total
uncertainties of the STAR 2013 data and their correlations, are shown in Fig.
4 as the blue hatched bands. The NNPDFpol1.1 uncertainties are shown as the
green bands for comparison. As seen from the plot, the data have now reached a
level of precision that makes it possible, for the first time, to conclude
that there is a clear asymmetry between the helicity distribution of $\bar{u}$
and $\bar{d}$, and it has the opposite sign from the $\bar{d}/\bar{u}$ flavor
asymmetry in the unpolarized sea.

Figure 4: The difference of $\bar{u}$ and $\bar{d}$ polarizations as a
function of $x$ at a scale of $Q^{2}$= 10 GeV2 before and after NNPDFpol1.1
[25] reweighting with STAR 2013 $W$ $A_{L}$ [16]. The green band shows the
NNPDFpol1.1 results [25] and the blue hatched band shows the corresponding
distribution after the STAR 2013 $W$ data are included by reweighting.

###  3.2 Double helicity asymmetries $A_{LL}$ and gluon polarization

The measurement of the gluon polarization inside protons has been a major
emphasis of the longitudinally polarized RHIC program. At RHIC, gluon
polarization can be accessed by measurements of the spin-dependent rates of
production of jets [26, 27, 28, 29, 19, 20, 21], dijets [30, 18, 19, 20, 21],
$\pi^{0}\mathrm{s}$ and charged pions, [31, 32, 33, 34, 35, 36, 23, 37, 24],
and direct photons [38]. Data from the RHIC run in 2009 have for the first
time shown that gluons inside a proton are polarized with a strong constraint
from the jet data at a center-of-mass energy of $\sqrt{s}=200\,\mathrm{GeV}$
[17, 25]. Perturbative QCD analyses [17, 25] of the world data, including 2009
inclusive jet and $\pi^{0}$ results, at next-to-leading order (NLO) precision,
suggest that gluon spins contribute $\simeq\\!40\%$ to the spin of the proton
for gluon fractional momenta $x>0.05$ at a scale of
$Q^{2}=10\,(\mathrm{GeV}/c)^{2}$. Results for dijet production provide a
better determination of the functional form of $\Delta g(x)$, compared to
inclusive observables, because of better constraints on the underlying
kinematics [39].

Figure 5: STAR results on inclusive jet $A_{LL}$ versus $x_{T}$ at $\sqrt{s}$
= 200 GeV [29, 20] and 510 GeV [19, 21] at mid-rapidity from data collected in
years 2009-2015, and evaluations from DSSV14 [17] and NNPDFpol1.1 (with its
uncertainty) [25] global analyses. The vertical lines are statistical
uncertainties. The boxes show the size of the estimated systematic
uncertainties. Scale uncertainties from polarization (not shown) are
$\pm$6.5%, $\pm$6.6%, $\pm$6.4% and $\pm$6.1% from 2009 to 2015, respectively.
Source: [21]. Figure 6: The impact of the recent jet and dijet[18, 19, 20, 21,
22], pion [23, 24] and $W$ [13, 14, 16] data on the $x$-dependence of the
gluon helicity distribution at $Q^{2}=10\,\mathrm{GeV}^{2}$ based on the
global fit by the DSSV group. The black curve with the $1\sigma$ uncertainty
light blue band illustrates the DSSV14 results [17], while the blue curve with
$1\sigma$ uncertainty band in dark blue [2] shows the preliminary results
after the inclusion of the new data.

Recent STAR results [19, 20, 21] and preliminary results [40, 22] on
longitudinal double-spin asymmetries of inclusive jet and dijet production at
center-of-mass energies of 200 GeV (Run-15) and 510 GeV (Run-12 and Run-13) at
mid and intermediate rapidity complement and improve the precision of previous
STAR measurements. Figure 5 shows recent STAR results on inclusive jet
$A_{LL}$ versus $x_{T}=2p_{T}/\sqrt{s}$ at $\sqrt{s}$ = 200 GeV and 510 GeV at
mid-rapidity from data collected in years 2009-2015, and evaluations from the
DSSV14 [17] and NNPDFpol1.1 [25] global analyses. The overall impact of the
recent jet and dijet [18, 19, 20, 21, 22], pion [23, 24] and $W$ [14, 16] data
on the $x$-dependence of the gluon helicity distribution at
$Q^{2}=10\,\mathrm{GeV}^{2}$ based on the global fit by the DSSV group is
presented in Fig. 6. The truncated moment of the gluon helicity from the new
DSSV evaluations [2] at $Q^{2}=10\,(\mathrm{GeV}/c)^{2}$ integrated with the
range of $x\in(0.001,0.05)$ is $0.173(156)$ and in the range of $x\in(0.05,1)$
is $0.218(27)$ (at 68% C.L.), which can be seen in the left panel of Fig. 1.

The truncated moment of the gluon helicity integrated from $x=0.0071$ to 1 at
$Q^{2}=10\,(\mathrm{GeV}/c)^{2}$ from the recent JAM global QCD analysis [41]
including a subset of RHIC data, i.e., STAR inclusive jet results, and
assuming the SU(3) flavor symmetry and PDF positivity is $0.39(9)$. Authors of
[41] also discuss the possibility of the solution with negative gluon
contribution if the PDF positivity constraint is removed from the global fit.
They argue that there is no fundamental theoretical requirement for PDF to be
positive at all values of $x$, and therefore it would be highly desirable to
have an observable which is linearly sensitive to gluon helicity distribution.
Direct photons coming mainly from the quark-gluon Compton process and dijets
narrowing down the parton kinematics are ideal probes to distinguish between
positive and negative gluon helicity solutions. Figure 7 demonstrates the
preference of positive solution with the PHENIX direct photon $A_{LL}$ data
[38]. Figure 8 shows that the STAR dijet data [21] also strongly disfavors
distributions with large and negative gluon helicities. In the plot the
asymmetries $A_{LL}$ are presented for four dijet event topologies, namely,
with forward-forward jets (top left), forward-central jets (top right),
central-central jets (bottom left), and forward-backward jets (bottom right),
where forward jet rapidity is $0.3<\eta<0.9$, central jet rapidity is
$|\eta|<0.3$, and backward jet rapidity is $-0.9<\eta<-0.3$. The forward-
forward and forward-central configurations probe the most asymmetric
collisions down to $x\simeq 0.015$. The forward-forward and central-central
events probe collisions with $|\cos\theta^{*}|$ near zero, whereas forward-
central and forward-backward events are more sensitive to larger
$|\cos\theta^{*}|$, where $\theta^{*}$ is the scattering angle in the center-
of-mass frame of scattering partons. In both Figs. 7 and 8, the DSSV14
calculations are plotted as the black curves with the $1\sigma$ uncertainty
bands marked in light blue. The blue curves with $1\sigma$ uncertainty bands
in dark blue show the impact of all the data sets included in the new
preliminary DSSV fit [2] as in Fig. 6. The curves for JAM $\Delta g<0$
solution [41] are presented in red.

Figure 7: PHENIX double-helicity asymmetry $A_{LL}$ vs $p_{T}$ for isolated
direct-photon production in polarized $pp$ collisions at $\sqrt{s}$=510 GeV at
midrapidity [38]. DSSV14 calculation is plotted as the black curve with the
$1\sigma$ uncertainty band marked in light blue. The blue curve with $1\sigma$
uncertainty band in dark blue shows the impact of all the data sets included
in the new preliminary DSSV fit [2] as in Fig. 6. The curve for JAM $\Delta
g<0$ solution [41] was calculated by W.Vogelsang. Figure 8: STAR double-
helicity asymmetries $A_{LL}$ for dijet production vs dijet invariant mass
$M_{inv}$ in polarized $pp$ collisions at $\sqrt{s}$=510 GeV at midrapidity
from 2013 data set [21]. DSSV14 evaluation [17] is plotted as the black curve
with the $1\sigma$ uncertainty band marked in light blue. The blue curve with
$1\sigma$ uncertainty band in dark blue shows the impact of all the data sets
included in the new preliminary DSSV fit [2] as in Fig. 6. The red curves show
the JAM $\Delta g<0$ solution [41] calculated by the DSSV group.

###  3.3 Nonlinear QCD effects

To understand where the saturation of gluon densities sets in, whether there
is a simple boundary that separates this region from that of more dilute
quark-gluon matter, is one of the most important physics cases of the RHIC
Cold QCD program and future EIC.

It is well known that PDFs grow rapidly at small-$x$. The power-law growth of
the gluon density can be explained by gluon splitting, which leads to a linear
evolution of gluon dynamics. But if one imagines how such a high number of
small-$x$ partons would fit in the (almost) unchanged proton radius, one
arrives at the picture that the gluons and quarks are packed very tightly in
the transverse plane. The typical distance between the partons decreases as
the number of partons increases, and can get small at low-$x$ (or for a large
nucleus instead of the proton). In QCD, the black disk limit states that the
total hadronic cross section cannot grow forever. Thus, the growth of gluon
density which can be described by BFKL evolution, has to be tamped at some
point. At very high density, partons may start to recombine with each other on
top of splitting. The recombination of two partons into one is proprtional to
the number of pairs of the partons. Therefore the BFKL function needs to be
modified by adding a nonlinear term of recombination. Saturation is a new
regime of QCD, where gluon splitting and recombination reach a balance. One
can define the saturation scale as the inverse of this typical transverse
interparton distance. Hence $Q_{s}$ indeed grows with $A$ and decreasing $x$.

Collisions between hadronic systems, $i.e.$, $pA$ and $dA$ at RHIC provide a
window to the parton distributions of nuclei at small momentum fraction $x$
(down to $10^{-3}$). Several RHIC measurements have shown that, at forward
pseudorapidities (deuteron going direction), the hadron yields are suppressed
in $dAu$ collisions relative to $pp$ collisions in inclusive productions [42,
43, 44, 45] and di-hadron correlations [45, 46]. However, for the inclusive
channel, it was indicated that the nuclear modified fragmentation can serve as
another interpretation beyond gluon saturation to explain the suppression. The
di-hadron correlation measurement can provide future test for the saturation
physics. For di-hadron correlation in $dA$, the contributions from double-
parton scatterings (DPS) to the $d$+$A$$\rightarrow\pi^{0}\pi^{0}$X cross
section are suggested as an alternative explanation for the suppression [47]
beyond gluon saturation. Therefore, it is important to make the same
measurements in the theoretically and experimentally cleaner $pA$ collisions.
Under the color glass condensate (CGC) framework [48, 49, 50], at a given $x$,
gluons from different nucleons are predicted to amplify the total transverse
gluon density by a factor of $A^{1/3}$ for a nucleus with mass number $A$.
RHIC 2015 $pp$, $pAl$, and $pAu$ datasets are ideal to study the
$A$-dependence by varying the nuclei species.

Figure 9:  Left: At $p_{T}^{trig}$ = 1.5$-$2 GeV/$c$ and $p_{T}^{asso}$ =
1.5$-$2 GeV/$c$, a linear dependence of the suppression of back-to-back
$\pi^{0}$ correlation as a function of $A^{1/3}$ is observed within the
uncertainties, the slope ($P$) is found to be $-0.09$ $\pm$ $0.01$. The plot
is from [51]. Right: The reconstructed invariant mass of two photons for $pp$,
$pAu$, and $dAu$ collisions. The background is higher in $dAu$ collisions in
comparison with the $pp$ and $pAu$ collisions. $pp$ and $pAu$ collisions are
similar.

The recent published forward di-$\pi^{0}$ correlation measured by the STAR
detector pioneered the observation of the dependence of nonlinear gluon
dynamics on the nuclear mass number $A$ [51], see the left panel of Fig. 9.
The area is extracted by a Gaussian fit of the back-to-back correlation
measured from each collision system. The area ratio of $pA/pp$ presents the
relative yields of back-to-back di-$\pi^{0}$s in $pA$ with respect to $pp$
collisions. The area ratio in $pAu$ over $pp$ is about 50% indicating a clear
suppression of back-to-back di-$\pi^{0}$ correlation in $pAu$ compared to $pp$
collisions. The same trend but smaller amount of suppression is observed in
$pAl$ collisions. The suppression is found to scale with $A$ and linearly
dependent on $A^{1/3}$. The extracted slope from the linear dependence will be
critical input for the gluon saturation model in CGC. Meanwhile, STAR
revisited the same measurement for $dAu$ collisions. It was predicted by
comparing the forward di-$\pi^{0}$ correlation in $pp$, $pAu$, and $dAu$
collisions, one can access the contribution from DPS [47].

For RHIC 2016 data, a large background of $\pi^{0}$ identification is found in
$dAu$ collisions, in comparison with the $pp$ and $pAu$ collisions from 2015
in the right panel of Fig. 9. The generated combinatoric correlation dominates
in $dAu$ collisions, which makes it very challenging to identify the signal
correlation. The forward di-$\pi^{0}$ correlation measurement favors the
cleaner $pA$ collisions rather than $dA$ collisions. It emphasizes the
importance of measuring the di-hadron correlation in $pA$ collisions with the
STAR Forward Upgrade in the future run 2024. The higher delivered integrated
luminosity for this run together with the Forward Upgrade will enable one to
study more luminosity-hungry processes and/or complementary probes to the
di-$\pi^{0}$ correlations, i.e. di-hadron correlations for charged hadrons,
photon-jet, photon-hadron and di-jet correlations. Utilizing the forward
tracking systems, the background for particle identification will be much
suppressed with respect to the current di-$\pi^{0}$ studies.

These results are crucial for the equivalent measurements at the EIC, which
are planned at close to identical kinematics, because only if non-linear
effects are seen with different complementary probes, i.e., $ep$ and $pA$, one
can claim a discovery of saturation effects and their universality. Therefore
it is imperative that analysis activities related to the unpolarized Cold-QCD
program continue to be supported throughout the upcoming years.

##  4 Three-dimensional Structure

Figure 10:  The $x$-$Q^{2}$ probed with data from the future EIC and Jlab-12
GeV as well as the current SIDIS data and the jet and $W$-boson data from
RHIC. All data are sensitive to the Sivers function and transversity times the
Collins FF in the TMD formalism.

STAR and PHENIX opened new territory in studying the 3D structure of the
proton in the region of momentum fractions down to $x\sim$ 0.01 and high
$Q^{2}$, a region not probed by prior experiments. See Fig. 10.

  * •

The collected unique sets of transversely polarized data in $pp$ and $pA$
collisions, including the most recent campaign with the forward upgrade, will
be finalized with the 2024 RHIC run by STAR and sPHENIX.

  * •

To accomplish the scientific mission of the transverse spin program, it is
imperative that analysis activities continue to be supported throughout the
upcoming years. These activities offer discovery potential of their own, and
they are critical for properly interpreting data from the future Electron-Ion
Collider.

  * •

STAR pioneered the novel use of jets and their substructure to study initial
and final state transverse momentum dependent (TMD) effects in polarized $pp$
collisions. For example, the measured single-spin asymmetries of hadrons in
jets probe the quark transversity distribution and Collins TMD fragmentation
function, and the single-spin asymmetry of dijet opening angle is sensitive to
the Sivers TMD parton distribution.

  * •

STAR has also measured quark transversities via dihadron interference
fragmentation functions. The results from early measurements have been
included in a global analysis, and found to provide significant constraints.
Ongoing analysis of more recent STAR data, together with the data that STAR
will record during 2024, will provide far more stringent constraints.

  * •

Substantial progress on the large forward transverse single-spin asymmetry
puzzle has been made. The $A_{N}$ of the isolated $\pi^{0}$s was found to be
significantly larger than that for non-isolated ones both in $pp$ and $pA$
collisions at STAR. The $A_{N}$ for $\pi^{0}$s at large $x_{F}$, far forward
pseudorapidity ($\eta>6)$, and $p_{T}<1$ GeV/$c$ at RHICf was found to be
comparable to that at the same $x_{F}$, but with $2.5<\eta<4$ and $p_{T}>2$
GeV/$c$ at STAR. The $A_{N}$ for electromagnetic jets was found to be small
but non-zero, which provided significant constraints to the quark Sivers
function. The $A_{N}$ for forward diffractive EM-jets has been measured and
found not to be the source of the large $A_{N}$. In fact, it favors a negative
contribution.

  * •

Transverse single-spin asymmetry $A_{N}$ of weak bosons, sensitive to the
Sivers TMD function, has been probed at STAR. With the increased precision
provided by 2017 data, STAR found smaller asymmetries than were suggested by
2011 data. As a result, the increased statistics of the 2022 dataset are
critical to improve the precision of our asymmetry measurements in order to
provide a conclusive test of the Sivers’ function sign change.

  * •

PHENIX has measured transverse single-spin asymmetries at mid-rapidity that
provide constraints on the twist-3 correlation functions of quarks and gluons,
including the first RHIC result of direct photon $A_{N}$, open heavy flavor
decay electron $A_{N}$, and high precision neutral meson $A_{N}$.

  * •

PHENIX and STAR have both measured the nuclear dependence of the forward
inclusive hadron single-spin asymmetries. PHENIX finds a strong nuclear
dependence for positive hadrons at $1.2<\eta<2.4$, whereas STAR finds a weak
nuclear dependence for $\pi^{0}$ at $2.7<\eta<3.8$. Neither the origin of the
nuclear dependence, nor the difference between the PHENIX and STAR results is
well understood at this time.

  * •

Transverse single-spin asymmetry of exclusive $J/\psi$ photoproduction in
ultra-peripheral collisions is expected to directly probe the generalized
parton density (GPD) distribution. The STAR forward detector and data beyond
2022 can measure unique kinematic phase space, e.g., close to the threshold
production energy of $J/\psi$, where a large asymmetry signal is expected.

###  4.1 Studies of initial and final state TMD effects with jets

STAR has pioneered the novel use of jets and their substructure to study
initial state and final state TMD effects in polarized $pp$ collisions.

Figure 11: Collins asymmetry plotted for identified $\pi^{+}$ (blue) and
$\pi^{-}$ (red) particles as a function of jet $p_{T}$ for jets that scatter
forward relative to the polarized beam ($x_{F}>0$) in the top panel and those
that scatter backward ($x_{F}<0$) in the lower panel, extracted from data
collected in 2012 and 2015 [52]. The full ranges of both $z$ and $j_{T}$ are
integrated over. Theoretical evaluations from [53] with their uncertainties
are presented for $\pi^{+}$ (blue) and $\pi^{-}$ (red). Source: [52].

The single-spin asymmetries of the azimuthal distribution of identified pions,
kaons, and protons in high-energy jets measured at STAR probe the collinear
quark transversity in the proton, coupled to the transverse momentum dependent
Collins fragmentation function [54, 55, 56]. This makes $pp$ collisions a more
direct probe of the Collins fragmentation function than SIDIS, where a
convolution with the TMD transversity distribution enters. The Collins
asymmetry in $pp$ collisions is an ideal tool to explore the fundamental QCD
questions of TMD factorization, universality, and evolution. Figure 11 shows
the recent results on combined 2012 and 2015 Collins asymmetries for charged
pions within jets as a function of jet $p_{T}$ [52]. By integrating over the
hadron longitudinal and transverse momenta within the jets, Fig. 11 is
sensitive primarily to the quark transversity. The measured asymmetries for
jets that scatter forward relative to the polarized beam are larger than
theoretical predictions [53], which are based on the transversity and Collins
fragmentation function from SIDIS and $e^{+}e^{-}$ processes within the TMD
approach. Alternatively, the asymmetries can be investigated as functions of
$z$, the fraction of jet momentum carried by the hadron, and $j_{T}$, the
momentum of the pion transverse to the jet axis, as shown in Fig. 12. This
provides a direct measurement of the kinematic dependence of the Collins
fragmentation function. The $j_{T}$ dependence appears to vary with $z$,
contrary to the assumptions of most current phenomenological models [54, 55,
56]. STAR has also published Collins asymmetry measurements from a smaller 500
GeV data set collected in 2011 [57]. While statistics are limited, the results
are consistent with those at 200 GeV for overlapping $x_{T}$, despite sampling
$Q^{2}$ that is larger by a factor of 6. Analysis of the higher statistics 510
GeV data collected in 2017 is underway and will provide unique insight into
the $Q^{2}$ evolution of the Collins TMD fragmentation function. Concurrent
with the Collins effect measurements, STAR has also measured azimuthal
modulations that are sensitive to the twist-3 analogs of the quark and gluon
Sivers functions and to linear polarization of gluons in transversely
polarized protons [57, 52]. Analysis is also underway to determine the
unpolarized TMD fragmentation functions.

Figure 12: Collins asymmetry plotted for identified $\pi^{+}$ (blue) and
$\pi^{-}$ (red) particles as a function of $j_{T}$ for four separate bins of
hadron $z$, in jets with $p_{T}>9.9$ GeV/$c$ and $0<\eta<0.9$. Theoretical
evaluations from [55] and [53] are also shown. Source: [52].

As shown in Fig. 10, data from 200 GeV $pp$ collisions from the upcoming run
2024 with the STAR Forward Upgrade will interpolate between the coverage that
we will achieve with the forward data collected at 510 GeV in 2022 at high-$x$
and the data at low-$x$ from the STAR mid-rapidity detectors. Overall, all
STAR data will provide valuable information about evolution effects and, with
the projected statistical precision presented in Fig. 13, will establish the
most precise benchmark for future comparisons to $ep$ data from the EIC. It is
also important to recognize that the hadron-in-jet measurements with the STAR
Forward Upgrade will provide a very valuable experience detecting jets close
to beam rapidity that will inform the planning for future jet measurements in
similar kinematics at the EIC.

Figure 13: Projected statistical uncertainties for STAR Collins asymmetry
measurements at $0<\eta<0.9$ in $pp$ at $\sqrt{s}$ = 200 and 510 GeV and $pAu$
at $\sqrt{s_{\mathrm{{}_{NN}}}}$ = 200 GeV. The points have arbitrarily been
drawn on the solid lines, which represent simple linear fits to the STAR
preliminary 200 GeV $pp$ Collins asymmetry measurements from 2015. (Note that
only one bin is shown spanning $0.1<z<0.2$ for 510 GeV $pp$, whereas three
bins are shown covering the same $z$ range for the 200 GeV measurements.)

STAR also has the unique opportunity to extend the Collins effect measurements
to nuclei. This will provide an alternative look at the universality of the
Collins effect in hadron production (by dramatically increasing the color flow
options of the sort that have been predicted to break factorization for TMD
PDFs like the Sivers effect [58, 59]) and explore the spin dependence of the
hadronization process in cold nuclear matter. STAR collected a proof-of-
principle dataset during the 2015 $pAu$ run that is currently under analysis.
Those data will provide the first estimate of medium-induced effects. However,
the small nuclear effects seen by STAR for forward inclusive $\pi^{0}$ $A_{N}$
[60] indicate that greater precision will likely be needed. Figure 13 shows
the projected statistical uncertainties for the $pAu$ Collins asymmetry
measurement at $\sqrt{s_{\mathrm{{}_{NN}}}}$ = 200 GeV from 2015 and 2024
data, compared to those for $pp$ at the same energy.

Figure 14: Preliminary results of the average transverse momentum
$\left<k_{T}\right>$ for individual partons, inverted using parton fractions
from simulation and tagged $\left<k_{T}\right>$ in data, plotted as a function
of summed pseudorapidities of the outgoing jets
$\eta_{\mathrm{total}}\sim\log(x_{1}/x_{2})$. (Positive
$\eta_{\mathrm{total}}$ represents dijets emitted in the direction of the
polarized beam.) The rightmost points represent the average of all the
$\eta_{\mathrm{total}}$ bins. The systematic uncertainty in
$\eta_{\mathrm{total}}$ is set to be non-zero to improve the visibility of the
error bars. Source: [61].

Another example of utilizing jets to unravel the internal TMD structure of the
proton is the measurement of the asymmetry of the spin-dependent ‘tilt’ of the
dijet opening angle, which is sensitive to the Sivers TMD PDF. For
transversely polarized protons, the Sivers effect probes whether the
transverse momentum $\vec{k}_{T}$ of the constituent quarks is preferentially
oriented in a direction perpendicular to both the proton momentum and its
spin. Figure 14 shows the first-ever observation of the Sivers effect in dijet
production from the 200 GeV transverse spin data that STAR recorded in 2012
and 2015 [61]. The jets are sorted according to their net charge $Q$, yielding
jet samples with enhanced contributions from $u$ quarks (positive $Q$) and $d$
quarks (negative $Q$), with a large set near $Q=0$ dominated by gluons. Simple
kinematics allow for conversion from the spin-dependent ‘tilt’ of the dijet
pair to a value of $k_{T}$ on an event-by-event basis. Finally, the results
are unfolded for the $k_{T}$ of individual partons. Such measurements are
crucial to explore questions regarding factorization of the Sivers function in
dijet hadroproduction [58, 59, 62, 63]. New data to be taken in 2024 will
reduce the uncertainties for the region of summed pseudorapidities of the
outgoing jets $|\eta_{3}+\eta_{4}|<1$ by about a factor of two. The increased
acceptance from the iTPC will reduce the uncertainties at
$|\eta_{3}+\eta_{4}|\approx 2.5$ by a much larger factor, while the Forward
Upgrade will enable the measurements to be extended to even larger values of
$|\eta_{3}+\eta_{4}|$. When combined with the 510 GeV data from Run-17 and
Run-22, the results will provide a detailed mapping vs. $x$ for comparison to
results for Sivers functions extracted from SIDIS, Drell-Yan, and vector boson
production.

###  4.2 Transversity from di-hadron interference fragmentation functions

Figure 15: A comparison of STAR published [64, 65] and preliminary [66] IFF
asymmetries vs. dipion invariant mass to predictions from the global analysis
of [67], which only included the 200 GeV data from 2006 in the fit. The
$p_{T}$ bins at 200 and 500 GeV have been chosen to sample similar values of
$x_{T}=2p_{T}/\sqrt{s}$. Source: [66].

STAR has also measured quark transversity via dihadron Interference
Fragmentation Functions (IFF) in 200 and 500 GeV $pp$ collisions [64, 65], as
shown in Fig. 15. The IFF is a collinear observable, so these measurements
provide a complementary probe of transversity relative to the Collins
asymmetry measurements that obeys different evolution equations. The results
from the first measurements at 200 GeV, which were based on data recorded
during 2006 [64], have been included together with IFF measurements from SIDIS
in a global analysis [67] that is also shown in Fig. 15. The STAR IFF
measurements were found to provide significant additional constraints on the
$u$\- and $d$-quark transversities. The dominant systematic uncertainties in
the global analysis arose from the current lack of knowledge regarding the
unpolarized gluon dihadron fragmentation functions. Analysis of the
unpolarized IFF function is underway at STAR that will help to reduce these
uncertainties. The analysis of IFF asymmetries with more recent STAR data
taken in 2017 and 2022 at 510 GeV, together with the data that STAR will
record during 2024 at 200 GeV, will provide far more stringent constraints on
quark transversities than have been obtained to date when they are included in
future global analyses.

###  4.3 Transverse single-spin asymmetry in the forward region

Figure 16:  Left: Transverse single-spin asymmetry $A_{N}$ as a function of
$x_{\mathrm{F}}$ for inclusive $\pi^{0}$ in $pp$ collisions up to RHIC
energies of 200 and 510 GeV. Middle: $A_{N}$ asymmetries for the isolated and
non-isolated $\pi^{0}$ in $pp$ collisions at 200 and 500 GeV. Right: The
Collins asymmetry for $\pi^{0}$ in an electromagnetic jet for $pp$ collisions
at $\sqrt{s}=$ 200 and 500 GeV. The plots are from [68].

STAR measurements have demonstrated the persistence of sizeable transverse
single-spin asymmetries $A_{N}$ for forward $\pi^{0}$ production at RHIC
energies up to 510 GeV with a weak energy dependence (see left panel of Fig.
16), where different QCD mechanisms including the high twist effect, TMD
effects like the Sivers or Collins effects, and diffractive processes could
all contribute. It is thus important to study different effects separately for
a full understanding of the underlying mechanism, and a series of measurements
were performed in $pp$ collsions at both 200 and 500 GeV and in $pA$
collisions at STAR [68, 60, 69].

Figure 17: Transverse single-spin asymmetry for diffractive EM-jet as a
function of $x_{F}$ in transversely polarized proton-proton collisions at
$\sqrt{s}=$ 200 GeV [69]. The blue points are for $x_{F}>0$. The red points
are for $x_{F}<0$ with a constant shift of -0.005 along x-axis for clarity.
The rightmost points are for $0.3<|x_{F}|<0.45$.

Figure 18:  Left: Transverse single-spin asymmetry as a function of $x_{F}$
for electromagnetic jets in transversely polarized proton-proton collisions at
$\sqrt{s}=$ 200 and 500 GeV [68]. Right: Comparison between the Sivers first
$k_{\perp}$-moments from SIDIS data and their reweighted SIDIS+jet (data from
STAR) in two frameworks: GPM and CGI-GPM [70].

Firstly, the topological dependence of the $\pi^{0}$ $A_{N}$ was studied, and
the $A_{N}$ of the isolated $\pi^{0}$’s (meaning no other particles around)
are significantly larger than the non-isolated ones, as shown in the middle
panel of Fig. 16. Consistent results were obtained in both $pp$ and $pA$
collisions with very weak $A$ dependence in $pA$ [68, 60]. This triggered
discussions on the possible contribution from the diffractive process, which
motivated a measurement of $A_{N}$ for singly and double diffractive events,
utilizing the STAR Roman Pot detectors to tag diffractive processes with
scattered protons close to the beamline. Figure 17 shows the preliminary
results for forward diffractive EM-jet $A_{N}$ as a function of $x_{F}$ at
$\sqrt{s}=$ 200 GeV [69]. The results favor a non-zero negative $A_{N}$ with
3.3$\sigma$ significance, so these diffractive processes are most probably not
the source of the large positive $A_{N}$ of $\pi^{0}$. The negative
contribution from diffractive jets is not currently described by theory.

In studying the contribution from the final-state effect, STAR also measured
the Collins asymmetry of $\pi^{0}$ in an electromagnetic jet, which is shown
in the right panel of Fig. 16. The measured Collins asymmetry was consistent
with zero, in agreement with a theoretical prediction based on collinear
twist-3 factorization, resulting from significant cancellation between Collins
effects of different quark flavors [55].

In a closely related study, RHICf has measured $A_{N}$ for neutral pions in
510 GeV $pp$ collisions at very large pseudorapidity ($\eta>6$), very large
$x_{F}$ (up to 0.8), and $p_{T}<1$ GeV/$c$ [71]. The asymmetries that they
found are similar to those at comparable $x_{F}$ and much higher $p_{T}$, as
shown in the left panel of Fig. 16. A very recent calculation [72] based on
diffractive triple Regge exchange provides a very good description of the
RHICf $A_{N}$ results.

Another study is the measurement of the $A_{N}$ for inclusive electromagnetic
jets, which is considered only related to the initial-state effect. The
results of electromagnetic jet $A_{N}$ in both 200 and 500 GeV $pp$ collisions
are shown in the left panel of Fig. 18. The electromagnetic jet $A_{N}$ was
found to increase with $x_{F}$, but the magnitude is much smaller than the
$\pi^{0}$ $A_{N}$. These data have been included in the recent global fit of
the Sivers function [70], and showed a significant impact in constraining the
Sivers function, as shown in the right panel of Fig. 18.

With the implementation of the Forward Upgrade at STAR in the $pp$ and $pA$
running in 2022 and 2024, we will be able to perform measurements with full
jets in the forward rapidity region and also the Collins asymmetry with charge
separated hadrons, which will provide a much deeper understanding of the
underlying QCD mechanism.

###  4.4 Transverse single-spin asymmetry of weak bosons

Proton-proton collisions at $\sqrt{s}$ = 510 GeV allow STAR to study the
evolution and sign change of the Sivers function with weak bosons at mid-
rapidity ($-1<y^{W^{\pm}/Z^{0}}<1$). By focusing on interactions in which the
final state involves only leptons, and hence the transverse partonic motion
must be in the initial state, one can test the predicted sign change in
$A_{N}$ relative to interactions in which these terms must appear in the final
state, such as SIDIS measurements. Following the low statistics proof-of-
principle measurement using the 2011 data, STAR measured the transverse
single-spin asymmetry $A_{N}$ for $W$ and $Z$ with 2017 data, which had about
14 times more integrated luminosity.

Figure 19:  Left: Transverse single-spin asymmetry of $Z^{0}$ from STAR 2011
and 2017 data. The results are compared with the calculation from [73]. Middle
and Right: Transverse single-spin asymmetry of $W^{\pm}$ from STAR 2017, and
the projected statistical uncertainties from 2017 and 2022 data. The results
are compared with calculation from [73] based on the next-to-next-to-next-to
leading log ($\mathrm{N}^{3}$LL) accuracy TMD evolution from [74].

In Fig. 19, the recent preliminary results on $A_{N}$ of $W/Z$ are compared
with predictions from [73, 74] that include STAR 2011 data. The recent global
QCD extraction of the Sivers function including STAR 2011 $W$ and $Z$ $A_{N}$
data from [75] can be found in Fig. 20. With the increased precision provided
by Run-17, we find smaller asymmetries than were suggested by Run-11. As a
result, the increased statistics of the 2022 dataset are critical to improve
the precision of our asymmetry measurements in order to provide a conclusive
test of the Sivers’ function sign change. Projected statistical uncertainties
of $W$ $A_{N}$ from combined 2017 and 2022 data can be found in Fig. 19. The
figure also illustrates that the improved tracking capabilities provided by
the STAR iTPC upgrade will allow us to push our mid-rapidity $W^{\pm}$ and $Z$
measurements to larger rapidity $y^{W/Z}$, a regime where the asymmetries are
expected to increase in magnitude and the anti-quark Sivers’ functions remain
largely unconstrained.

Figure 20:  The first transverse moment $xf_{1T}^{\perp(1)}$ of the Sivers TMD
as a function of $x$ for the up (left panel) and down quark (right panel)
extracted from world data including STAR 2011 $W/Z$ data. Solid band: the 68%
confidence interval obtained in this work at $Q^{2}=4$ GeV2. The plot is from
[75].

###  4.5 Transverse single-spin asymmetries of direct photons and heavy flavor
decay leptons

PHENIX has reported the first direct photon transverse single-spin asymmetry
result at RHIC [76]. The asymmetry was measured at midrapidity $|\eta|<0.35$
in $pp$ collisions at $\sqrt{s}=$ 200 GeV. Photons do not interact via the
strong force, and at this kinematics they are produced dominantly by the
quark-gluon Compton process. Therefore, the measurement offers a clean probe
of gluon dynamics that is only sensitive to initial-state effects. The
asymmetry is shown in Fig. 21 and is consistent with zero to within 1% across
the measured $p_{{}_{T}}$ range. The result is also compared with predictions
from collinear twist-3 correlation functions. The solid green curve shows the
contribution from $qgq$ correlation function [77] while the dashed (blue) and
dotted (red) curves are from $ggg$ correlation functions [78]. Given the small
predicted contributions from $qgq$ correlation functions to the asymmetry, the
result can provide a constraint on the $ggg$ correlation function. sPHENIX is
expected to significantly improve direct photon $A_{N}$ measurements shrinking
the uncertainties by more than a factor of two.

Figure 21: Transverse single-spin asymmetry of isolated direct photons at
$\sqrt{s}=$ 200 GeV compared with calculations from $qgq$ and $ggg$
correlation functions. Source: [76].

Similarly, the production of open heavy flavor at RHIC energies is dominated
by gluon-gluon hard interactions. As such, also in single-spin asymmetries of
heavy flavor decay leptons no final-state effect contributions are expected,
and one is almost entirely sensitive to the initial state effects of the gluon
correlators. The recent heavy flavor decay electron single-spin asymmetries at
central rapidities obtained at PHENIX [79] are the first that quantify the
gluon correlator contributions in two theoretical models [80, 81], as can be
seen in Fig. 22. While each decay lepton asymmetry is only sensitive to a
linear combination of the two model parameters, the combination of both
charges enables the determination of both. In the 2024 data taking period,
these measurements can be augmented by sPHENIX measurements that reconstruct D
mesons directly and are expected to provide even higher precision to the tri-
gluon correlator.

Figure 22: Transverse single-spin asymmetries of heavy flavor decay electrons
at $\sqrt{s}=$ 200 GeV [79] including parameterizations of the tri-gluon
correlator in two theoretical models and the best values fitting the data [80,
81].

###  4.6 Nuclear dependence of single spin asymmetries

In 2015, RHIC also investigated polarized proton-nucleus collisions with
either Al or Au beams. These have been utilized to study the $A$ dependence of
the nonzero single-spin asymmetries that were observed for hadrons in the
forward region. In PHENIX the asymmetries for charged hadrons at rapidities of
1.2 to 2.4 were studied. A strong nuclear dependence was observed that was
consistent with an $A^{-1/3}$ suppression for positive hadrons [82], as shown
in Fig. 23. A similar suppression is also seen as a function of the centrality
of the collisions.

Figure 23: $A$ dependence of transverse single-spin asymmetries of positively
charged hadrons at $\sqrt{s}=$ 200 GeV at pseudo-rapidities of 1.2 to 2.4
measured at PHENIX [82], and sPHENIX projected uncertainties for data to be
collected with streaming readout.

STAR has also published the $A$ dependence for neutral pions at forward
rapidities of 2.7 to 3.8 and higher $x_{F}$ that also show a suppression of
the asymmetries [60]. However, in that rapidity region the suppression appears
much smaller than seen by PHENIX, as seen in Fig. 24. The initial motivation
for studying the nuclear dependence of the single-spin asymmetries originates
from possible saturation effects on these asymmetries, but it has since been
realized that the presented measurements neither reach $x$ nor scales that are
low enough for such effects to be relevant [83]. As such, there is at present
no clear understanding of the mechanism that produces the suppression of these
asymmetries.

The data to be collected by sPHENIX in $pp$ and $pAu$ collisions would not
only considerably improve the precision of PHENIX measurements for charged
hadron TSSA (Fig. 23), but also allow for fine binning of TSSA in $p_{T}$ and
$x_{F}$ in extended ranges. That will provide invaluable information for
studying rich phenomena behind TSSA in hadronic collisions, utilizing RHIC’s
unique capabilities to collide high energy polarized protons and heavy nuclei.

Figure 24: The exponent, $P$, for nuclear $A$ dependence of the $\pi^{0}$
transverse single-spin asymmetry ratio of $pA$ to $pp$ as a function of
$x_{F}$ at $\sqrt{s}=$ 200 GeV at $2.7<\eta<3.8$ at STAR [60]. The main
difference of two types of fits is with and without correlated uncertainties.

In the far forward region also the nuclear dependence of neutron asymmetries
was extracted as a function of transverse momentum and the longitudinal
momentum fraction [84, 85]. Neutron asymmetries in proton-proton collisions
can be described by the interference of pion and other meson interactions
between the two colliding nucleons [86] and are found to be negative. In
contrast, the $pAl$ asymmetries are on average close to zero, while the $pAu$
asymmetries change sign and have a significantly larger magnitude. It was
found that the origin of this nuclear dependence originates from the
additional contribution of ultra-peripheral collisions that increase
quadratically with the charge of the nucleus [87]. When correlating the
asymmetries with event activity related to hadronic activity, one indeed sees
that the asymmetries remain negative while the events more likely to originate
from ultra-peripheral collisions show even larger, positive asymmetries
already for $pAl$ collisions.

###  4.7 Ultra-peripheral collisions

Constraints on GPDs have mainly been provided by exclusive reactions in deep
inelastic scattering (DIS), e.g. deeply virtual Compton scattering. RHIC, with
its unique capability to collide transversely polarized protons at high
energies, has the opportunity to measure $A_{N}$ for exclusive $J/\psi$
production in ultra-peripheral collisions (UPCs) [88]. In such a UPC process,
a photon emitted by the opposing beam particle ($p$ or $A$) collides with the
polarized proton. The measurement is at a fixed $Q^{2}\sim
M_{J/\psi}^{2}\approx 10$ GeV2 and $10^{-4}<x<10^{-1}$. A nonzero asymmetry
would be the first signature of a nonzero GPD $E_{g}$ for gluons, which is
sensitive to spin-orbit correlations and is intimately connected with the
orbital angular momentum carried by partons in the nucleon and thus with the
proton spin puzzle.

The Run-15 $p^{\uparrow}Au$ data allowed a proof-of-principle of such a
measurement. A trigger requiring back-to-back energy deposits in the Barrel
Electromagnetic Calorimeter selected $J/\psi$ candidates. The $e^{+}e^{-}$
mass distribution after selection cuts is shown in the left of Fig. 25, and
the pair $p_{T}$ distribution of the $J/\psi$ mass peak is shown on the right
of that figure. The data are well described by the STARlight model [89]
(colored histograms in the figure), including the dominant
$\gamma$+$p^{\uparrow}\rightarrow J/\psi$ signal process and the
$\gamma$+$Au\rightarrow$$J/\psi$ and
$\gamma$+$\gamma$$\rightarrow$$e^{+}e^{-}$ background processes. The left of
Fig. 26 shows the STAR preliminary measurement (solid circle marker) of the
transverse asymmetry $A_{N}^{\gamma}$ for the $J/\psi$ signal, which has a
mean photon-proton center-of-mass energy $W_{\gamma p}\approx 24$ GeV. The
result is consistent with zero. Also shown is a prediction based on a
parameterization of $E_{g}$ [90]; the present data provide no discrimination
of this prediction.

Figure 25: Mass distribution of selected $e^{+}e^{-}$ pairs (left), and
$p_{T}$ distribution of the $J/\psi$ mass peak (right). The colored histograms
are the indicated processes modelled by STARlight and the sum fit to the data.

Figure 26:  Left: The measured $J/\psi$ transverse asymmetry $A_{N}^{\gamma}$
and a prediction based on a parameterization of $E_{g}$. Right: The accepted
cross section for $\gamma+p^{\uparrow}\rightarrow J/\psi$ for various detector
pseudorapidity $\eta$ ranges; the black curve shows the result for the full
STAR detector with the Forward Upgrade and the iTPC.

This measurement can be greatly improved with a high statistics transversely
polarized $p^{\uparrow}Au$ Run-24. The integrated luminosity for the Run-15
measurement was 140 nb-1; Run-24 will provide about 1.2 pb-1, allowing a
sizeable reduction of statistical uncertainty in the same $W_{\gamma p}$
range. In addition, the Forward Upgrade and iTPC will provide a significant
extension of the $W_{\gamma p}$ range of the measurement. The right panel of
Fig. 26 shows the accepted cross section for $\gamma$+$p^{\uparrow}\rightarrow
J/\psi$ for various detector pseudorapidity ranges. With the full detector,
the sensitive cross section is a factor of five times the central barrel
alone. Also, the accepted region has a lower mean $W_{\gamma p}\approx 14$
GeV. Predictions based on $E_{g}$ parameterizations such as shown in the
figure have a larger asymmetry at lower $W_{\gamma p}$, with increased
possibility of a nonzero result. The projected statistical uncertainty on
$A_{N}^{\gamma}$ is shown in the left of Fig. 26 (blue square marker),
offering a powerful test of a non-vanishing $E_{g}$. Alternatively, the
increased statistics will allow a measurement of $A_{N}^{\gamma}$ in bins of
$W_{\gamma p}$.

The UPC cross section scales with $\sim Z^{2}$ of the the nucleus emitting the
photon; for protons this is $1/79^{2}$ relative to Au nuclei, which makes
analogous measurements in $pp$ collisions extremely luminosity-hungry.
Therefore, the $pAu$ run is important for this measurement.

##  5 Appendix

###  5.1 STAR Forward Upgrade

The STAR forward upgrade consists of four major new subsystems, an
electromagnetic calorimeter, a hadronic calorimeter and a tracking system,
formed from a silicon detector and a small-strip Thin Gap Chambers tracking
detector. It has superior detection capabilities for neutral pions, photons,
electrons, jets, and leading hadrons within the pseudorapidity range 2.5 <
$\eta$ < 4, see Fig. 27. The construction of the electromagnetic and hadronic
calorimeters was successfully completed by the end of 2020. They were fully
installed, instrumented, and commissioned during the 2021 RHIC running period.
The tracking detectors were installed in summer and fall 2021, on schedule and
ready for the start of Run-22. Note that the entire construction,
installation, and commissioning of the four systems were completed in the
pandemic period. Enormous efforts were made to keep the forward upgrades on
schedule. During Run-22, despite all the difficulties from the machine side,
the forward upgrades performed exceptionally well and took data smoothly
throughout the run. The forward upgrades will continue taking data in parallel
with sPHENIX through Run-25.

Figure 27: STAR detector with Forward Upgrades

  * •

Forward Calorimeter System:

The Forward Calorimeter System (FCS) consists of an Electro-Magnetic
Calorimeter (Ecal) with 1486 towers, and a Hadronic Calorimeter (Hcal) with
520 towers. All SiPM sensors, front-end electronics boards and readout &
triggering boards called DEP were installed, commissioned and calibrated
during Run-21. Signal splitter boards for the west EPD detector were installed
before Run-22, and the west EPD was used as pre-shower detector in the
electron triggers. FPGA code for FCS triggers was developed in fall 2021, and
total of 29 triggers, including triggers for electrons, di-electrons, jets,
di-jets, hadrons, and photons were commissioned and verified within a few days
of RHIC starting to deliver stable $pp$ collisions, and then used for data
taking throughout Run-22 successfully. FCS operations during Run-22 were
successful and smooth. The only minor exceptions were 3 low-voltage power
supply modules needing to be replaced, and occasional power cycling of
electronics being needed due to beam related radiation upsets in the
electronics. All 1486 channels of Ecal worked with no bad channels, and the
Hcal had only a couple of dead channels. Radiation damage to the SiPM sensors
due to beam was within expectations. There was an unexpected loss of signal
amplitudes of $\sim$20% per week in the Ecal near the beam, which turned out
to be radiation damage in the front-end electronics boards. The loss of signal
was compensated during Run-22 by changing the gain factors on the DEP boards,
attenuator settings in the front-end electronics, and raising the voltage
settings tower by tower based on LED signals. Details of the radiation damage
on the front-end electronics are currently under investigation.

  * •

Small-strip Thin Gap Chambers:

The sTGC has four identical planes, each plane has four identical pentagonal
shaped gas chambers. These gas chambers are made of double-sided and diagonal
strips that give $x$,$y$,$u$ in each plane. Sixteen chambers and about 5 spare
chambers were built at Shandong University in China. A custom designed and
fabricated aluminum frame allowed to fit the detector inside the pole-tip of
the STAR magnet and around the beam-pipe on the west side of STAR. The sTGC
chambers are operated with a quenching gas mixture of $n$-Pentane and CO2 at a
ratio of 45%:55% by volume at a typical high voltage of 2900 V. This gas
mixture allowed the chambers to operate in a high amplification mode. The sTGC
was fully installed prior to the start of Run-22, and the detector was fully
commissioned during the first few weeks of the run. The operating point of the
high voltage was scanned for optimum efficiency. The gas chambers were stable
at the desired operational high voltage and at the high luminosity, also the
leakage current was well within the operational limits. In-house, a newly
designed and built gas system for mixing, and supplying the gas along a long-
heated path to deliver to the chambers, met the above requirements, and
performed exceptionally well during Run-22.

  * •

Forward Silicon Tracker:

The Forward Silicon Tracker (FST) consists of three identical disks, and each
disk contains 12 modules. Each module has 3 single-sided double-metal Silicon
mini-strips sensors which are read out by 8 APV chips. The module production
was done by NCKU, UIC, and SDU. The readout was done by BNL and IU. The
cooling was provided by NCKU and BNL. The installation of the FST was
completed on August 13th, 2021, and the first $pp$ 510 GeV collision data were
recorded on December 15, 2021. The FST ran smoothly through the whole Run-22,
and the detector operation via slow control software was minimal to the shift
crew.

###  5.2 sPHENIX Detector

sPHENIX is a major upgrade to the PHENIX experiment at RHIC capable of
measuring jets, photons, charged hadrons, and heavy flavor probes. sPHENIX
will play a critical role in the completion of the RHIC science mission,
focused on the studies of the microscopic nature of Quark-Gluon Plasma.
Polarized proton collisions as well as proton-nucleus collisions will also
provide key opportunities for cold QCD measurements.

sPHENIX is a central rapidity detector ($|\eta|<1.1$) built around the Babar
solenoid with magnetic field up to 1.5T. The major systems are a high
precision tracking system, and electromagnetic and hadronic calorimeters, see
Fig. 28.

Figure 28: sPHENIX detector layout.

The electromagnetic calorimeter is a compact tungsten-scintillating fiber
design located inside the solenoid. The outer hadronic calorimeter consists of
steel in which scintillator tiles with light collected by wavelength shifting
fibers are sandwiched between tapered absorber plates that project nearly
radially from the interaction point. It also serves as a flux return of the
1.5 T superconducting solenoid. The inner HCal is instrumented with
scintillating tiles similar to the tiles used in the Outer HCal, and serves as
a support structure of the electromagnetic calorimeter. The calorimeters use a
common set of silicon photomultiplier photodetectors and amplifier and
digitizer electronics. Based on test beam data, such a calorimeter system is
expected to provide the energy resolution of
$\sigma_{E}/E=13\%/\sqrt{E[GeV]}\oplus 3\%$ for electromagnetic showers, and
$\sigma_{E}/E=65\%/\sqrt{E[GeV]}\oplus 14\%$ for hadrons.

The central tracking system consists of a small Time Projection Chamber (TPC),
micro vertex detector (MVTX) with three layers of Monolithic Active Pixel
Sensors (MAPS), and two layers of the intermediate silicon strip tracker
within the inner radius (INTT). Such a system provides momentum resolution
$\sigma_{pT}/p_{T}<0.2\%\cdot p_{T}\oplus 1\%$ for $p_{T}=$0.2–40 GeV/c, and
Distance of Closest Approach (DCA) resolved at 10 $\mu$m for $p_{T}>2$ GeV/c.
The INTT with its fast integration time resolves beam crossings and provides
pileup suppression.

The other sPHENIX subsystems are the Minimum Bias Detector (MBD) consisting of
the refurbished PHENIX Beam-Beam Counter, Event Plane Detector (sEPD)
consisting of two wheels of scintillator tiles positioned at $2<|\eta|<4.9$
and serving for event plane measurements, and Micromegas-based TPC Outer
Tracker (TPOT), offering calibration of beam-induced space charge distortions
in TPC.

High speed data acquisition system is designed to be capable of taking minimum
bias $AuAu$ collisions at 15 kHz with greater than 90% live time, and jet and
photon triggers for $pp$ and $pA$ operation. The DAQ system is design to be
capable to work in hybrid mode: along with triggered data it will collect a
significant fraction ($\sim 10\%$) of all collision data from tracking
detectors in streaming readout regime, which will greatly extend physics
program in $pp$ and $pAu$ running.

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