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Spin Physics at PHENIX

Situated at the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory, the PHENIX experiment has for almost two decades been at the forefront of investigations into spin structure and dynamics in high-energy nuclear physics. Although decommissioned in 2016, the PHENIX collaboration has released a number of new results over the past several years that continue to inform the field. Recent longitudinal spin measurements uncover the role of gluon and sea quark polarization in the proton. Transverse spin measurements probe the transverse momentum-dependent (TMD) distributions and higher-twist multiparton correlators that are needed to fully explain partonic dynamics in the initial and final state. Additionally, the effects of heavy ions on spin have been studied by comparing transverse spin measurements between p+p and p+A collisions. These recent results and their wider implications are presented.

PHENIX

String-based axial and helicity-flip GPDs: A comparison to lattice QCD

We construct an analytic, string-based representation of the nucleon’s axial and helicity-flip conformal moments of generalized parton distributions (GPDs) that holds for skewness and for both the quark and gluon channels. The starting point is the Mellin-Barnes resummation of the conformal partial-wave expansion, where the moments are parametrized by open- (Reggeon) and closed-string (Pomeron) trajectories with slopes determined by experimental form factors and meson/glueball spectroscopy. The forward limits are fixed by the empirical unpolarized and polarized parton distributions. Polynomiality, crossing symmetry, and support are satisfied by construction. After next-to-leading order Dokshitzer-Gribov-Lipatov-Altarelli-Parisi/Efremov-Radyushkin-Brodsky-Lepage evolution to μ = 2 GeV our analytic framework (i) reproduces some of the currently available lattice moments of E and H˜ in the nonsinglet sector, (ii) predicts sea-quark and gluon polarized moments that will be testable by forthcoming simulations and experiments at Jefferson Lab and the future Electron-Ion Collider, and (iii) yields axial and helicity-flip GPDs in x-space in reasonable agreement with lattice QCD.

Gauge-gravity dualities

Two-pion contribution to the hadronic vacuum polarization with staggered quarks

We present results from the first lattice QCD calculation of the two-pion contributions to the light-quark connected vector-current correlation function obtained from staggered-quark operators. We employ the MILC Collaboration’s gauge-field ensemble with 2 + 1 + 1 flavors of highly improved staggered sea quarks at a lattice spacing of a ≈ 0.15 fm with a light sea-quark mass at its physical value. The two-pion contributions allow for a refined determination of the noisy long-distance tail of the vector-current correlation function, which we use to compute the light-quark connected contribution to hadronic vacuum polarization (HVP) with improved statistical precision. We compare our results with traditional noise-reduction techniques used in lattice QCD calculations of the light-quark connected HVP, namely, the so-called fit and bounding methods. We observe a factor of roughly 3 improvement in the statistical precision in the determination of the HVP contribution to the muon’s anomalous magnetic moment over these approaches. We also lay the group theoretical groundwork for extending this calculation to finer lattice spacings with increased numbers of staggered two-pion taste states.

Lahert, Shaun [Utah U.; Illinois U., Urbana] (ORCI

An Iterative Machine Learning Framework for Event Classification and Monte Carlo Tuning in SpinQuest

The E1039/SpinQuest experiment at Fermi National Accelerator Laboratory uses a 120~GeV proton beam from the Main Injector incident on transversely polarized proton and deuteron targets, using $NH_3$ and $ND_3$, respectively. In addition to measuring the Sivers asymmetry in Drell--Yan $pp$ and $pd$ scattering from sea quarks, SpinQuest will study transverse-spin effects, particularly the transverse single-spin asymmetry (TSSA) in $J/\psi$ production. The angular distributions from the $J/\psi$ decay could play an important role in understanding the gluon contribution to the proton spin structure. However, before extracting these angular distributions, it is necessary to isolate signal events originating from the target from events produced by other sources and from the combinatorial background. To effectively and accurately classify the target events, it is important to ensure that the simulated events are properly tuned to the experimental physics channels. We have introduced an iterative technique to match simulated and experimental events and to classify the physics channels using deep neural networks and a generative model based on normalizing flows.

Hossain, Forhad [Virginia U. (main)] (ORCID:000000

Collins asymmetries for pion-in-jet production in polarized ℓp collisions at the EIC

We study Collins azimuthal asymmetries for pion-in-jet production in polarized lepton-proton collisions, extending previous analyses of polarized pp scattering to a complementary and theoretically simpler process. We keep adopting a simplified transverse momentum dependent (TMD) approach, with a collinear configuration for the initial state, and employ the transversity and Collins fragmentation functions as extracted from semi-inclusive deep inelastic scattering and $e^{+}e^{-}$ annihilation processes. We then compute azimuthal asymmetries for the Electron-Ion Collider (EIC) kinematics, both within a leading order (LO) approach and by including quasireal photon exchange in the Weizsäcker-Williams approximation. Although this contribution is relevant in the whole kinematical range explored, it does not spoil the dominance of quark-initiated channels, leaving only a marginal role to their gluon counterparts. In this respect, Collins asymmetries in lepton-proton processes allow for a much clearer access to the transversity distribution, including its sea-quark component. As we will argue, a comparison with future EIC data could represent a further step in testing the hypothesis of the universality of the Collins function as well as of the TMD factorization for this class of processes.

Azimuthal asymmetries

Exploring the Nucleon Structure via Deep Electroproduction Processes

Understanding the internal structure of the nucleon is a fundamental goal of modern physics, which aims at a comprehensive framework describing the internal dynamics of quarks and gluons. Among other structure functions, Generalized Parton Distributions (GPDs) offer a powerful framework for describing the nucleon dynamics by correlating the longitudinal momentum and the transverse position of its internal partons. Such a correlation provides a three-dimensional picture of the nucleon and enables access to fundamental properties, including the internal pressure distributions and the parton’s angular momentum contribution to the nucleon's total spin, thereby playing a central role in resolving the nucleon spin puzzle. At the Thomas Jefferson National Facility (JLab), polarized electron beam experiments allow for probing GPDs through the measurement of hard exclusive processes. Among the cleanest experimental channels, we find the electro-production of a real photon through the Deeply Virtual Compton Scattering (DVCS) mechanism. The first data-taking period of the CLAS12 program, taking place in 2018, allowed for unique DVCS Beam Spin Asymmetry (BSA) measurements in the phase space covered by a 10.6 GeV polarized electron beam impinging on an unpolarized liquid hydrogen target. Although detecting all final-state particles ensures exclusivity of the process, conservation laws indicate that it is not mandatory. I adopt an approach omitting the direct detection of the recoil proton, providing a simplified yet effective event selection strategy that boosts statistics and gives access to a larger phase space sensitive to the underlying GPD dynamics through BSA and cross section measurements. The Double DVCS (DDVCS) process promises a dedicated mapping of GPDs. Contributing to the electro-production of a lepton pair cross-section, the DDVCS reaction extends DVCS by allowing the final-state photon to be virtual, enriching the kinematic phase space and providing unique access to the internal correlations encoded by GPDs. A feasibility study is conducted to assess the potential of future DDVCS measurements at Jefferson Lab and the future Electron-Ion Collider (EIC). While Jefferson Lab will provide DDVCS measurements in the valence region through the SoLID$\mu$ and $\mu$CLAS12 experimental projects, in the long term, the EIC will provide complementary measurements in the sea region, both accessing unprecedented information about GPDs in a phase space region otherwise inaccessible. Taken together, these investigations demonstrate both the current capabilities and future opportunities for probing GPDs through exclusive processes. The experimental analysis of DVCS at CLAS12 provides precise measurements within an established framework, while the phenomenological study of DDVCS opens the door to richer and more comprehensive explorations with future detectors and facilities.

Alvarado, Juan [Université Paris-Saclay: Gif-sur-Y