Polarized parton distributions from NLO QCD analysis of world DIS and SIDIS data

The combined analysis of polarized DIS and SIDIS data is performed in NLO QCD. The new parametrization on polarized PDFs is constructed. The uncertainties on PDFs and their first moments are estimated applying the modified Hessian method. Special attention is paid to the impact of novel SIDIS data on the polarized distributions of light sea and strange quarks. In particular, the important question of polarized sea symmetry is studied in comparison with the latest results on this subject.     

Valence and sea contributions to the nucleon spin

The first moments of the polarized valence parton distribution functions (PDFs) truncated to the wide Bjorken x region 0.004<x<0.7 are directly (without any fitting procedure) extracted in the next to leading order (NLO) QCD from both COMPASS and HERMES data on pion production in polarized semi-inclusive DIS (SIDIS) experiments. The COMPASS and HERMES data are combined in two ways and two scenarios for the fragmentation functions (FFs) are considered. Two procedures are proposed for an estimation of light sea quark contributions to the proton spin. Both lead to the conclusion that these contributions are compatible with zero within the errors.     

QCD analysis of DIS and SIDIS data

The combined analysis of polarized DIS and SIDIS data is performed in NLO QCD using two alternative procedures: standard fitting procedure and the recently developed direct new method. The results from two methods are compared. The especial attention is paid to the light sea and strange PDFs.     

QCD Analysis of the semi-inclusive HERMES and COMPASS data

The first moments of polarized valence PDFs, responsible for the respective contributions to the nucleon spin, are extracted in NLO QCD from the data of COMPASS and HERMES collaborations on the semi-inclusive difference asymmetries. To this end the new method of QCD analysis (alternative to the usual global fit analysis) is applied. Using the obtained results on valence PDFs the first moments of polarized sea PDFs are reconstructed. They turn out surprisingly small: compatible with zeros within the errors.     

QCD analysis of the semi-inclusive COMPASS and HERMES data

The first moments of polarized valence parton distribution functions truncated to the wide Bjorken x region 0.004 < x < 0.7 are directly (without any fitting procedure) extracted in the NLO QCD from combined semi-inclusive DIS data of COMPASS and HERMES collaborations. Two scenarios for fragmentation functions are considered. Applying the proposed original procedure to these results we estimate the contributions of sea u and d quarks to the proton spin, which turn out to be simply zero within the errors.     

Shares of sea and valence quarks in the proton spin puzzle

The first moments of the polarized valence parton distribution functions truncated to the wide Bjorken x region 0.004 < x < 0.7 are directly (without any fitting procedure) extracted in NLO QCD from the combined COMPASS and HERMES semi-inclusive deep inelastic scattering data. Applying the proposed original procedure to these results, we estimate the contributions of light sea quarks to the proton spin, which occur just zero within the errors.     

Polarised Drell-Yan measurements at COMPASS-II

The spin structure of the nucleon and its Parton Distribution Functions (PDFs) are important topics studied by the COMPASS experiment at CERN. So far, the transverse momentum dependent PDFs (TMD PDFs) of the proton and deuteron have been studied in Semi-Inclusive Deep Inelastic Scattering (SIDIS). The Drell-Yan (DY) process is a complementary way to access the TMD PDFs, using a transversely polarised target. Studying the angular distributions of dimuons from the DY events produced in the collisions of a π^? beam with 190 GeV/c momentum off a transversely polarised proton target (NH₃) we are able to extract the azimuthal spin asymmetries, which are generated by 4 out of the 8 TMD PDFs needed to describe the nucleon structure at leading order QCD. The expected sign change in Sivers and Boer-Mulders functions when accessed from DY and SIDIS will be checked [1]. The opportunity to study, in the same experiment, the TMD PDFs from both SIDIS and DY processes is unique at COMPASS. The COMPASS II Proposal [2] was approved by CERN including one year for polarised DY measurements; the beginning of the DY data taking is scheduled for 2014. The feasibility of the measurement was proven by several beam tests performed so far.     

Polarized parton distribution in the relativistic quark exchange framework

The Spin dependent gluon and sea quark distributions of the proton and the neutron are extracted in the leading order (LO) and the next-to-leading order (NLO) QCD. The relativistic quark exchange model is used to calculate the related valence quark spin dependent structure function. The inverse Mellin transform technique is performed to evaluate the polarized x-dependent distributions of the gluon and the sea quark from the various moments of the valence quarks. It is shown that the calculated spin structure functions (SSF) of the proton and the neutron are in good agreement with the available data, such as E143, SMC, E142, E154 and Hermes experiments. A comparison is also made with the other theoretical models. Finally it is shown that the above calculated parton distributions improve the SSF of the proton and the neutron. Received: 4 January 1999 / Revised version: 12 April 1999     

Six “beyond Collins and Sivers” transverse spin asymmetries at COMPASS

COMPASS is a fixed-target high energy physics experiment at the SPS at CERN [1]. One of the important objectives of the experiment is the exploration of the transverse spin structure of the nucleon via spin dependent azimuthal asymmetries in single-hadron production in deep inelastic scattering of polarized leptons off transversely polarized target. For this purpose a series of measurements were made in COMPASS, using 160 GeV/c longitudinally polarized muon beam and transversely polarized ⁶LiD (in 2002, 2003 and 2004) and NH₃ (in 2007 and 2010) targets. Till now main attention was focused on Collins and Sivers asymmetries and obtained results play an important role in the general understanding of the three-dimensional nature of the nucleon and mechanism of SIDIS processes in terms of Transverse Momentum Dependent (TMD) Parton Distribution Functions (PDFs) and Fragmentation Functions (FFs). In addition to these two measured leading-twist effects, the SIDIS cross-section counts six more target transverse spin dependent azimuthal effects, which have their own well defined leading or higher-twist interpretation in terms of QCD parton model. So far COMPASS presented preliminary results for these asymmetries from deuteron [2, 3] and “proton-2007” data [4]. In this contribution we review the results obtained with the last “proton-2010” data sample.     

QCD analysis of experimental polarized deep-inelastic-scattering data

A detailed review of the current state of investigations into polarized deep inelastic scattering (DIS) is presented. Special attention is given to the methods of the QCD analysis of experimental data on these processes and to the methods of extrapolation of polarized structure functions and polarized quark distributions in the regions inaccessible to current experiments. In the case of pure inclusive processes, the QCD analysis of all worldwide data, including the latest COMPASS data, is presented in detail. Special attention is given to such important components of the nucleon-spin problem as the polarized strangeness and polarized gluon distribution. The features of SIDIS processes are considered; in particular, the role of fragmentation functions in the analysis of the semi-inclusive data is discussed. The methods of extracting the fragmentation functions from experimental data are considered in detail, and the corresponding results are presented. The results of analysis of the existing semi-inclusive polarized data both in the QCD leading order and in the next-to-leading order are considered. Special attention is given to non-standard, so-called difference asymmetries, which make it possible to minimize the dependence of results of analysis on the fragmentation functions. The current methods of QCD analysis of semi-inclusive polarized data are critically reviewed. An alternative method of QCD analysis of semi-inclusive data is presented for next-to-leading order QCD. Advantages of the method in practical applications are illustrated by the example of analysis of the HERMES data.     

\Lambda, \bar{\Lambda} polarization and spin transfer in lepton deep-inelastic scattering

The flavor and helicity distributions of the and hyperons for both valence and sea quarks are calculated in a perturbative QCD (pQCD) based model. We relate these quark distributions to the fragmentation functions of and , and calculate the z-dependence of the longitudinal spin transfer to and in lepton deep-inelastic scattering (DIS). It is shown that the spin transfer to the is compatible with the first HERMES results at DESY, and further tests are suggested. We also make predictions for the z-dependence of the and longitudinal polarizations in neutrino (antineutrino) DIS processes. We investigate the sea contribution to the fragmentation functions, and we test a possible scenario where the sea quarks in (or the sea antiquarks in ) are negatively polarized, whereas the sea antiquarks in the (or the sea quarks in ) are positively polarized. The asymmetry of the polarized fragmentation functions of the sea quarks and antiquarks to and provides a way to understand the different behavior between the and spin transfers observed in the recent E665 experiment at FNAL. Received: 5 April 2000 / Published online: 26 July 2000     

Connection formulas between the different QCD orders in application to the valence parton distribution functions

Formulas directly connecting parton distribution functions (PDFs) at the leading (LO) and next to leading (NLO) QCD orders are applied with respect to both unpolarized and polarized valence PDFs. It is shown that the connection formulas allow without any restriction on the allowed Q ² range for the analyzed data to produce improved LO results on valence PDFs, which strongly differ from the standard parametrizations on these quantities, and which could be obtained within the standard approach only by using the data produced at very high Q ² values (that is hardly possible in reality).     

Analyzing the nucleon spin in weak interaction processes at HERA energies

We investigate the possibility to measure the spin content carried by the different quark flavors in a nucleon by means of polarized deep inelastic scattering with W^± exchange at HERA. Such measurements require a polarized proton beam. The expected inclusive and semi-inclusive asymmetries are sizable and for realistic luminosites the expected statistical accuracies are good enough to extract new and relevant information on the valence quark and the strange sea distributions.     

Flavor asymmetry of polarized antiquark distributions and semi-inclusive DIS

The –expansion of QCD suggests large flavor asymmetries of the polarized antiquark distributions in the nucleon. This is confirmed by model calculations in the large– limit (chiral quark–soliton model), which give sizable results for and . We compute the contributions of these flavor asymmetries to the spin asymmetries in hadron production in semi-inclusive deep–inelastic scattering. We show that the large flavor asymmetries predicted by the chiral quark–soliton model are consistent with the recent HERMES data for spin asymmetries in charged hadron production. Received: 30 November 1999 / Published online: 17 March 2000     

Radiative corrections to the structure functions and sum rules in polarized dis

The one-loop NLO radiative corrections (RC) to the observables in polarized DIS using assumption that a quark is an essential massive particle are considered. If compared with classical QCD formulae the obtained results are identical for the unpolarized and different for polarized sum rules, that can be explained as the influence of the finite quark mass effects on NLO QCD corrections. The explicit expression for one-loop NLO QCD contribution to the structure function g ₂ is presented.     

Extraction of parton distributions and \alpha_{\mathrm{s}} from DIS data within a Bayesian treatment of systematic errors

We have performed a NLO QCD global fit of BCDMS, NMC, H1 and ZEUS data with full account of point-to-point correlations using the Bayesian approach to the treatment of systematic errors. Parton distributions in the proton with their experimental uncertainties, including both statistical and systematic, are obtained. The gluon distribution in a wide region of x is found to be softer than the gluon distribution extracted in standard global analyses which include prompt photon data. We obtain a robust estimate of C.L.) based on Chebyshev's inequality, which is compatible with an earlier determination of from the DIS data, but is less dependent on high-twist effects. Received: 5 May 1997 / Revised version: 12 October 1998 / Published online: 8 September 1999     

Thermodynamical model for proton spin

The spin content of the proton, is studied in the thermodynamical model of a nucleon. In this study, the different ingredients and their contributions to the spin are studied. The chemical potentials of constituent quarks, spin contributions coming from valence quarks and asymmetries are calculated and compared with the available data. We find that this statistical model with number conservation of valence quarks reproduces the naive quark model prediction for the spin content of the proton.     

Parton distribution functions at LO,NLO and NNLO with correlated uncertainties between orders

Sets of parton distribution functions (PDFs) of the proton are reported for the leading (LO), next-to-leading (NLO) and next-to-next-to-leading-order (NNLO) QCD calculations. The parton distribution functions are determined with the HERAFitter program using the data from the HERA experiments and preserving correlations between uncertainties for the LO, NLO and NNLO PDF sets. The sets are used to study cross-section ratios and their uncertainties when calculated at different orders in QCD. A reduction of the overall theoretical uncertainty is observed if correlations between the PDF sets are taken into account for the ratio of \(WW\) di-boson to \(Z\) boson production cross sections at the LHC.