Polarized Parton Densities Research Articles

Next-to-next-to-leading order evolution of polarized parton densities in the Larin scheme

In many calculations involving polarized twist-2 parton densities to higher order in the strong coupling constant one uses the Larin scheme to describe chiral effects in dimensional regularization. Upon forming observables, the scheme dependence cancels. Still one needs a corresponding regularization scheme to compute the contributing building blocks, like massless and massive Wilson coefficients, as well as the massive three-loop operator matrix elements used in the variable flavor number scheme. These are matched to the evolved parton distribution functions in the Larin scheme. Starting with suitable input distributions we provide the solution of scale evolution of the different polarized parton distribution functions in Bjorken x space for a wide range of virtualities Q2 in the Larin scheme, at next-to-leading, at next-to-next-to-leading order for the first time. We also illustrate the deviation between the parton distributions in the Larin and MS¯ schemes numerically. Published by the American Physical Society 2024

Recent data analysis to revisit the spin structure function of the nucleon in Laplace space

Considering a fixed-flavor number scheme and based on Laplace transformation, we perform leading-order and next-to-leading-order QCD analyses that include world data on polarized structure functions ${g}_{1}$ and ${g}_{2}$. During our analysis, taking the DGLAP evolution equations, we employ the Jacobi polynomials expansion technique. In our recent analysis we utilize the recent available data and consequently include more data than what we did in our previous analysis. We obtain good agreements between our results for the polarized parton densities and nucleon structure functions with all available experimental data and some common parametrization models.

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.

Polarized parton densities and spin dependent structure function of the nucleon

We study the polarized parton distribution functions (PPDFs) from recent experimental data at the next-to-leading order (NLO) approximation in the fixed-flavor number scheme. In this analysis, we can compare our results with experimental data such as very recent COMPASS data. It would be very worth to study the PPDFs parametrization form when we want to use this new COMPASS data in QCD analysis on polarized proton structure and parton distribution functions.

Next-to-next-to-leading order QCD analysis of spin-dependent parton distribution functions and their uncertainties: Jacobi polynomials approach

We present a first QCD analysis of next-to-next-leading-order (NNLO) contributions of the spin-dependent parton distribution functions (PPDFs) in the nucleon and their uncertainties using the Jacobi polynomial approach. Having the NNLO contributions of the quark-quark and gluon-quark splitting functions in perturbative QCD (Nucl. Phys. B 889 (2014) 351-400), one can obtain the evolution of longitudinally polarized parton densities of hadrons up to NNLO accuracy of QCD. A very large sets of recent and up-to-date experimental data of spin structure functions of the proton $g_1^p$, neutron $g_1^n$, and deuteron $g_1^d$ have been used in this analysis. The predictions for the NNLO calculations of the polarized parton distribution functions as well as the proton, neutron and deuteron polarized structure functions are compared with the corresponding results of the NLO approximation. We form a mutually consistent set of polarized PDFs due to the inclusion of the most available experimental data including the recently high-precision measurements from {\tt COMPASS16} experiments (Phys. Lett. B 753 (2016) 18-28). We have performed a careful estimation of the uncertainties using the most common and practical method, the Hessian method, for the polarized PDFs originating from the experimental errors. The proton, neutron and deuteron structure functions and also their first moments, $\Gamma^{\rm p, n, d}$, are in good agreement with the experimental data at small and large momentum fraction of $x$. We will discuss how our knowledge of spin-dependence structure functions can improve at small and large value of $x$ by the recent {\tt COMPASS16} measurements at CERN, the {\tt PHENIX} and {\tt STAR} measurements at RHIC, and at the future proposed colliders such as Electron-Ion collider (EIC).

The three-loop splitting functions in QCD: The helicity-dependent case

We present the next-to-next-to-leading order (NNLO) contributions to the main splitting functions for the evolution of longitudinally polarized parton densities of hadrons in perturbative QCD. The quark–quark and gluon–quark splitting functions have been obtained by extending our previous all Mellin-N calculations to the structure function g1 in electromagnetic deep-inelastic scattering (DIS). Their quark–gluon and gluon–gluon counterparts have been derived using third-order fixed-N calculations of structure functions in graviton-exchange DIS, relations to the unpolarized case and mathematical tools for systems of Diophantine equations. The NNLO corrections to the splitting functions are small outside the region of small momentum fractions x where they exhibit a large double-logarithmic enhancement, yet the corrections to the evolution of the parton densities can be unproblematic down to at least x≈10−4.

Importance of fragmentation functions in determining polarized parton densities

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 et al. (DSS) and Hirai et al. (HKNS). The sensitivity of the extracted polarized PDFs to the new FFs is discussed.

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.

The role of semi inclusive DIS data in determining polarized PDFs

A new combined NLO QCD analysis of the polarized inclusive and semi-inclusive DIS data is presented. In contrast to previous combined analyses, the 1/Q2 terms (kinematic –target mass corrections, and dynamic – higher twist corrections) in the expression for the nucleon spin structure function g1 are taken into account. The new COMPASS data are included in the analysis. The impact of the semi-inclusive (SIDIS) data on the polarized parton densities (PDFs) and on the higher twist corrections is demonstrated. The incompatibility of the polarized strange quark density obtained from DIS and from SIDIS data is discussed.

Determination of polarized parton densities from a QCD analysis of inclusive and semi-inclusive deep inelastic scattering data

A new combined next to leading order QCD analysis of the polarized inclusive and semi-inclusive deep inelastic lepton-hadron scattering (DIS) data is presented. In contrast to previous combined analyses, the $1/Q^2$ terms (kinematic - target mass corrections, and dynamic - higher twist corrections) in the expression for the nucleon spin structure function $g_1$ are taken into account. The new COMPASS data are included in the analysis. The impact of the semi-inclusive data on the polarized parton densities (PDFs) and on the higher twist corrections is discussed. The new results for the PDFs are compared to our (Leader, Sidorov, Stamenov) LSS'06 PDFs, obtained from the fit to the inclusive DIS data alone, and to those obtained from the de Florian, Sassot, Stratmann, and Vogelsang global analysis.

Longitudinal polarization of hyperons in the forward region in polarizedppcollisions

We study the longitudinal polarization of hyperons and anti-hyperons at forward pseudorapidity, $2.5<\eta<4$, in singly polarized $pp$ collisions at RHIC energies by using different parameterizations of the polarized parton densities and different models for the polarized fragmentation functions. The results show that the $\Sigma^+$ polarization is able to distinguish different pictures on spin transfer in high energy fragmentation processes; and the polarization of $\Lambda$ and $\bar\Lambda$ hyperons can provide sensitivity to the helicity distribution of strange sea quarks. The influence from beam remnant to hyperon polarization in the forward region is also discussed.

Some remarks on methods of QCD analysis of polarized DIS data

The results on polarized parton densities obtained using different methods of QCD analysis of the present polarized DIS data are discussed. Their dependence on the method used in the analysis, accounting or not for the kinematic and dynamic 1=Q 2 corrections to spin structure function g1, is demonstrated. It is pointed out that the precise data in the preasymptotic region require a more careful matching of the QCD predictions to the data in this region in order to determine the polarized parton densities correctly.

Gaugino-pair production in polarized and unpolarized hadron collisions

We present an exploratory study of gaugino-pair production in polarized and unpolarized hadron collisions, focusing on the correlation of beam polarization and gaugino/Higgsino mixing in the general minimal supersymmetric standard model. Helicity-dependent cross sections induced by neutral and charged electroweak currents and squark exchanges are computed analytically in terms of generalized charges, defined similarly for chargino-pair, neutralino-chargino associated, and neutralino-pair production. Our results confirm and extend those obtained previously for negligible Yukawa couplings and nonmixing squarks. Assuming that the lightest chargino mass is known, we show numerically that measurements of the longitudinal single-spin asymmetry at the existing polarized $pp$ collider RHIC and at possible polarization upgrades of the Tevatron or the LHC would allow for a determination of the gaugino/Higgsino fractions of charginos and neutralinos. The theoretical uncertainty coming from factorization scale and squark mass variations and the expected experimental error on the lightest chargino mass is generally smaller than the one induced by the polarized parton densities, so that more information on the latter would considerably improve on the analysis.

Recent results on polarized PDFs and higher twist

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. It is demonstrated 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 and gluon polarizations. It is also shown that the uncertainties in the determination of the polarized parton densities are significantly reduced. We find also that the present inclusive DIS data cannot rule out a negative polarized and changing in sign gluon densities. The present status of the proton spin sum rule is discussed.

Impact of CLAS and COMPASS data on polarized parton densities and higher twist

We have reanalyzed the world data on inclusive polarized deep inelastic scattering (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 function of $x$, cannot be ruled out on the basis of the present DIS data.

Sea quark polarization and semi-inclusive DIS data

We investigate the potential impact of forthcoming Jefferson Lab semi-inclusive polarized deep inelastic scattering proton measurements in the determination of the sea quark polarization in the nucleon by means of a next to leading order global QCD analysis. Specifically, we estimate the resulting improvement in the constraints on polarized parton densities for the different flavors, which is found to be significant for up and strange quarks, and the correlation between remaining uncertainty ranges for each of the parton species.

Role of positivity constraints in determining polarized parton densities

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.

Sea quark and gluon polarization in the nucleon at NLO accuracy

We investigate the sea quark polarization in the nucleon by means of a combined next to leading order analysis to the recently enlarged set of inclusive and semi-inclusive polarized deep inelastic scattering data. Using the Lagrange multiplier method, we asses the uncertainty inherent to the extraction of the different spin dependent parton densities in a QCD global fit, and the impact of the increased set of semi-inclusive data now available. We comment on future prospects at RHIC and JLAB and their potential impact in the future determination of polarized parton densities.

Higher twist analysis of the nucleong 1 structure function

Different methods to extract the polarized parton densities from the world polarized DIS data are considered. The higher twist correctionsh N (x)/Q 2 to the spin dependent proton and neutrong 1 structure functions are taken into account and found to be nonnegligible 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 present status of our knowledge of the polarized parton densities, or, why we need a neutrino factory

The importance of a neutrino factory for the determination of the polarized parton densities is emphasized.