Polarized Parton Distributions Research Articles

QED corrections to parton distributions and Altarelli–Parisi splitting functions in the polarized case

We discuss the effect of QED corrections in the evolution of polarized parton distributions. We solve the corresponding evolution equations exactly to {mathcal {O}}(alpha ) and {mathcal {O}}(a_{textrm{S}}^2) in Mellin N-space, extending the available techniques for pure QCD evolution. To accomplish this, we introduce, for the first time, the Altarelli–Parisi polarized kernels at LO in QED. Furthermore, we perform a phenomenological analysis of the QED effects on polarized parton distributions (pPDFs), proposing different scenarios for the polarized photon density. Finally, we quantify the impact of the corresponding QED contributions to the polarized structure function g_1. We show that the relative corrections to both the pPDFs and the g_1 structure function are approximately at the few percent level, which is the order of magnitude expected considering the value of alpha .

An analysis of polarized parton distribution functions with nonlinear QCD evolution equations

We present the polarized parton distribution functions from a QCD analysis of the worldwide polarized deep inelastic scattering data, based on the dynamical parton distribution model. All the sea quarks and gluons are dynamically generated from QCD radiations, with the nonperturbative input comprising only the polarized valence quark distributions. This approach leads to a simple parametrization, which has only seven free parameters. In the analysis, we apply the DGLAP equations with parton-parton recombination corrections. For the first step, the DGLAP equations, parton-parton recombination corrections, and experimental observable g1 are all evaluated at the leading order. The parameterized nonperturbative input at an extremely low Q02 reproduces well the spin-dependent structure functions measured at high Q2. Comparisons with experimental observations and some other polarized parton distribution functions are also shown. Our results are in good agreement with the experimental data and consistent with some other parameterized models. Furthermore, our analysis presents the positive polarized gluon distribution and it suggests that the gluon distribution plays an important role to the proton spin content. The polarized antiquark distributions are non-zero at high Q2 but quite small compared to polarized valence quark distributions, based on this dynamical parton model analysis. This analysis gives smaller statistical uncertainties for the polarized sea quark and gluon distributions, thanks to the fewer free parameters used for the parametrization of the initial polarized PDFs.

Longitudinal double helicity asymmetry $A_{LL}$ from direct photon, jet and charged pion production in polarized $\vec{p}+\vec{p}$ collisions

Understanding the proton spin composition from the quarks and gluons spin polarization and their motion is important to test various kinds of sum rules and nonperturbative properties of hadrons. At the Relativistic Heavy Ion Collider (RHIC), we collide longitudinally polarized proton beams and measure the double helicity asymmetry A_{LL}ALL, which is an important physical quantity for extracting the polarized parton distribution functions (PDFs) of the proton. Direct photon, jet and charged pion production are good channels to probe the gluon spin polarization inside the proton, with the ability to probe also the sign of the gluon spin. Direct photon production is the theoretically ``cleanest’’ channel, with little fragmentation contribution, but limited by statistics. On the other hand, jet and charged pion production have more statistics, but include more hard processes and hadronization effects. I will present the recent measurements of direct photon, jet and charged pion A_{LL}ALLs at PHENIX and show their complementary roles in extracting the gluon spin.

GT(x) contribution to single spin asymmetries in SIDIS

Motivated by a novel origin of transverse single spin asymmetry (SSA) in semi-inclusive Deep Inelastic Scattering (SIDIS) uncovered by some of us, we quantitatively investigate its impact on the theoretical understanding of the mechanism responsible for SSA. This new contribution from the quark-initiated channel first appears in two-loop perturbation theory and involves the $g_T(x)$ distribution. We point out another entirely analogous piece from the gluon-initiated channel proportional to the gluon helicity distribution $\Delta G(x)$. Both contributions are solely expressed in terms of twist-two polarized parton distribution functions and twist-two fragmentation functions in the Wandzura-Wilczek approximation, such that they can be unambiguously evaluated without introducing free parameters. We make predictions for measurements of the asymmetries $A_{UT}$ at the future Electron-Ion Collider (EIC), and find that $A_{UT}$ associated with the $\sin (\phi_h-\phi_S)$, $\sin \phi_S$ and $\sin (2\phi_h-\phi_S)$ harmonics can reach up to 1-2\% even at the top EIC energy.

W-boson production in polarized proton-proton collisions at RHIC through next-to-next-to-leading order in perturbative QCD

We perform a study of W-boson production in polarized proton-proton collisions through next-to-next-to-leading order (NNLO) in perturbative QCD. This calculation is required to extend the extraction of polarized parton distribution functions to NNLO accuracy. We present differential distributions at s=510 GeV, relevant for comparison to measurements from the Relativistic Heavy Ion Collider (RHIC). The NNLO QCD corrections significantly reduce the scale dependence of the cross section. We compare the longitudinal single-spin asymmetries as a function of lepton pseudorapidity to RHIC data. The asymmetries exhibit excellent stability under perturbative QCD corrections.

Polarized parton distribution functions: parametrization and transverse momentum dependence

We extract the polarized parton distribution functions (PPDFs) of proton. To this end we do a global analysis on recent and up-to-dated experimental data of polarized nucleon and deuteron structure functions at the NLO accuracy of perturbative QCD. We use the Jacobi polynomials expansion technique to do the required analyses. To achieve a more realistic estimation of the PPDFs and observable uncertainties we employ the Hessian error propagation. Following that we apply a theoretical approach which is based on imposing Lorentz structure in the parton model to investigate the transverse momentum dependence of these PPDFs. In this approach, the transverse momentum dependent (TMD) polarized parton distributions, which are also called the helicity distributions, are related to the integrated ones. This relation is indicating the priority and importance of data analysis for PPDFs. The results show a convenient general treatment expected for TMD densities which are in fact resulted from data analysis and fitting processes of integrated PPDFs in an adequate and a proper way.

Measurement of Longitudinal Single-Spin Asymmetry for W± Production in Polarized Proton+Proton Collisions at STAR

The contribution from the sea quark polarization to the nucleon spin is an important piece for the complete understanding of the nucleon spin structure. The production of W ± bosons in longitudinally polarized p+p collisions at the RHIC collider at Brookhaven National Laboratory provides a unique probe of the sea quark polarization, through the parity-violating single-spin asymmetry, AL . At the STAR experiment, the W bosons that decay through the W → ev channel at mid-rapidity (|η <1.3) can be effectively determined with the Electromagnetic Calorimeters and Time Projection Chamber. The STAR measurements of AL for W boson from datasets taken in 2011 and 2012 at =510 GeV have been included in the global analysis of polarized parton distribution functions, and provided significant constraints on the helicity distribution functions of and quarks. The final AL results from 2013 STAR data sample are reported, which is about three times larger than the total integrated luminosity of previous years. The combined results of AL for 2011-2013 data are also given. A flavor asymmetry of light sea quark helicity distribution, , is confirmed from a re-weighting of global analysis NNPDFpol1.1 after including the new AL results. In addition, results on the double-spin asymmetries ALL for W ±, and AL for Z/γ* production are also reported.

Constructing phase space distributions with internal symmetries

We discuss an ab initio world-line approach to constructing phase space distributions in systems with internal symmetries. Starting from the Schwinger-Keldysh real time path integral in quantum field theory, we derive the most general extension of the Wigner phase space distribution to include color and spin degrees of freedom in terms of dynamical Grassmann variables. The corresponding Liouville distribution for colored particles, which obey Wong's equation, has only singlet and octet components, while higher moments are fully constrained by the Grassmann algebra. The extension of phase space dynamics to spin is represented by a generalization of the Pauli-Lubanski vector; its time evolution via the Bargmann-Michel-Telegdi equation also follows from the phase space trajectories of the underlying Grassmann coordinates. Our results for the Liouville phase space distribution in systems with both spin and color are of interest in fields as diverse as chiral fluids, finite temperature field theory and polarized parton distribution functions. We also comment on the role of the chiral anomaly in the phase space dynamics of spinning particles.

Nucleon spin structure and measurements on sea quark polarization at RHIC

The nucleon spin structure in terms of its parton constituents is a fundamental question in QCD. The sea quark contribution to the nucleon spin is an important piece for a complete understanding of the nucleon spin structure. The production of W bosons in longitudinally polarized proton-proton collisions at RHIC provides a unique probe for the sea quark polarization, through the parity-violating single-spin asymmetry A L = ( σ + − σ − ) / ( σ + + σ − ) . At RHIC, W ’s can be detected via the leptonic channel W → e ν with the kinematics of the decay lepton alone. Longitudinally polarized proton-proton collision events at s =500 GeV were recorded at RHIC through the years 2009, 2011, 2012 and 2013. Both STAR and PHENIX experiments completed their measurements on longitudinal single spin asymmetries for W bosons as a function of decay lepton rapidity. These results provide new constraints on sea quark polarizations through the QCD global analyses, which clearly indicate the existence of a flavor asymmetry in the polarization of the light-quark sea, Δ u ¯ > Δ d ¯ , in the proton for parton momentum fraction range of 0.05 x d ¯ > u ¯ over a wide x range has been observed. On the other hand, the phenomenological studies showed that the spin transfer to Λ ¯ anti-hyperons provides a natural connection to helicity or transversity distributions of strange and anti-strange quarks in the proton. STAR experiment made the first and an improved measurement on the longitudinal spin transfer D LL to Λ and Λ ¯ hyperons in longitudinally polarized proton-proton collisions at 200 GeV. STAR also completed the first measurement on transverse spin transfer D LL to Λ and Λ ¯ hyperons in transversely polarized proton-proton collisions at 200 GeV. These data and future measurements with higher precision and larger momentum fraction in the forward region at RHIC will shed new lights on the polarized parton distributions for strange and anti-strange quark in the nucleon.

Study of the Drell-Yan process with the pair-production of polarized tau leptons in collisions of polarized proton beams

The new method for studying polarized parton distribution functions via the Drell-Yan process with tau production is proposed. The hadronic decay of tau to single charged pi-meson and neutrino is utilised for determination of the polarization state of the tau-lepton. The key feature of our approach is that we do not sum over the polarizations states of tau, but preserve this information through energies ofpions produced in corresponding decays. The new method in addition to existing ones should improve the accuracy of measurements of polarized structure functions of hadrons. In the current work, the feasibility of such an approach is assessed through numerical simulations.

Properties of structure functions from helicity components of light quarks and antiquarks in the statistical model

In the quantum statistical parton distributions approach proposed more than one decade ago to describe the parton structure, new properties are now understood, in particular, the relation between quarks and antiquarks which leads to very specific properties. The simultaneous treatment of unpolarized and polarized Parton Distribution Functions (PDFs) allows a determination of thermodynamical potentials (the master parameters of the model) which drive their behavior and as a consequence those of the structure functions. The existence of a possible relation between the gluon and a $q~\bar q$ pair leads to define a toy model for the unpolarized and polarized gluon. In view of forthcoming experimental results in the large $x$ region specific predictions made by the model are presented.

Inclusive jet production as a probe of polarized parton distribution functions at a future EIC

We present a detailed phenomenological study of polarized inclusive jet production in electron-proton collisions at a future Electron-Ion Collider (EIC). Our analysis is performed at next-to-leading order in perturbative QCD using the numerical code DISTRESS and includes all relevant partonic channels and resolved photon contributions. We elucidate the role of different kinematic regions in probing different aspects of proton and photon structure. We emphasize the importance of inclusive jet measurements and high collision energies at a future EIC in order to further constrain the polarized gluon distribution of the proton.

Impact of recent COMPASS data on polarized parton distributions and structure functions

We perform a new extraction of polarized parton distribution functions (PPDFs) from the spin structure function experimental data in the fixed-flavor number scheme (FFNS). In this analysis, we include recent proton and deuteron spin structure functions obtained by the \texttt{COMPASS} collaboration. We examine the impact of the \texttt{new COMPASS} proton and deuteron data on the polarized parton densities and compare with results from our previous study (KATAO PPDFs), which used the Jacobi polynomial approach. We find the extracted PPDFs of the proton, neutron, and deuteron structure functions are in very good agreement with the experimental data. The results for extracted PPDFs are also compared with available theoretical models from the literature.

Improved parton distribution functions at the physical pion mass

We present the first lattice results on isovector unpolarized and longitudinally polarized parton distribution functions (PDFs) at physical pion mass. The PDFs are obtained using the large-momentum effective field theory (LaMET) framework where the full Bjorken-$x$ dependence of finite-momentum PDFs, called "quasi-PDFs", can be calculated on the lattice. The quasi-PDF nucleon matrix elements are renormalized nonperturbatively in RI/MOM-scheme. However, the recent renormalized quasi-PDFs suffer from unphysical oscillations that alter the shape of the true distribution as a function of Bjorken-$x$. In this paper, we propose two possible solutions to overcome this problem, and demonstrate the efficacy of the methods on the 2+1+1-flavor lattice data at physical pion mass with lattice spacing 0.09~fm and volume $(5.76\mbox{ fm})^3$.

Longitudinal Double Spin Asymmetries of π0 - Jet Correlations in Polarized Proton Collisions at s = 510 GeV at STAR

One of the primary goals of the spin physics program at STAR is to constrain the polarized gluon distribution function, [Formula: see text], by measuring the longitudinal double-spin asymmetry ([Formula: see text]) of various final-state channels. Using a jet in the mid-rapidity region [Formula: see text] correlated with an azimuthally back-to-back [Formula: see text] in the forward rapidity region [Formula: see text] provides a new possibility to access the [Formula: see text] distribution at Bjorken-[Formula: see text] down to 0.01. Compared to inclusive jet or inclusive [Formula: see text] measurements, this channel also allows to constrain the initial parton kinematics. In these proceedings, we will present the status of the analysis of the [Formula: see text]-jet [Formula: see text] in longitudinally polarized proton+proton collisions at [Formula: see text] =510 GeV with 80 pb[Formula: see text] of data taken during the 2012 RHIC run. We also compare the projected [Formula: see text] uncertainties to theoretical predictions of the [Formula: see text] by next-to-leading order (NLO) model calculations with different polarized parton distribution functions.

Determination of the proton spin structure functions for 0.05&lt;Q2&lt;5GeV2 using CLAS

We present the results of our final analysis of the full data set of g_1^p(Q^2), the spin structure function of the proton, collected using CLAS at Jefferson Lab in 2000-2001. Polarized electrons with energies of 1.6, 2.5, 4.2 and 5.7 GeV were scattered from proton targets (15^NH_3 dynamically polarized along the beam direction) and detected with CLAS. From the measured double spin asymmetries, we extracted virtual photon asymmetries A_1^p and A_2^p and spin structure functions g_1^p and g_2^p over a wide kinematic range (0.05 GeV^2 < Q^2 < 5 GeV^2 and 1.08 GeV < W < 3 GeV), and calculated moments of g_1^p. We compare our final results with various theoretical models and expectations, as well as with parameterizations of the world data. Our data, with their precision and dense kinematic coverage, are able to constrain fits of polarized parton distributions, test pQCD predictions for quark polarizations at large x, offer a better understanding of quark-hadron duality, and provide more precise values of higher-twist matrix elements in the framework of the Operator Product Expansion.

Transversely polarized Drell-Yan asymmetry ATT at NLO

We present the first fully differential next-to-leading order QCD calculation for lepton production in transversely polarized hadronic collisions, $p\ensuremath{\uparrow}p\ensuremath{\uparrow}\ensuremath{\rightarrow}{\ensuremath{\ell}}^{\ifmmode\pm\else\textpm\fi{}}X$, where the lepton arises from the decay of an electroweak gauge boson. The calculation is implemented in the Monte-Carlo like code che that already includes the unpolarized and longitudinally polarized cross sections and may be readily used to perform a comparison to experimental data and to extract information on the related parton distributions. We analyze the perturbative stability of the cross-section and double spin asymmetry ${A}_{TT}$ at RHIC kinematics. We find that the QCD corrections are non-negligible even at the level of asymmetries and that they strongly depend on the lepton kinematics. Furthermore, we present two scenarios for transversely polarized parton distributions, based on the de Florian-Sassot-Stratmann-Vogelsang (DSSV) set of longitudinally parton densities and fully evolved to NLO accuracy, that can be used for the evaluation of different observables involving transverse polarization.

Photon structure studied at an electron ion collider

A future electron ion collider (EIC) will be able to provide collisions of polarized electrons with protons and heavy ions over a wide range of center-of-mass energies (20 GeV to 140 GeV) at an instantaneous luminosity of $1{0}^{33}\ensuremath{-}{10}^{34}\text{ }\text{ }{\mathrm{cm}}^{\ensuremath{-}2}\text{ }{\mathrm{s}}^{\ensuremath{-}1}$. One of its promising physics programs is the study of the partonic structure of quasireal photons. Measuring dijets in quasireal photoproduction events, one can effectively access the underlying parton dynamics of the photons. In this paper, we discuss the feasibility of tagging resolved photon processes and measuring the dijet cross section as a function of jet transverse momentum in the range of $0.01&lt;{x}_{\ensuremath{\gamma}}^{\mathrm{rec}}&lt;1$ at an EIC. It will be shown that both unpolarized and polarized parton distributions in the photon can be extracted, and that the flavor of the parton can be tagged at an EIC.

Study of spin-dependent structure functions of He3 and H3 at NNLO approximation and corresponding nuclear corrections

We determine polarized parton distribution functions (PPDFs) and structure functions from recent experimental data of polarized deep inelastic scattering (DIS) on nuleons at next-to-next-to-leading order (NNLO) approximation in perturbative quantum chromodynamic (pQCD). The nucleon polarized structure functions are computed using the Jacobi polynomial approach while target mass corrections (TMCs) are included in our fitting procedure. Having extracted the polarized spin structure functions, we extend our study to describe $^3{\mathrm He}$ and $^3{\mathrm H}$ polarized structure functions, as well as the Bjorken sum rule. We also explore the importance of the nuclear corrections on the polarized nuclear structure functions at small and large values of $x$. Our results are compared with the recent available and high precision polarized $^3{\mathrm He}$ and $^3{\mathrm H}$ experimental data.

Nucleon spin structure functions at NNLO in the presence of target mass corrections and higher twist effects

We extract polarized parton distribution functions (PPDFs), referred to as "KTA17," together with the highly correlated strong coupling $\alpha_s$ from recent and up-to-date $g_1$ and $g_2$ polarized structure functions world data at next-to-next-to-leading order in perturbative QCD. The stability and reliability of the results are ensured by including nonperturbative target mass corrections as well as higher-twist terms which are particularly important at the large-$x$ region at low Q$^2$. Their role in extracting the PPDFs in the nucleon is studied. Sum rules are discussed and compared with other results from the literature. This analysis is made by means of the Jacobi polynomials expansion technique to the DGLAP evolution. The uncertainties on the observables and on the PPDFs throughout this paper are computed using standard Hessian error propagation which served to provide a more realistic estimate of the PPDFs uncertainties.