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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Quark sivers function at small x: spin-dependent odderon and the sub-eikonal evolution

We apply the formalism developed earlier for studying transverse momentum dependent parton distribution functions (TMDs) at small Bjorken x to construct the small- x asymptotics of the quark Sivers function. First, we explicitly construct the complete fundamental “polarized Wilson line” operator to sub-sub-eikonal order: this object can be used to study a variety of quark TMDs at small x . We then express the quark Sivers function in terms of dipole scattering amplitudes containing various components of the “polarized Wilson line” and show that the dominant (eikonal) term which contributes to the quark Sivers function at small x is the spin-dependent odderon, confirming the re- cent results of Dong, Zheng and Zhou. Our conclusion is also similar to the case of the gluon Sivers function derived by Boer, Echevarria, Mulders and Zhou. We also analyze the sub-eikonal corrections to the quark Sivers function using the constructed “polarized Wilson line” operator. We derive new small- x evolution equations re-summing double-logarithmic powers of α s ln 2 (1 /x ) with α s the strong coupling constant. We solve the corresponding novel evolution equations in the large- N c limit, obtaining a sub-eikonal correction to the spin-dependent odderon contribution. We conclude that the quark Sivers function at small x receives contributions from two terms and is given by ${f}_{1T}^{\perp q}\left(x,{k}_T^2\right)={C}_O\left(x,{k}_T^2\right)\frac{1}{x}+{C}_1\left({k}_T^2\right){\left(\frac{1}{x}\right)}^0+\cdots$ with the function C O ( x, ${k}_T^2$) varying slowly with x and the ellipsis denoting the subasymptotic and sub-sub-eikonal (order- x ) corrections.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

Eikonal spin-dependent odderon and gluon Sivers function of a proton and its small-𝑥 evolution

The matrix element in the proton of the eikonal Odderon operator, with a helicity flip, has been shown to correspond to the dipole gluon Sivers function. We employ a three quark light-front model of the proton to determine the Sivers function at moderately small 𝑥 0 ∼ 0.1 and transverse momentum 𝑘 ⊥ ≲ 1 GeV. The model light-cone (LC) wave function predicts the properties of 𝑥⁢𝑓$^{⊥⁢𝑔}_{1⁢𝑇⁡}$(𝑥,𝑘 ⊥ ) such as its overall magnitude, the position of its peak in 𝑘 ⊥ , and its behavior at small 𝑘 ⊥ . We then compute numerically the Balitsky-Fadin-Kuraev-Lipatov anomalous dimension characterizing the power-law tail at 𝑘 ⊥ ≳ 1.5 GeV of the gluon Sivers function at small (but preasymptotic) LC momentum fractions 𝑥 ∼ 𝑥 0 ⁢𝑒 −1/𝛼 𝑠 : 𝑥⁢𝑓$^{⊥⁢𝑔}_{1⁢𝑇⁡}$⁡(𝑥,𝑘 ⊥ ) ∼ 𝑘$^{−3.3}_{⊥}$.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Quark Sivers Function at Small-$x$: Leading contribution from the Spin-Dependent Odderon

We present the calculation of the leading contribution to the quark Sivers function at small-Bjorken x as in [1]. This calculation uses the high energy scattering approximation and operator formalism developed in [2,3] to obtain a dominant contribution to the quark Sivers function coming from the spin-dependent odderon, in agreement with the results of [4]. We then calculate this dominant contribution in the diquark model of the proton to obtain a small-x estimate for the Sivers function.

Santiago, M. Gabriel↗
DOE OSTI2025

Gluon Sivers function from forward exclusive χ c 1 photoproduction on unpolarized protons

Exclusive production of a χ c 1 axial vector quarkonia in photon-proton scattering at high energies requires a C -odd t -channel exchange. In the limit of vanishing momentum transfer this occurs either via the exchange of a photon, the Primakoff process, where the spin of the proton does not change. For axial-vector meson production, as a consequence of the Landau-Yang theorem, the Primakoff cross section is finite as t → 0 . Alternatively, a C -odd spin dependent Odderon can be exchanged, which involves a spin flip of the proton. The resulting cross section is related to the square of the collinear trigluon correlator or the k ⊥ -moment of the gluon Sivers function. Using two models for the gluon Sivers function from the literature we compute the ratio of Sivers to Primakoff cross sections and the angular coefficient λ θ governing the angular distribution of the χ c 1 → J / ψ + γ decay as functions of x . We point out that these observables constrain the magnitude of the gluon Sivers function at small x which could be accessed in electron-proton scattering and ultraperipheral proton-proton and nucleus-proton collisions. Published by the American Physical Society 2025

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Reweighting the Sivers function with jet data from STAR

The reweighting procedure that using Bayesian statistics incorporates the information contained in a new data set, without the need of re-fitting, is applied to the quark Sivers function extracted from Semi-Inclusive Deep Inelastic Scattering (SIDIS) data. We exploit the recently published single spin asymmetry data for the inclusive jet production in polarized pp collisions from the STAR Collaboration at RHIC, which cover a much wider x region compared to SIDIS measurements. The reweighting method is extended to the case of asymmetric errors and the results show a remarkable improvement of the knowledge of the quark Sivers function.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Reweighting the quark Sivers function with STAR jet data

The Bayesian reweighting procedure is applied for the first time to a TMD distribution, the quark Sivers function extracted from SIDIS data. By exploiting the recent published single spin asymmetry data for the inclusive jet production in p^\uparrow p p ↑ p collisions from the STAR collaboration at RHIC, we show how such a procedure allows to incorporate the information contained in the new data set, without the need of re-fitting, and to explore a much wider x x region compared to SIDIS measurements. The reweighting method is also extended to the case of asymmetric errors, and the results show a significant improvement on the knowledge of the quark Sivers function.

Flore, Carlo↗
DOE OSTI2024

Unveiling Sea Quark Dynamics: Measuring Sivers Asymmetry with Polarized Target at SpinQuest

SpinQuest is a cutting-edge, high-luminosity Drell-Yan experiment utilizing polarized hy- drogen and deuterium targets to measure the Sivers asymmetry for the light sea quarks in the nucleon. Detecting a nonzero Sivers asymmetry would provide clear evidence for nonzero or- bital angular momentum of sea quarks. The Sivers asymmetry presents itself as an azimuthal asymmetry in the production of virtual photons via the Drell-Yan process, and SpinQuest will be able to measure this asymmetry using the existing SeaQuest dimuon spectrometer. In addi- tion to making measurements sensitive to the sea quark Sivers function, we will also measure the azimuthal asymmetry in the production of J/ψ particles, which is sensitive to the gluon Sivers function. Additionally, observing a sign change in the Sivers asymmetry between this measurement and future measurements at the Electron-Ion Collider would be a test of a funda- mental prediction of Quantum Chromodynamics. In this poster we will review the physics and technology underpinning the experiment.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

SpinQuest in 10 Minutes

The SpinQuest experiment at Fermi National Accelerator Laboratory uses a 120 GeV proton beam from the Main Injector, incident upon transversely polarized protons and deuterons using $NH_3$ and $ND_3$ targets, respectively. SpinQuest will perform the first measurement of the Sivers asymmetry in Drell-Yan \(pp\) and \(pd\) scattering from sea quarks, thereby contributing to the world data to extract the Sivers function for the light sea quarks. This function describes the correlation between the momentum direction of the struck quark and the spin of its parent nucleon. A non-vanishing Sivers function for the sea quarks is evidence that there is sea quark orbital angular momentum (OAM). There are additional opportunities to study transverse-spin effects with the SpinQuest experiment, particularly the transverse single-spin asymmetry (TSSA) in \( J/\psi \) production. An update on the current status and progress of the experiment will be given.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Measurements of the $Z$ 0 /$γ$* cross section and transverse single spin asymmetry in 510 GeV $p$ + $p$ collisions

The differential cross section for Z 0 production, measured as a function of the boson’s transverse momentum (p T ), provides important constraints on the evolution of the transverse momentum dependent parton distribution functions (TMDs). The transverse single spin asymmetry (TSSA) of the Z 0 is sensitive to one of the polarized TMDs, the Sivers function, which is predicted to have the opposite sign in p + p → W/Z + X from that which enters in semi-inclusive deep inelastic scattering. In this Letter, the STAR Collaboration reports the first measurement of the Z 0 /γ* differential cross section as a function of its p T in p+p collisions at a center-of-mass energy of 510 GeV, together with the Z 0 /γ* total cross section. We also report the measurement of Z 0 /γ* TSSA in transversely polarized p+p collisions at 510 GeV.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Transverse Single-Spin Asymmetries of Midrapidity Direct Photons and Neutral Mesons at PHENIX

Results are presented for the transverse single-spin asymmetries of direct photons, neutral pions, and eta mesons for |\eta|<0.35 | η | < 0.35 from p^\uparrow + p p ↑ + p collisions with \sqrt{s} = 200 s = 200 GeV at PHENIX. As hadrons, \pi^0 π 0 and \eta η mesons are sensitive to both initial- and final-state effects and at midrapidity probe the dynamics of gluons along with a mix of quark flavors. Because direct photon production does not include hadronization, the direct photon TSSA is only sensitive to initial-state effects and at midrapidity provides a clean probe of the gluon dynamics in transversely polarized protons. All three of these results will help constrain the collinear twist-3 trigluon correlation function as well as the gluon Sivers function, improving our knowledge of spin-dependent gluon dynamics in QCD.

Lewis, Nicole↗
DOE OSTI2026

Small-𝑥 asymptotics of the leading-twist flavor-singlet quark TMDs

In this paper, we investigate the small-𝑥 behavior of the flavor-singlet, leading-twist quark transverse-momentum-dependent parton distribution functions (TMDs) using the light-cone operator treatment. This formalism allows us to express TMD operators at small 𝑥 in terms of polarized dipole amplitudes, enabling a systematic approach to their small-𝑥 evolution. We derive the evolution equations for these TMDs and solve them within the large-𝑁 𝑐 approximation under the linearized, double-logarithmic approximation, where 𝑁 𝑐 represents the number of quark colors. Expanding on previous work on unpolarized and helicity TMDs, we present the small-𝑥 asymptotics for a comprehensive set of TMDs, including the Sivers function, helicity worm-gear, transversity, pretzelosity, Boer-Mulders, and transversity worm-gear distributions. Our results provide a complete picture of the small-𝑥 asymptotic behavior for all leading-twist flavor-singlet quark TMDs. We also discuss the implications of our findings for phenomenological applications and outline potential avenues for further research, particularly in understanding nonlinear effects and extending beyond the double-logarithmic approximation and large-𝑁 𝑐 approximations.

Adamiak, Daniel [Thomas Jefferson National Acceler↗
DOE OSTI2022

Sivers extraction with Neural Network

Pseudo-data with simulated experimental errors can be generated to train an ensemble of Artificial Neural Networks (ANN) implemented on a regression to extract Transverse Momentum-dependent Distributions (TMDs). A preliminary analysis is presented on the reliability in extraction of the Sivers function imposed in the pseudo-data given the bounds on the experimental errors, data sparsity, and complexity of phase-space.

Fernando, Ishara↗
DOE OSTI2021

Proceedings of RIKEN BNL Research Center Workshop: Small-x Physics in the EIC Era [Slides]

Understanding the high energy limit of hadronic and nuclear collisions is at the forefront of nuclear and particle physics. When boosted to ultrahigh energies, all hadrons and nuclei eventually transform into a universal form of matter called the Color Glass Condensate (CGC). The CGC is characterized by the high density (saturation) of small-x gluons which leads to distinct experimental signatures. Tantalizing hints of the CGC have been observed at HERA, RHIC and the LHC, but the prospects for the discovery of the CGC are more promising at future experiments such as the Electron-Ion Collider (EIC) at BNL Indeed, according to the National Science Academy report published in 2019, one of the three major goals of the EIC is to address the nature of the gluon saturation. (The other two are the mass and spin structure of the nucleons.) With this in mind, the small-x community is gearing up to meet the challenges of the EIC era. Over the past several years, there has been impressive progress in the next-to-leading order (NLO) calculations in the CGC framework of various observables such as single hadron production in proton-nucleus collisions, inclusive and exclusive dijet and trijet production in Deep Inelastic Scattering (DIS), jet-plus-photon production in DIS, etc. We expect that NLO calculations will be the standard tool to confront future experimental data at the EIC. Another emerging trend of the community is the interplay between small-x physics and spin physics. The RHIC result for the gluon helicity ΔG has underscored the necessity to understand the longitudinal spin structure of the proton at small-x. There have been theoretical indications that a significant fraction of spin and orbital angular momentum is stored in the small-x region. As for the transversely polarized proton, a surprising new connection between the gluon Sivers function at small-x and the QCD Odderon has been pointed out and its implications at the EIC has been discussed. In view of these developments, we think it is timely to organize a dedicated workshop on small-x physics to summarize the present status of the field and to discuss future directions. A major focus of this workshop will be to identify outstanding problems that could significantly benefit from collaborative efforts amongst scientists working on formal, phenomenological, and computational aspects of small-x physics.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Beam Non-Uniformity Characterization at the SpinQuest and DarkQuest Experiments

The SpinQuest experiment, including upgrades to SpinQuest designed to increase sensitivity to dark sector searches (commonly known as DarkQuest), utilizes the high-intensity 120 GeV proton beam delivered by the Fermilab Accelerator Complex to probe the inner structure of nucleons and search for new physics beyond the Standard Model. The SpinQuest beam is extracted from the Main Injector synchrotron at Fermilab in what is known as a slow spill . The slow spill involves a complex non-linear half-integer extraction method, which results in non-uniform beam behavior. SpinQuest observes spikes of very high intensity beam which can saturate detectors and reduce trigger efficiency, significantly impacting the experiment's sensitivity. In this project we address this challenge by developing an analysis framework to characterize the beam delivered to SpinQuest. By discovering trends within each spill and by comparing thousands of spills, we can better inform the Accelerator Division and improve the slow spill extraction. We have also begun a collaboration with the Accelerator Division in order to simulate the slow spill and improve the magnet ramp process controls which will improve the uniformity of the beam. These improvements will directly enhance the physics reach of SpinQuest/DarkQuest, increasing their sensitivity to key measurements such as the Sivers function and searches for new physics.

Dolen, James William [Purdue U., Calumet] (ORCID:0↗
DOE OSTI2025

Beam Commissioning Result of Polarized Target at SpinQuest

SpinQuest is a fixed-target experiment at Fermilab to measure the Drell-Yan process using transversely polarized NH$_3$ and ND$_3$ targets and unpolarized 120-GeV proton beam. In the Drell-Yan process, a quark in one scattering hadron and an anti-quark in the other hadron annihilate into a virtual photon and then decay into a muon (lepton) pair. The angular distribution of final-state muon pairs with respect to the target polarization is sensitive to the Sivers function of light antiquarks in the nucleon, which is one of the eight Transverse Momentum Dependent (TMD) parton distribution functions. The intensity of the proton beam is as high as $10^{12}$ protons/second, in order to accumulate the required statistics of Drell-Yan events. The polarized target system at SpinQuest has been carefully designed to accommodate such a high beam intensity. It is equipped with an evaporation refrigerator with a cooling power of around 5 W at 1 K. The target temperature is maintained at 1 K even under heat load caused by the proton beam and the DNP microwave. The target system and the spectrometer were commissioned with the proton beam from May through July 2024. The experimental setup of SpinQuest and the performance of the target system during the beam commissioning is reported.

Nakano, Kenichi [Virginia U.]↗