We review recent progress towards a determination of a set of polarized parton distributions from a global set of deep-inelastic scattering data based on the NNPDF methodology, in analogy with the unpolarized case. This method is designed to provide a faithful and statistically sound representation of parton distributions and their uncertainties. We show how the FastKernel method provides a fast and accurate method for solving the polarized DGLAP equations. We discuss the polarized PDF parametrizations and the physical constraints which can be imposed. Preliminary results suggest that the uncertainty on polarized PDFs, most notably the gluon, has been underestimated in previous studies.
Polarized parton distribution functions are determined by using asymmetry A_1 data from longitudinally polarized deep inelastic scattering experiments. From our χ^2 analysis, polarized u-valence, d-valence, antiquark, and gluon distributions are obtained. We propose one set of leading-order distributions and two sets of next-to-leading-order ones as the longitudinally-polarized parton distribution functions.
We discuss possible studies of parton distributions at the proposed 50-GeV PS facility. First, comments are given in general on the importance of large-x physics for finding new physics. Second, polarized deuteron reactions are discussed in connection with new structure functions which are specific for a spin-1 hadron. Third, if the polarized proton-deuteron Drell-Yan process is studied at the facility, it could provide information on the light-antiquark flavor asymmetry in the polarized distributions.
We present a physical model for polarized and unpolarized structure functions and parton density functions (PDFs) of the proton and the neutron. It reproduces the data on F_2^p(x,Q^2) for 0.00001<x<1 and 2.5<Q^2<5000 GeV^2, F_2^p(x)-F_2^n(x), F_2^n(x)/F_2^p(x), xg(x), dbar(x)-ubar(x), d(x)/u(x), the Gottfried sum, the fractional momentum of charged partons and the polarized structure functions g_1^{p,n}(x), at various Q^2. We present for the first time, proton and neutron PDFs which do not assume charge symmetry. Contrary to the common practice, we explain polarized and unpolarized data with a…
New fragmentation functions (FFs) are extracted from a NLO QCD fit to the preliminary COMPASS data on pion and kaon multiplicities. It is shown that the new kaon FFs are very different from those of De Florian at al. (DSS) and Hirai et al. (HKNS). The sensitivity of the extracted polarized PDFs to the new FFs is discussed.
Different methods to extract the polarized parton densities from the world polarized DIS data are considered. The higher twist corrections $h^N(x)/Q^2$ to the spin dependent proton and neutron $g_1$ structure functions are found to be non-negligible and important in the QCD analysis of the present experimental data. Their role in determining the polarized parton densities in the framework of the different approaches is discussed.
The impact of positivity constraints on the polarized parton densities has been studied. Special attention has been paid to the role of positivity constraints in determining the polarized strange quark and gluon densities, which are not well determined from the present data on inclusive polarized DIS.
Polarized parton distribution functions are determined by using world data from the longitudinally polarized deep inelastic scattering experiments. A new parametrization of the parton distribution functions is adopted by taking into account the positivity and the counting rule. From the fit to the asymmetry data A_1, the polarized distribution functions of u and d valence quarks, sea quarks, and gluon are obtained. The results indicate that the quark spin content is ΔΣ=0.20 and 0.05 in the leading order (LO) and the next-to-leading-order (NLO) MS-bar scheme, respectively. However, if x depende…
We report the polarized parton distributions proposed by the Asymmetry Analysis Collaboration (AAC). Using parametrized distributions at Q^2=1 GeV^2 and measured A_1 data, we determine optimum polarized distributions in the leading order (LO) and next-to-leading order (NLO). We find that the polarized antiquark distribution is not well determined particularly at small x. It could lead to a rather small quark spin content in comparison with usually-quoted values of 10-30%. In our analysis, it varies from 5% to 28% depending on the small-x extrapolation. It is necessary to have small-x (<10^{-3}…
We derive relations between polarized transverse momentum dependent distribution functions (TMDs) and the usual parton distribution functions (PDFs) in the 3D covariant parton model, which follow from Lorentz invariance and the assumption of a rotationally symmetric distribution of parton momenta in the nucleon rest frame. Using the known PDF $g_{1}^{q}(x)$ as input we predict the $x$- and $\mathbf{p}_{T}$-dependence of all polarized twist-2 naively time-reversal even (T-even) TMDs.
We present predictions of the unweighted and weighted double spin asymmetries related to the transversal helicity distribution $g_{1T}$ and the longitudinal transversity distribution $h_{1L}^\perp$, two of eight leading-twist transverse momentum dependent parton distributions (TMDs) or three-dimensional parton distribution functions (3dPDFs), in the polarized proton-antiproton Drell-Yan process at typical kinematics on the Facility for Antiproton and Ion Research (FAIR). We conclude that FAIR is ideal to access the new 3dPDFs towards a detailed picture of the nucleon structure.
We present a new leading and next-to-leading QCD analysis of the world data on inclusive polarized deep inelastic scattering. A new set of polarized parton densities is extracted from the data and the sensitivity of the results to the newly incorporated SLAC/E155 proton data is discussed.
We report recent studies of the Asymmetry Analysis Collaboration (AAC) on polarized parton distribution functions (PDFs). Using the data on the spin symmetry A_1 in deep inelastic lepton scattering, we investigate optimum polarized PDFs. Their uncertainties are estimated by the Hessian method. The uncertainties are large for the polarized antiquark and gluon distributions. We discuss the role of accurate SLAC-E155 proton data on the determination of the PDFs. The obtained distributions are compared with other parametrization results.
The present status of the longitudinal polarized parton densities (PDFs) and the contribution of their first moments to the nucleon spin is discussed. Special attention is paid to the role of higher twist effects in determining the PDFs and to the polarized strange quark and gluon densities, which are still not well determined from the present data.
Nuclear parton distribution functions are obtained by a chi^2 analysis of lepton deep inelastic experimental data. It is possible to determine valence-quark distributions at medium x and antiquark distributions at small x; however, the distributions in other x regions and gluon distributions cannot be fixed. We need a variety of experimental data and also further analysis refinements.
In this talk we summarize main results of a recent determination of the polarized deeply inelastic parton distributions to NLO from the world data. In the analysis the LO and NLO parton densities and their $1σ$ statistical errors were derived and parameterized. The strong coupling constant $α_s(M_Z^2)$ is determined $α_s(M_Z^2) = 0.113 \pm 0.004 {\rm (stat.)} \pm~0.004 {\rm (fac.)} +0.008/-0.005 {\rm (ren.)}$ Comparisons of the low moments of the parton densities with recent lattice results are given. A detailed error-analysis of the gluon density is performed.
Structure functions of polarized spin-1 hadrons will be measured at various accelerator facilities in the near future. Recently, transverse-momentum-dependent and collinear parton distribution functions were theoretically proposed at twist 3 and twist 4 in addition to the twist-2 ones, so that full investigations became possible for structure functions of spin-1 hadrons in the same level with those of the spin-1/2 nucleons. Furthermore, twist-3 tensor-polarized multiparton distribution functions were also recently found for spin-1 hadrons. In this work, we show relations among the collinear pa…
A survey is given on the present knowledge of the polarized parton distribution functions. We give an outlook for further developments desired both on the theoretical as well on the experimental side to complete the understanding of the spin--structure of nucleons in the future.
While the total orbital angular momentum (OAM) of a definite quark flavor in a longitudinally-polarized nucleon can be obtained through a sum rule involving twist-two generalized parton distribution (GPDs), its distribution as a function of parton momentum in light-front coordinates is more complicated to define and measure because it involves intrinsically twist-three effects. In this paper, we consider two different parton OAM distributions. The first is manifestly gauge invariant, and its moments are local operators and calculable in lattice QCD. We show that it can potentially be measured …
We have re-analyzed the world data on inclusive polarized DIS, in both NLO and LO QCD, including the new HERMES and COMPASS data. The updated NLO polarized densities are given in both the $\rm \bar{MS}$ and JET schemes. The impact of the new data on the results is discussed.
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 function…
Parton recombination corrections to the standard spin-dependent Altarelli-Parisi evolution equation are considered in a nonlinear evolution equation. The properties of this recombination equation and its relation with the spin-averaged form are discussed.
We analyze the polarized Drell-Yan processes with spin-1/2 and spin-1 hadrons in a parton model. Quark and antiquark correlation functions are expressed in terms of possible combinations of Lorentz vectors and pseudovectors with the constrains of Hermiticity, parity conservation, and time-reversal invariance. Then, we find tensor polarized distributions for a spin-1 hadron. The naive parton model predicts that there exist 19 structure functions. However, there are only four or five non-vanishing structure functions, depending on whether the cross section is integrated over the virtual-photon t…
We discuss the determination of polarized parton distributions from a next-to-leading order analysis of recent experimental data. We extract the first moment of the polarized quark and gluon distribution and assess the corresponding uncertainties, with special regard to those related to scheme dependence.
We have re-analyzed the world data on inclusive polarized DIS, in both NLO and LO QCD, including the very precise JLab Hall A neutron data, and have studied the role of positivity constraints, and demonstrated their importance, in determining the strange and gluon densities. We have shown that higher twist corrections are essential in the analysis of the present data on the structure function g1. A consistent QCD analysis is achieved, and results for the polarized parton densities are given in both the MSbare and JET schemes.
We discuss polarized parton distributions and their effects on spin asymmetries at RHIC. In particular, transversity distributions and transverse spin asymmetry are studied. First, we show the $Q^2$ evolution difference between a transversity distribution and a corresponding longitudinally polarized distribution. The difference could be an important test of perturbative QCD in high-energy spin physics. Then, the transverse spin asymmetry $A_{TT}$ is calculated with possible transversity distributions. Next, we study antiquark flavor asymmetry $Δ_{_T} \bar u/ Δ_{_T} \bar d$ in the transversity …
A fit to proton, neutron and deuteron spin asymmetries is presented and polarized parton distributions in nucleon are given. These densities have their roots in the MRS fit for unpolarized case. The integrals of polarized distributions are compared with the experimental figures. The role of polarized gluons is also discussed.
Di-jet photoproduction in polarized ep collisions at HERA is studied as a possible tool to determine the parton content of circularly polarized photons. The concept of the `effective parton density' approximation is extended to the spin-dependent case.
We present results on the quark and gluon polarization in the nucleon obtained in a combined next to leading order analysis to the available inclusive and semi-inclusive polarized deep inelastic scattering data.
I briefly review the physics of skewed parton distributions. Special emphasis is put on the relevance of target polarization, and on the different roles of small and of intermediate x_B.
The impact of the recent very precise CLAS and COMPASS g_1/F_1 data on polarized parton densities and higher twist effects is discussed. We demonstrate that the low Q^2 CLAS data improve essentially our knowledge of higher twist corrections to the spin structure function g1, while the large Q^2 COMPASS data influence mainly the strange quark and gluon polarizations which slightly decrease. We find also that the present inclusive DIS data cannot rule out a negative polarized and changing in sign gluon densities.
We have re-analyzed the world data on inclusive polarized DIS including the very precise CLAS proton and deuteron data, as well as the latest COMPASS data on the asymmetry $A_1^d$, and have studied the impact of these data on polarized parton densities and higher twist effects. We demonstrate that the low $Q^2$ CLAS data improve essentially our knowledge of higher twist corrections to the spin structure function $g_1$, while the large $Q^2$ COMPASS data influence mainly the strange quark density. In our new analysis we find that a negative polarized gluon density, or one that changes sign as a…
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 contains only the polarized valence quark distributions. This approach leads to a simple parametrization, which has only four free parameters. In the analysis, we apply the DGLAP equations with parton-parton recombination corrections. The parameterized nonperturbative input at an extremely low $Q_0^2$ repro…
The distribution of the spin of the nucleon among its constituents can be parametrized in the form of polarized parton distribution functions for quarks and gluons. Using all available data on the polarized structure function $g_1(x,Q^2)$, we determine these distributions both at leading and next-to-leading order in perturbation theory. We suggest three different, equally possible scenarios for the polarized gluon distribution, which is found to be only loosely constrained by current experimental data. We examine various possibilities of measuring polarized parton distributions at future exper…
In this talk results from a new QCD analysis in leading (LO) and next--to--leading (NLO) order are presented. New parametrizations of the polarized quark and gluon densities are derived together with parametrizations of their fully correlated 1$σ$ error bands. Furthermore the value of $α_s(M_Z^2)$ is determined. Finally a number of low moments of the polarized parton densities are compared with results from lattice simulations.
In order to examine polarized strange quark distribution, semi-inclusive $D/\Dbar$ production in neutrino deep inelastic scattering is studied including ${\cal O}(α_s)$ corrections. Cross section and spin asymmetry are calculated by using various parametrizations of polarized parton distribution functions. It is found that $\Dbar$ production is promising to directly extract the polarized strange sea.
The helicity dependent parton distributions describe the number density of partons with given longitudinal momentum x and given polarization in a hadron polarized longitudinally with respect to its motion. After the discovery, more than 70 years ago, that the proton is not elementary, the observation of Bjorken scaling in the late 1960s lead to the idea of hadrons containing almost pointlike constituents, the partons. Since then, Deep Inelastic Scattering (DIS) has played a crucial role in our understanding of hadron structure. Through DIS experiments it has been possible to link the partons t…
We review various methods used to estimate uncertainties in quantum correlation functions, such as parton distribution functions (PDFs). Using a toy model of a PDF, we compare the uncertainty estimates yielded by the traditional Hessian and data resampling methods, as well as from explicitly Bayesian analyses using nested sampling or hybrid Markov chain Monte Carlo techniques. We investigate how uncertainty bands derived from neural network approaches depend on details of the network training, and how they compare to the uncertainties obtained from more traditional methods with a specific unde…
The small $x$ behaviour of polarized parton distributions is related to non-leading reggeons in the framework of the high-energy effective action. Double-logarithmic contributions to the reggeon interaction beyond the ones included in the GLAP equation are encountered in all polarized parton distributions. The transversity distributions of quarks and gluons behave similar at small $x$. Contribution to the spin workshop at DESY-Zeuthen, September 1997.
A review of the present knowledge on polarized parton distributions is given. The effects of perturbative evolution on these distributions are discussed qualitatively and a comparison of various recent parametrizations is made.
We review the main results of next-to-leading order QCD analyses of polarized deep-inelastic scattering data, with special attention to the assessment of theoretical uncertainties.
We calculated the polarized parton distributions in leading order approximation in QCD from valon model. Polarized structure function of the nucleon are analyzed in the polarized valon model in which a nucleon is assumed to be a bound state of three polarized valence quark cluster(valons). It is shown that the results of the model calculation agree rather well with the SMC and available experimental data . Our results for $Γ_{1}$ of hadron and deuteron are in good agreement with experimental data for some value of $Q^{2}$.
Global analysis has been performed within the next-to-leading order in Quantum Chromodynamics (QCD) to determine polarized parton distributions with new experimental data in spin asymmetries. The new data set includes JLab, HERMES, and COMPASS measurements on spin asymmetry A_1 for the neutron and deuteron in lepton scattering. Our new analysis also utilizes the double-spin asymmetry for pi^0 production in polarized pp collisions, A_{LL}^{pi^0}, measured by the PHENIX collaboration. Because of these new data, uncertainties of the polarized PDFs are reduced. In particular, the JLab, HERMES, and…
A next-to-leading order (NLO) QCD analysis of the spin-dependent parton distributions $Δf^γ(x,Q^2)$ of the longitudinally polarized photon and of its structure function $g_1^γ(x,Q^2)$ is performed within the framework of the radiative parton model. The important issues of a suitably chosen factorization scheme and related boundary conditions are discussed in detail. The typical effects of the NLO corrections are quantitatively studied for two very different conceivable scenarios for the NLO polarized parton distributions $Δf^γ(x,Q^2)$.
We study photoproduction of jets and single-inclusive hadrons in a polarized ep collider mode of HERA at sqrt(s)=300 GeV, examining the sensitivity of the cross sections and their asymmetries to the proton's polarized gluon distribution and to the completely unknown parton distributions of polarized photons. We also present for the first time the NLO corrections to the direct part of polarized single-inclusive hadron photoproduction.
We investigate the polarized parton distribution functions (PDFs) and their uncertainties by using the world data on the spin asymmetry A_1. The uncertainties of the polarized PDFs are estimated by the Hessian method. The up and down valence-quark distributions are determined well. However, the antiquark distributions have large uncertainties at this stage, and it is particularly difficult to fix the gluon distribution. The χ^2 analysis produces a positively polarized gluon distribution, but even Δg(x)=0 could be allowed according to our uncertainty estimation. In comparison with the previous …
Some simple relations between unpolarized and polarized quark parton distributions have direct experimental consequences which will be presented here. In particular, we will see that it is possible to relate the deep inelastic structure functions $F_2$ and $g_1$, both for proton and deuteron, in fair agreement with experimental data.
We derive new positivity bounds on spin-dependent parton distributions in multicolored QCD. They are stronger than Soffer inequality. We check that the new inequalities are stable under one-loop DGLAP evolution to higher normalization points.
The capabilities of a neutrino factory in the determination of polarized parton distributions from charged-current deep-inelastic scattering experiments is discussed. We present a study of the accuracy in the determination of polarized parton distributions that would be possible with such a facility. We show that these measurements have the potential to distinguish between different theoretical scenarios for the proton spin structure.
Polarized parton distributions and structure functions of the nucleon are analyzed in the improved valon model. The valon representation provides a model to represent hadrons in terms of quarks, providing a unified description of bound state and scattering properties of hadrons. Polarized valon distributions are seen to play an important role in describing the spin dependence of parton distributions in the leading order (LO) and next-to-leading order (NLO) approximations. In the polarized case, a convolution integral is derived in the framework of the valon model. The Polarized valon distribut…
We show in general that there are 108 structure functions in the proton-deuteron Drell-Yan processes. However, there exist only 22 finite ones after integrating the cross section over the virtual-photon transverse momentum \vec Q_T or after taking the limit Q_T->0. There are 11 new structure functions in comparison with the ones of the proton-proton reactions, and they are related to the tensor structure of the deuteron. Parton-model analyses indicate an important tensor structure function V_T^{UQ_0}, which can be measured by a quadrupole spin asymmetry. The Drell-Yan process has an advantage …
Motivated by the possibility that it may be misleading to assume SU(3) symmetry in the analysis of hyperon β-decays, we study the sensitivity of the polarized parton densities, derived from the world data on inclusive polarized deep inelastic lepton-nucleon scattering, to variation of the value of the nonsinglet axial charge a_8 from its SU(3) value of 3F-D.
We study an influence of precise data on uncertainty of polarized parton distribution functions. This analysis includes the SLAC-E155 proton target data which are precise measurements. Polarized PDF uncertainties are estimated by using the Hessian matrix. We examine correlation effect between the antiquark and gluon uncertainties. It suggests that reducing the gluon uncertainty is needed to determine the polarized antiquark distribution clearly.
Using differential cross-section data of inclusive $W$ and $Z/γ^\ast$ boson production and of their production in association with jets, and differential cross-section data of top-quark pair production in the lepton + jets and dilepton channels in proton$-$proton collisions at the CERN Large Hadron Collider at center-of-mass energies of $\sqrt{s}=7$ and 8 TeV, together with deep inelastic scattering data from electron$-$proton collisions at the HERA collider, several determinations of parton distribution functions of the proton have been performed by the ATLAS experiment. The results are prese…
The CTEQ and MRS parton distributions involve a substantial number (~30) of parameters that are fit to a large number (~900) of data. Typically, these groups produce fits that represent a good fit to the data, but there is no substantial attempt to determine the errors associated with the fits. Determination of errors would involve consideration of the experimental statistical and systematic errors and also the errors in the theoretical formulas that relate the measured cross sections to parton distributions. We discuss the principles that would be needed in such an error analysis. These princ…
We present a technique for implementing in a fast way, and without any approximations, higher-order calculations of partonic cross sections into global analyses of parton distribution functions. The approach, which is set up in Mellin-moment space, is particularly suited for analyses of future data from polarized proton-proton collisions, but not limited to this case. The usefulness and practicability of this method is demonstrated for the semi-inclusive production of hadrons in deep-inelastic scattering and the transverse momentum distribution of ``prompt'' photons in pp collisions, and a cas…
I review the current status of the determination of helicity-dependent, or polarized, parton distribution functions from a comprehensive analysis of experimental data in perturbative quantum chromodynamics. I illustrate the latest achievements driven by new measurements in polarized proton-proton collisions at the Relativistic Heavy Ion Collider, namely the first evidence of a sizable polarized light sea quark asymmetry and of a positive polarized gluon distribution in the proton. I discuss which are the open issues in the determination of polarized distributions, and how these may be addresse…
We have used QCD and polarized deep-inelastic scattering data to construct x-dependent polarized parton distributions. These flavor dependent distributions evolve under the NLO DGLAP equations, satisfy positivity constraints and agree well with the data. We perform all of the analysis in x-space, avoiding difficulties with moments, and use these distributions to predict spin observables. The small-x behavior is sensitive to the model for the polarized gluon distribution.
We report global analysis results for polarized parton distribution functions in the nucleon. The optimum distributions are determined by using spin asymmetry data on polarized lepton scattering on proton, neutron, and deuteron. Their uncertainties are estimated by the Hessian method. As a result, polarized quark distributions are relatively well determined, whereas the polarized gluon distribution has a large uncertainty band. We find that the obtained gluon distribution is compatible with recent Δg/g measurements in high-p_T hadron productions.
We extract the pion fragmentation functions and their uncertainties from a judicious choice of e+e- and semi-inclusive DIS data. These are used to study the error propagation in the extraction of polarized parton densities from semi-inclusive DIS asymmetries. We conclude that the uncertainties on polarized PDs have been underestimated in the past.
