Polarized Parton Distributions Research Articles

Flavor structure of the unpolarized and longitudinally polarized sea-quark distributions in the nucleon

It is now widely recognized that a key to unravel the nonperturbative chiral-dynamics of QCD hidden in the deep-inelastic-scattering observables is the flavor structure of sea-quark distributions in the nucleon. We analyze the flavor structure of the nucleon sea in both of the unpolarized and longitudinally polarized parton distribution functions (PDFs) within a single theoretical framework of the flavor SU(3) chiral quark soliton model (CQSM), which contains only one adjustable parameter $\Delta m_s$, the effective mass difference between the strange and nonstrange quarks. A particular attention is paid to a nontrivial correlation between the flavor asymmetry of the unpolarized and longitudinally polarized sea-quark distributions and also to a possible particle-antiparticle asymmetry of the strange quark distributions in the nucleon. We also investigate the charge-symmetry-violation (CSV) effects in the parton distribution functions exactly within the same theretical framework, which is expected to provide us with valuable information on the relative importance of the asymmetry of the strange and antistrange distributions and the CSV effects in the valence-quark distributions inside the nucleon in the resolution scenario of the so-called NuTeV anomaly in the extraction of the Weinberg angle.

Meson polarized distribution function and mass dependence of the nucleon parton densities

The polarized distribution functions of mesons, including pion, kaon and eta, using the proton structure function, are calculated. We are looking for a relationship between the polarized distribution of mesons and the polarized structure of nucleons. We show that the meson polarized parton distributions leads to zero total spin for the concerned mesons, considering the orbital angular momentum of quarks and gluons inside the meson. Two separate Monte Carlo algorithms are applied to compute the polarized parton distributions of the kaon. Via the mass dependence of quark distributions, the distribution function of the eta meson is obtained. A new method by which the polarized sea quark distributions of protons are evolved separately — which cannot be performed easily using the standard solution of DGLAP equations — is introduced. The mass dependence of these distributions is obtained, using the renormalization group equation which makes their evolutions more precise. Comparison between the evolved distributions and the available experimental data validates the suggested solutions for separated evolutions.

Evidence for polarization of gluons in the proton.

We discuss the impact of recent high-statistics Relativistic Heavy Ion Collider data on the determination of the gluon polarization in the proton in the context of a global QCD analysis of polarized parton distributions. We find evidence for a nonvanishing polarization of gluons in the region of momentum fraction and at the scales mostly probed by the data. Although information from low momentum fractions is presently lacking, this finding is suggestive of a significant contribution of gluon spin to the proton spin, thereby limiting the amount of orbital angular momentum required to balance the proton spin budget.

QCD analysis of polarized DIS and the SIDIS asymmetry world data and light sea-quark decomposition

The results of our new QCD analysis of helicity parton distributions of the nucleon at full next-to-leading order (NLO) accuracy in the fixed-flavor number scheme will be presented. Performing a combined QCD fit on the global sets of latest inclusive and the semi-inclusive polarized deep inelastic scattering data, we are able to extract new polarized parton distribution functions (PPDFs) at the input scale $Q_{0}^2=1$ GeV$^2$. Particulary, we have calculated PPDFs considering light sea-quark decomposition and the results are compared with the experimental data and the most precise theoretical models obtained by recent analyses. The latest COMPASS2010 SIDIS data, which were not available for the previous analyses, are employed in the current analysis and the effect of COMPASS SIDIS data is studied in detail. Also the uncertainties of PPDFs are determined using the standard Hessian technique.

Theoretical Description of Deeply Virtual Compton Scattering off 3He

Recently, coherent deeply virtual Compton scattering (DVCS) off $^3$He nuclei has been proposed to access the neutron generalized parton distributions (GPDs). In Impulse Approximation (IA) studies, it has been shown, in particular, that the sum of the two leading twist, quark helicity conserving GPDs of $^3$He, $H$ and $E$, at low momentum transfer, is dominated by the neutron contribution, so that $^3$He is very promising for the extraction of the neutron information. Nevertheless, such an extraction could be not trivial. A technique, able to take into account the nuclear effects included in the IA analysis in the extraction procedure, has been therefore developed. In this work, the IA calculation of the spin dependent GPD $\tilde H$ of $^3$He is presented for the first time. This quantity is found to be largely dominated, at low momentum transfer, by the neutron contribution, which could be extracted using arguments similar to the ones previously proposed for the other GPDs. The known forward limit of the IA calculation of $\tilde H$, yielding the polarized parton distributions of $^3$He, is correctly recovered. The knowledge of the GPDs $H, E$ and $\tilde H$ of $^3$He will allow now the evaluation of the cross section asymmetries which are relevant for coherent DVCS off $^3$He at Jefferson Lab kinematics, an important step towards the planning of possible experiments.

Measurements of the mid-rapidity parity violating spin asymmetries for W ± bosons at PHENIX

The parity violating W± single spin asymmetry, in longitudinally polarized p + p collisions, can give us a clean way to access the \(\Delta \bar u\) and \(\Delta \bar d\) polarized parton distribution functions. The current status of the analysis of the 2011 data set and future prospects will be presented.

The Effect of Polarized DIS Hadronization Process on the Determination of Polarized Parton Distributions

The Effect of Polarized DIS Hadronization Process on the Determination of Polarized Parton Distributions

The impact of target mass correction on polarized parton distribution functions

Considering the nonzero mass effect of the target in extracting polarized parton distribution functions (PPDFs) in preasymptotic region is not negligible. We extract PPDFs from available proton structure function data and study the numerical effects of target mass corrections (TMCs). PPDFs with and without this correction are compared.

Coherent deeply virtual Compton scattering off3He and neutron generalized parton distributions

It has been recently proposed to study coherent deeply virtual Compton scattering (DVCS) off 3He nuclei to access neutron generalized parton distributions (GPDs). In particular, it has been shown that, in Impulse Approximation (IA) and at low momentum transfer, the sum of the quark helicity conserving GPDs of 3He, H and E, is dominated by the neutron contribution. This peculiar result makes the 3He target very promising to access the neutron information. We present here the IA calculation of the spin dependent GPD tilde-H of 3He. Also for this quantity the neutron contribution is found to be the dominant one, at low momentum transfer. The known forward limit of the IA calculation of tilde-H, yielding the polarized parton distributions of 3He, is correctly recovered. The extraction of the neutron information could be anyway non trivial, so that a procedure, able to take into account the nuclear effects encoded in the IA analysis, is proposed. These calculations, essential for the evaluation of the coherent DVCS cross section asymmetries, which depend on the GPDs H, E and tilde-H, represent a crucial step for planning possible experiments at Jefferson Lab.

Polarized parton distributions at an electron–ion collider

We study the potential impact of inclusive deep-inelastic scattering data from a future electron–ion collider (EIC) on longitudinally polarized parton distributions (PDFs). We perform a PDF determination using the NNPDF methodology, based on sets of deep-inelastic EIC pseudodata, for different realistic choices of the electron and proton beam energies. We compare the results to our current polarized PDF set, NNPDFpol1.0, based on a fit to fixed-target inclusive DIS data. We show that the uncertainties on the first moments of the polarized quark singlet and gluon distributions are substantially reduced in comparison to NNPDFpol1.0, but also that more measurements may be needed to ultimately pin down the size of the gluon contribution to the nucleon spin.

Transverse force on quarks in deep-inelastic scattering

The interaction-dependent part of the ${x}^{2}$ moment of the twist-3 polarized parton distribution ${g}_{2}(x)$ is related to the transverse force acting on the active quark in deep-inelastic scattering off a transversely polarized nucleon immediately after it has absorbed the virtual photon. Similarly, the ${x}^{2}$ moment of the chirally odd twist-3 unpolarized parton distribution $e(x)$ can be related to the transverse force experienced by a transversely polarized quark ejected from a transversely polarized nucleon.

Erratum: NLO analytical solutions to the polarized parton distributions, based on the Laplace transformation [Phys. Rev. D87, 114012 (2013)

Erratum: NLO analytical solutions to the polarized parton distributions, based on the Laplace transformation [Phys. Rev. D<b>87</b>, 114012 (2013)

NLO analytical solutions to the polarized parton distributions, based on the Laplace transformation

By using the Laplace transformation, the analytical solutions of the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution equations at the leading-order and next-to-leading-order (NLO) approximations for the gluon, singlet, and nonsinglet quark polarization inside the nucleon are obtained. At NLO approximation, a second Laplace transformation is required. Complete NLO calculations need an iteration method, which we try to employ. As an efficiently mathematical tool, we employ the Jacobi polynomials to extract the polarized nucleon structure, using the analytical solutions for the polarized parton densities. Optimum nucleon structure functions are determined by a ${\ensuremath{\chi}}^{2}$ analysis of the available experimental data, and their uncertainties are estimated by the Hessian method. Our results for nucleon and deuteron structure functions are in good agreement with all available experimental data and fitting parametrization models.

Unbiased determination of polarized parton distributions and their uncertainties

We present a determination of a set of polarized parton distributions (PDFs) of the nucleon, at next-to-leading order, from a global set of longitudinally polarized deep-inelastic scattering data: NNPDFpol1.0. The determination is based on the NNPDF methodology: a Monte Carlo approach, with neural networks used as unbiased interpolants, previously applied to the determination of unpolarized parton distributions, and designed to provide a faithful and statistically sound representation of PDF uncertainties. We present our dataset, its statistical features, and its Monte Carlo representation. We summarize the technique used to solve the polarized evolution equations and its benchmarking, and the method used to compute physical observables. We review the NNPDF methodology for parametrization and fitting of neural networks, the algorithm used to determine the optimal fit, and its adaptation to the polarized case. We finally present our set of polarized parton distributions. We discuss its statistical properties, test for its stability upon various modifications of the fitting procedure, and compare it to other recent polarized parton sets, and in particular obtain predictions for polarized first moments of PDFs based on it. We find that the uncertainties on the gluon, and to a lesser extent the strange PDF, were substantially underestimated in previous determinations.

Polarized semi-inclusive electroweak structure functions at next-to-leading-order

We present a next-to-leading order (NLO) computation of the full set of polarized and unpolarized electroweak semi-inclusive DIS (SIDIS) structure functions, whose knowledge is crucial for a precise extraction of polarized parton distributions. We focus on the phenomenology of the polarized structure functions for the kinematical conditions that could be reached in an Electron-Ion-Collider. We show that the NLO corrections are sizeable, particularly in the small-$x$ range. We test the sensitivity of these structure functions on certain quark distributions and compare it to the situation of inclusive DIS and electromagnetic SIDIS.

Symmetry breaking effect on determination of polarized and unpolarized parton distributions

We perform a new extraction for unpolarized and polarized parton distribution functions considering a flavor decompositions for sea quarks and applying very recent deep inelastic scattering (DIS) and semi inclusive deep inelastic scattering (SIDIS) data in the fixed flavor number scheme (FFNS) framework. In the new symmetry breaking scenario the light quark and antiquark densities are extracted separately and new parametrization forms are determined for them. The heavy flavors contribution, including charm and bottom quarks, are also taken to be account for unpolarized distributions.

Non-singlet spin structure function $g_{1}^{\rm NS}(x,t)$ in the DGLAP approach

An analytical solution of the non-singlet polarized parton distribution Δq NS(x,Q 2) = (Δu(x,Q 2) − Δd(x,Q 2)) is obtained by solving the DGLAP (Gribov and Lipatov, Sov. J. Nucl. Phys. 15, 438 (1972); Lipatov, ibid, 20, 94 (1975); Dokshitzer, Sov. Phys. JETP 46, 641 (1997); Altarelli and Parisi, Nucl. Phys. B126, 298 (1977)) equation by the method of characteristics. We then evaluate the non-singlet spin-dependent structure function $g_1^{\rm NS}$ . The result is compared with the data from HERMES (Airapetian et al, Phys. Rev. D75, 012007 (2007)).

FLAVOR AND SPIN DEPENDENT STRUCTURE OF THE NUCLEON AND MESON

We employ the polarized chiral constituent quarks to extract the polarized structure function of the nucleon. The polarized valon model is used to calculate the spin dependence of parton distribution functions of meson. The connection between the polarized structure of the proton and the Goldstone bosons, using the chiral quark model (χQM) is analyzed and the spin dependence of the parton distribution functions for pion and kaon, is obtained thoroughly. These functions are evolved to high Q2 values, using the singlet, nonsinglet and quark–gluon moments (ΔMS, ΔMNS, ΔMgq) which are convoluted with the polarized valon distributions. The polarized valon distributions for meson are computed, based on a phenomenological method and a comparison between polarized and unpolarized parton distribution functions for pion and kaon are performed. As a consequence of the χQM, the SU (3)f symmetry breaking for the spin dependent of the nucleon sea distributions is achieved. The required polarized parton distributions of the proton will be obtained from the parton distribution functions of the polarized meson via the related convolution integral which are existed in the χQM. Following that the analytical result for the proton's spin structure function, [Formula: see text], is obtained and compared with experimental data. Finally, the parton orbital angular momentum of meson are introduced and the total spin of the meson, based on this quantity and the first moment of distributions for gluon and singlet sectors, are obtained.

Measurement of Sea Quark Polarization with W Boson Production at PHENIX

W boson production is observed in = 500 [GeV] proton proton collision at RHIC-PHENIX experiment. The single longitudinal spin asymmetry AL(p̄p → W+X) is measured via decay positrons in the mid rapidity region. The measured asymmetry −0.83 ± 0.31 ± (11% scale uncertainty) is consistent within uncertainty to calculations from various polarized parton distribution functions.

Cross section and double helicity asymmetry for η mesons and their comparison to π0 production at PHENIX

The η cross section and double helicity asymmetry as a function of transverse momentum have been measured at √s = 200 GeV at the PHENIX experiment at RHIC. The cross section data serve as important input to the extraction of η fragmentation functions, which were essentially unknown before. With the availability of fragmentation functions the asymmetry data can be included in future pQCD fits in order to further constrain the polarized parton distribution functions, in particular the helicity-dependent gluon distribution function. In addition, the η to π0 cross section ratio as a function of transverse momentum has been extracted in a single pass over the same data set, thus minimizing systematic uncertainties. The inclusion of these data in future fragmentation function extractions should allow for more precise results for both particle species.