Sivers Asymmetry Research Articles

High-Statistics Measurement of Collins and Sivers Asymmetries for Transversely Polarized Deuterons

New results are presented on a high-statistics measurement of Collins and Sivers asymmetries of charged hadrons produced in deep inelastic scattering of muons on a transversely polarized LiD6 target. The data were taken in 2022 with the COMPASS spectrometer using the 160 GeV muon beam at CERN, statistically balancing the existing data on transversely polarized proton targets. The first results from about two-thirds of the new data have total uncertainties smaller by up to a factor of three compared to the previous deuteron measurements. Using all the COMPASS proton and deuteron results, both the transversity and the Sivers distribution functions of the u and d quark, as well as the tensor charge in the measured x range are extracted. In particular, the accuracy of the d quark results is significantly improved. Published by the American Physical Society 2024

Transverse momentum weighted Sivers asymmetries in SIDIS and Drell-Yan processes at COMPASS

We investigate the transverse momentum weighted Sivers asymmetries in the processes with transversely polarized proton target, including the PhTzMpsin⁡(ϕh−ϕS) weighted asymmetry in charged hadron production in semi-inclusive deeply inelastic scattering (SIDIS) and the qTMpsin⁡(ϕS) weighted asymmetry in π−p Drell-Yan process. These asymmetries can be expressed as the product of the transverse-moments of the transverse momentum dependent (TMD) parton distribution functions (PDFs) and fragmentation functions (FFs). Using the parametrization for the Sivers function of the proton, the unpolarized PDFs of proton and pion, and the unpolarized FF of charged hadron, we present the numerical calculation for weighted Sivers asymmetries in SIDIS and Drell-Yan processes at the kinematics of COMPASS. We find that our prediction for the SIDIS process is in agreement with the recent COMPASS measurement. Recent new high-statistics data of Sivers asymmetry measured in SIDIS process and Drell-Yan process from COMPASS favored the sign change of Sivers function. High-precision experimental data of weighted asymmetries are still needed to test the sign change property of the Sivers function between SIDIS and Drell-Yan processes and to constrain the sea quark Sivers function.

The Sivers asymmetry in charged Kaon and Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document} hyperon produced SIDIS process at electron ion colliders

We investigate the single transverse-spin asymmetry with a sin(ϕh-ϕS)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sin (\\phi _h-\\phi _S)$$\\end{document} modulation in the charged Kaon produced and in Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document} hyperon produced SIDIS process within the theoretical framework of transverse momentum dependent (TMD) factorization at the next-to-leading-logarithmic order. The asymmetry is contributed by the convolution of Sivers function and the unpolarized fragmentation function D1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$D_1$$\\end{document} for the produced hadron. The parametrization for the proton Qiu–Sterman function, which is closely related to the Sivers function, is adopted to numerically estimate the Sivers asymmetry at the kinematical region of Electron Ion Collider (EIC) and Electron Ion Collider in China (EicC). The TMD evolution of the TMD parton distribution functions are considered by employing the non-perturbative Sudakov form factor. It is found that the predicted Sivers asymmetries AUTsin(ϕh-ϕS)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$A_{UT}^{\\sin (\\phi _h-\\phi _S)}$$\\end{document} as functions of x, z and PhT\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$P_{hT}$$\\end{document} are sizable at the kinematical configurations of both EIC and EicC. The strange constituent of the produced charged Kaon and Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document} hyperon in the final state can be a promising probe of the sea quark Sivers function as well as the flavor dependence in the proton target. Therefore, it is important to utilize the future EIC facilities to constrain the sea quark distribution functions as well as the validity of the generalized universality of the Sivers function.

Collins and Sivers transverse-spin asymmetries in inclusive muoproduction of ρ0 mesons

The production of vector mesons in deep inelastic scattering is an interesting yet scarcely explored channel to study the transverse spin structure of the nucleon and the spin-dependence of fragmentation. The COMPASS collaboration has performed the first measurement of the Collins and Sivers asymmetries for inclusively produced ρ0 mesons. The analysis is based on the data set collected in deep inelastic scattering in 2010 using a 160GeV/cμ+ beam impinging on a transversely polarized NH3 target. The ρ0 mesons are selected from oppositely charged hadron pairs, and the asymmetries are extracted as a function of the Bjorken-x variable, the transverse momentum of the pair and the fraction of the energy z carried by the pair. Indications for positive Collins and Sivers asymmetries are observed.

Sivers and Boer-Mulders TMDs of the proton in a light-front quark-diquark model

We obtain the leading twist T-odd quark transverse momentum-dependent parton distribution functions (TMDs) of the proton, namely, the Sivers function ${f}_{1T}^{\ensuremath{\perp}q}(x,{p}_{\ensuremath{\perp}}^{2})$ and the Boer-Mulders function ${h}_{1}^{\ensuremath{\perp}q}(x,{p}_{\ensuremath{\perp}}^{2})$, in a light-front quark-diquark model constructed with the wave functions predicted by the soft-wall AdS/QCD. The gluon rescattering is crucial to predict nonzero T-odd TMDs. We study the utility of a nonperturbative $SU(3)$ gluon rescattering kernel going beyond the usual approximation of perturbative $U(1)$ gluons. The spin asymmetries in semi-inclusive deep inelastic scattering (SIDIS) associated with these T-odd TMDs are found to be consistent with HERMES and COMPASS data. We further predict the Sivers asymmetries of pion production in the SIDIS process in the kinematical region of the Electron-Ion Collider (EIC) and the EIC in China. We also evaluate the generalized Sivers and Boer-Mulders shifts and compare them with the available lattice QCD simulations.

Transverse spin asymmetries for inclusive $\rho^0$ production in SIDIS at COMPASS

The production of vector mesons in SIDIS is a particularly interesting channel to study the polarized fragmentation and related phenomena. Preliminary COMPASS results for the first measurement of inclusive \rho^0ρ0 Collins and Sivers transverse-spin asymmetries are presented here for the first time. The analysis is based on the data-set collected by COMPASS in 2010 using a 160 GeV/c \mu^+μ+ beam and a transversely polarized NH_3NH3 target. The asymmetries are extracted as function of Bjorken-x, of the total transverse momentum of the oppositely charged hadron pair and of the fraction of available energy z carried by the pair. Indications for positive Collins and Sivers asymmetries are obtained as expected from models.

Resummation of the Sivers asymmetry in heavy flavor dijet production at the Electron-Ion Collider

We review our transverse momentum dependent factorization and resummation formalism for heavy flavor dijet production at the EIC. In this formalism, we have calculated the heavy flavor mass corrections in the collinear-soft and jet functions, and in the resummed expression for the cross section. By establishing this formalism, we then study the effects of the mass corrections by providing predictions at the EIC for the massive case and for the case where the mass is neglected. We find that the heavy flavor mass effects can give sizable corrections to the predicted asymmetry.

Azimuthal single- and double-spin asymmetries in semi-inclusive deep-inelastic lepton scattering by transversely polarized protons

A comprehensive set of azimuthal single-spin and double-spin asymmetries in semi-inclusive leptoproduction of pions, charged kaons, protons, and antiprotons from transversely polarized protons is presented. These asymmetries include the previously published HERMES results on Collins and Sivers asymmetries, the analysis of which has been extended to include protons and antiprotons and also to an extraction in a three-dimensional kinematic binning and enlarged phase space. They are complemented by corresponding results for the remaining single-spin and double-spin asymmetries for transverse target-polarization orientation.

Sivers asymmetry in inelastic $J/ψ$ leptoproduction at the EIC

We study the Sivers asymmetry in inelastic J/\psiJ/ψ leptoproduction, ep^\uparrow \to e+ J/\psi+Xep↑→e+J/ψ+X, within a transverse momentum dependent scheme, the so-called generalized parton model (GPM). The effects of final-state interactions are properly taken into account by employing the color-gauge invariant GPM (CGI-GPM). For the J/\psiJ/ψ formation the non-relativistic QCD (NRQCD) framework is adopted. Predictions for unpolarized cross sections and maximized Sivers asymmetries at EIC energies are given.

Measurement of Target Spin (in)dependent Asymmetries in Dimuon Production in Pion-Nucleon Collisions at COMPASS

The exploration of the transverse spin structure of the nucleon is one of the main topics of the COMPASS phase-II experiment. In 2015 and 2018 COMPASS performed Drell–Yan (DY) measurements using a 190 GeV \pmb{\pi^-}𝛑− beam interacting with a transversely polarized NH\pmb{_{3}}3 target and unpolarized W target. The azimuthal asymmetries in DY with transversely polarized NH_{3}3 target are sensitive to various transverse momentum dependent parton distribution functions. Preliminary results on the Sivers asymmetry are consistent with the QCD prediction for a sign-change of Sivers functions in DY. The angular coefficients \pmb{\lambda}𝛌, \pmb{\mu}𝛍 and \pmb{\nu}𝛎 that describe the unpolarized part of the DY cross section have been extracted from the data collected with W target. The preliminary results on the angular coefficients indicate the violation of the Lam–Tung relation, consistent with the observation in earlier DY experiments with pion beams.

Predictions for the Sivers single-spin asymmetry from holographic QCD

A new approach to nonperturbative QCD, holographic light-front QCD, provides a comprehensive model for hadron dynamics and spectroscopy, incorporating color confinement, a universal hadron mass scale, the prediction of a massless pion in the chiral limit, and connections between the spectroscopy of mesons, baryons and tetraquarks across the full hadron spectrum. In this article we present predictions for the Sivers asymmetry and related transverse momentum distributions for the proton based on the light-front wavefunctions of the baryon eigenstate predicted by holographic QCD.

Leading and higher twist transverse momentum dependent parton distribution functions in the spectator model

Transverse momentum dependent parton distribution functions, also abbreviated as TMDs, offer a three-dimensional picture of hadrons by taking the intrinsic transverse momentum of the parton into consideration. Hence, they are very important for us to understand the structure of hadrons. In this article, we calculate and summarize all TMDs of quark through the spectator model, from twist-2 to twist-4. Especially, we give complete results of TMDs at twist-4. We adopt a general analytical framework to calculate TMDs, with both scalar and axial-vector spectators being considered. All TMDs are calculated analytically in the light-cone coordinate, and single gluon rescattering is considered to generate T-odd TMDs. T-even TMDs are also calculated to this level, maybe for the first time. Different from the traditional point of view, the twist-4 TMDs can contribute to some physical observables like azimuthal asymmetries. An approximate formula of the Sivers asymmetry, including twist-4 TMDs, is given.

Potential linear and angular momentum in the scalar diquark model

We present an analytic two-loop calculation within the scalar diquark model of the potential linear and angular momenta, defined as the difference between the Jaffe-Manohar and Ji notions of linear and angular momenta. As expected by parity and time-reversal symmetries, a direct calculation confirms that the potential transverse momentum coincides with the Jaffe-Manohar (or canonical) definition of average quark transverse momentum, also known as the quark Sivers shift. We examine whether initial/final-state interactions at the origin of the Sivers asymmetry can also generate a potential angular momentum in the scalar diquark model.

QCD evolution of the gluon Sivers function in heavy flavor dijet production at the Electron-Ion Collider

Using Soft-Collinear Effective Theory, we develop the transverse-momentum-dependent factorization formalism for heavy flavor dijet production in polarized-proton-electron collisions. We consider heavy flavor mass corrections in the collinear-soft and jet functions, as well as the associated evolution equations. Using this formalism, we generate a prediction for the gluon Sivers asymmetry for charm and bottom dijet production at the future Electron-Ion Collider. Furthermore, we compare theoretical predictions with and without the inclusion of finite quark masses. We find that the heavy flavor mass effects can give sizable corrections to the predicted asymmetry.

The Sivers asymmetry in hadronic dijet production

We study the single spin asymmetry in the back-to-back dijet production in transversely polarized proton-proton collisions. Such an asymmetry is generated by the Sivers functions in the incoming polarized proton. We propose a QCD formalism in terms of the transverse momentum dependent parton distribution functions, which allow us to resum the large logarithms that arise in the perturbative calculations. We make predictions for the Sivers asymmetry of hadronic dijet production at the kinematic region that is relevant to the experiment at the Relativistic Heavy Ion Collider (RHIC). We further compute the spin asymmetries in the selected positive and negative jet charge bins, to separate the contributions from u- and d-quark Sivers functions. We find that both the sign and size of our numerical results are roughly consistent with the preliminary results from the STAR collaboration at the RHIC.

Global analysis of the Sivers functions at NLO+NNLL in QCD

We perform global fit to the quark Sivers function within the transverse momentum dependent (TMD) factorization formalism in QCD. We simultaneously fit Sivers asymmetry data from Semi-Inclusive Deep Inelastic Scattering (SIDIS) at COMPASS, HERMES, and JLab, from Drell-Yan lepton pair production at COMPASS, and from W/Z boson at RHIC. This extraction is performed at next-to-leading order (NLO) and next-to-next-to leading logarithmic (NNLL) accuracy. We find excellent agreement between our extracted asymmetry and the experimental data for SIDIS and Drell-Yan lepton pair production, while tension arises when trying to describe the spin asymmetries of W/Z bosons at RHIC. We carefully assess the situation, and we study in details the impact of the RHIC data and their implications through different ways of performing the fit. In addition, we find that the quality of the description of W/Z vector boson asymmetry data could be strongly sensitive to the DGLAP evolution of Qiu-Sterman function, besides the usual TMD evolution. We present discussion on this and the implications for measurements of the transverse-spin asymmetries at the future Electron Ion Collider.

Jet Charge: A Flavor Prism for Spin Asymmetries at the Electron-Ion Collider

We propose the jet charge observable as a novel probe of flavor structure in the nucleon spin program at the electron ion collider (EIC) and develop the underlying framework from first principles. We show that jet charge measurements can substantially enhance the sensitivity of spin asymmetries to different partonic flavors in the nucleon. This sensitivity can be further improved by constructing the jet charge using only a subset of hadron species (pions or kaons) in the jet. As an example, we use the Sivers asymmetry in back-to-back electron-jet production at the EIC to show that the jet charge can be a unique tool in constraining the Sivers function for different partonic flavors.

Azimuthal single- and double-spin asymmetries in semi-inclusive deep-inelastic lepton scattering by transversely polarized protons

A comprehensive set of azimuthal single-spin and double-spin asymmetries in semi-inclusive leptoproduction of pions, charged kaons, protons, and antiprotons from transversely polarized protons is presented. These asymmetries include the previously published HERMES results on Collins and Sivers asymmetries, the analysis of which has been extended to include protons and antiprotons and also to an extraction in a three-dimensional kinematic binning and enlarged phase space. They are complemented by corresponding results for the remaining four single-spin and four double-spin asymmetries allowed in the one-photon-exchange approximation of the semi-inclusive deep-inelastic scattering process for target-polarization orientation perpendicular to the direction of the incoming lepton beam. Among those results, significant non-vanishing cos (ϕ−ϕS) modulations provide evidence for a sizable worm-gear (II) distribution, {g}_{1mathrm{T}}^qleft(x,{mathrm{p}}_T^2right) . Most of the other modulations are found to be consistent with zero with the notable exception of large sin (ϕS) modulations for charged pions and K+.

Jet-based measurements of Sivers and Collins asymmetries at the future electron-ion collider

We present predictions and projections for hadron-in-jet measurements and electron-jet azimuthal correlations at the future Electron-Ion Collider (EIC). These observables directly probe the three-dimensional (3D) structure of hadrons, in particular, the quark transversity and Sivers parton distributions and the Collins fragmentation functions. We explore the feasibility of these experimental measurements by detector simulations and discuss detector requirements. We conclude that jet observables have the potential to enhance the 3D imaging EIC program.

Transverse single spin asymmetry AUTsin(ϕh−ϕS) for single hadron production in semi-inclusive DIS

In this paper, we study the single spin asymmetry ${A}_{UT}^{\mathrm{sin}({\ensuremath{\phi}}_{h}\ensuremath{-}{\ensuremath{\phi}}_{S})}$ of a single hadron production in semi-inclusive deep inelastic scattering within the framework of transverse momentum dependent factorization up to the next-to-leading logarithmic order of QCD. The asymmetry is a contribution of the convolution of the Sivers function and the unpolarized fragmentation function. Specifically, the Sivers function in the coordinate space and perturbative region can represent the convolution of the $C$ coefficients and the corresponding collinear correlation functions, among which the Qiu-Sterman function is the most relevant one. We perform a detailed phenomenological analysis of the Sivers asymmetry at the kinematics of the HERMES and the COMPASS measurements. It is found that the obtained ${x}_{B}$-, ${z}_{h}$-, and ${P}_{h\ensuremath{\perp}}$-dependent asymmetries are basically consistent with the HERMES and the COMPASS measurements.