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.     

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.     

New target transverse spin dependent azimuthal asymmetries from COMPASS experiment

In general, eight target transverse spin-dependent azimuthal modulations are allowed in semi inclusive deep inelastic scattering of polarized leptons on a transversely polarized target. In the QCD parton model four of these asymmetries can be interpreted within the leading order approach. Two of them, namely Collins and Sivers effects were already measured by HERMES and COMPASS experiments. Other two leading twist and remaining four azimuthal asymmetries which can be interpreted as twist-three contributions have been measured for the first time in COMPASS using a 160 GeV/c longitudinally polarized (P _l }~ −0.8) muon beam and a transversely polarized ⁶LiD target. We present here the preliminary results from the 2002–2004 data. on behalf of the COMPASS collaboration     

Collins effect and single spin azimuthal asymmetriesin the HERMES and COMPASS experiments

Predictions are made for single spin azimuthal asymmetries due to the Collins effect in pion production from semi-inclusive deeply inelastic scattering off transversely and longitudinally polarized targets for the HERMES and COMPASS experiments. The x-dependence of the asymmetries is evaluated using the parton distribution functions from the chiral quark-soliton model. The overall normalization of the predicted asymmetries is determined by the information on the Collins fragmentation function extracted from previous HERMES data on azimuthal asymmetries from a longitudinally polarized target. The single spin asymmetries A _UT from the transversely polarized proton target are found to be about for positive and neutral pions both at HERMES and COMPASS. For a longitudinally polarized target we obtain for COMPASS and .Received: 18 September 2003, Published online: 26 November 2003     

Measurement of the polarized parton distribution functions at HERMES

The HERMES experiment at DESY has measured the inclusive and semi-inclusive double-spin asymmetries of polarized positrons scattering from polarized hydrogen and deuterium targets in the kinematic range of Bjørken-x 0.023 < x < 0.06 and 1 GeV ² < Q ² < 10 GeV². A RICH detector was installed for the deuterium running period and by providing the identification of charged pions and kaons has enabled the first measurement of charged kaon asymmetries. Based on the measured proton and deuterium asymmetries the polarized quark distributions have been extracted in leading-order pQCD.Received: 30 September 2002, Published online: 22 October 2003PACS: 13.60.Hb Total and inclusive cross-sections (including deep-inelastic processes) - 13.88. + e Polarization in interactions and scatteringJ. Stewart: For the HERMES Collaboration     

Semi-Inclusive Deep Inelastic Scattering processes from small to large P<Subscript>T</Subscript>

We consider the azimuthal and P_T-dependence of hadrons produced in unpolarized Semi-Inclusive Deep Inelastic Scattering (SIDIS) processes, within the factorized QCD parton model. It is shown that at small P_T values, P _T ≲ 1GeV/c, lowest-order contributions, coupled to unintegrated (transverse-momentum-dependent) quark distribution and fragmentation functions, describe all data. At larger P_T values, P _T ≳ 1GeV/c, the usual pQCD higher-order collinear contributions dominate. Having explained the full P_T range of available data, we give new detailed predictions concerning the azimuthal and P_T-dependence of hadrons which could be measured in ongoing or planned experiments by HERMES, COMPASS and JLab Collaborations.     

Spin structure function of deuteron g<Subscript>1</Subscript><Superscript>d</Superscript> from COMPASS

New results on the longitudinal inclusive spin asymmetry A ₁ ^d in the range 1 < Q ² < 100(GeV/c)^2 and 0.004 < x < 0.7 are presented. From these results we derive the spin-dependent structure function g ₁ ^d which we use to evaluate the scale-invariant flavor-singlet axial charge . The contribution of the measured region is evaluated by a QCD fit of the world data. The data were obtained by the COMPASS experiment at CERN using a 160GeV polarized muon beam scattered off a large double-cell polarized ⁶LiD target. The results are in agreement with those from previous experiments and improve considerably the statistical accuracy in the region x < 0.03.     

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.     

Sivers effect for pion and kaon production in semi-inclusive deep inelastic scattering

We study the Sivers effect in the transverse single spin asymmetries (SSA) for pion and kaon production in semi-inclusive deep inelastic scattering (SIDIS) processes. We perform a fit of which, by including recent high-statistics experimental data for pion and kaon production from HERMES and COMPASS Collaborations, allows a new determination of the Sivers distribution functions for quarks and antiquarks with u , d and s flavours. Estimates for forthcoming SIDIS experiments at COMPASS and JLab are given.     

Intrinsic polarized strangeness and \Lambda ^0 polarization in deep-inelastic production

We propose a model for the longitudinal polarization of baryons produced in deep-inelastic lepton scattering at any , based on static SU(6) quark-diquark wave functions and polarized intrinsic strangeness in the nucleon associated with individual valence quarks. The free parameters of the model are fixed by fitting NOMAD data on the longitudinal polarization of hyperons in neutrino collisions. Our model correctly reproduces the observed dependences of the polarization on the kinematic variables. Within the context of our model, the NOMAD data imply that the intrinsic strangeness associated with a valence quark has anticorrelated polarization. We also compare our model predictions with results from the HERMES and E665 experiments using charged leptons. Predictions of our model for the COMPASS experiment are also presented. Received: 25 May 2002 / Revised version: 8 June 2002 / Published online: 7 October 2002     

COMPASS results on transverse spin asymmetries in identified two-hadron production in SIDIS

COMPASS is a fixed target experiment at CERN where nucleon spin structure and hadron spectroscopy are investigated using a 160 GeV/c polarized μ⁺ beam. An important part of its physics program are the measurements of single spin asymmetries (SSA) in semi-inclusive deep inelastic scattering (SIDIS) on transversely polarized targets. Data on a deuteron target (⁶LiD) were taken in 2002–04. After taking the first data on a transversely polarized proton target (NH₃) in 2007, a full year of data taking followed in 2010 to increase precision. The SSA of identified hadron pairs consisting of charged pions and/or kaons from the 2010 data are shown for the first time and compared to model predictions and results from HERMES.     

Spin structure of the nucleon—status and recent results

After the initial discovery of the so-called “spin crisis in the parton model” in the 1980s, a large set of polarization data in deep inelastic lepton-nucleon scattering was collected at labs like SLAC, DESY and CERN. More recently, new high precision data at large x and in the resonance region have come from experiments at Jefferson Lab. These data, in combination with the earlier ones, allow us to study in detail the polarized parton densities, the Q² dependence of various moments of spin structure functions, the duality between deep inelastic and resonance data, and the nucleon structure in the valence quark region. Together with complementary data from HERMES, RHIC and COMPASS, we can put new limits on the flavor decomposition and the gluon contribution to the nucleon spin. In this report, we provide an overview of our present knowledge of the nucleon spin structure and give an outlook on future experiments. We focus in particular on the spin structure functions g₁ and g₂ of the nucleon and their moments.     

Transversity and T-odd PDFs from Drell–Yan processes with <Emphasis Type="Italic">pp</Emphasis>, <Emphasis Type="Italic">pD</Emphasis> and <Emphasis Type="Italic">DD</Emphasis> collisions

We estimate the single-spin asymmetries (SSA) which provide the access to transversity as well as to Boer–Mulders and Sivers PDFs via investigation of the single-polarized Drell–Yan (DY) processes with pp, pD and DD collisions available to RHIC, NICA, COMPASS, and J-PARC. The feasibility of these SSA is studied with the new generator of polarized DY events. The estimations performed demonstrate that there exist kinematical regions where SSA are presumably measurable. Most useful for PDFs extraction are the limiting kinematical ranges, where one can neglect the sea PDFs contributions which occur at large values of the Bjorken variable x. It is of interest that, contrary to the Sivers PDF, the transversity PDF is presumably accessible only in a particular kinematical region. Contrary to the option with the symmetric collider mode (RHIC, NICA), this is of importance for the COMPASS experiment and the future J-PARC facility, where the fixed-target mode is available.     

Spin physics at COMPASS

Results for the spin structure of the nucleon from the COMPASS data taking periods 2002 to 2004 are presented. The quark contribution to the nucleon spin, following from a QCD fit to the new data, turns out to be significantly larger than it was derived from the previous world data. The new data favour, on the other side, a comparatively small gluon polarisation in the range x _g ≈ 0.1. In the data taken with the deuteron target polarised transversely the related asymmetries are found to be small on the level of accuracy reached so far, indicating a cancellation of the proton and neutron contributions. This is in agreement, for both the Collins and the Sivers asymmetry, with recent theoretical calculations. Also, a step towards the understanding of angular-momentum contributions with COMPASS is taken by the evaluation of asymmetries in exclusive vector meson production.     

The (spin) structure of the nucleon

A selection of new data obtained by the HERMES experiment at DESY is presented, which provides new insight into the QCD structure of the nucleon. Using polarized lepton beams and polarized targets, the spin-dependent structure function g ₁(x) has been determined for ¹ H, ² H and ³ He. By also observing one of the produced hadrons it has been possible to extract the polarization distribution of individual quark flavours in the nucleon as well. Further information on nucleon structure has been obtained by observing (almost) exclusive reactions, which can be interpreted in terms of the recently introduced generalized parton distributions (GPDs). As an example of such data measurements of both the beam-spin and beam-charge asymmetries resulting from deeply virtual Compton scattering (DVCS) are presented. By embedding the deep-inelastic scattering process in the nuclear environment additional information can be obtained on nucleon structure and some QCD effects. The potential of this technique is illustrated by showing new results on tagged structure functions and hadronization in nuclei.Received: 30 September 2002, Published online: 22 October 2003PACS: 13.60.Hb Total and inclusive cross-sections (including deep-inelastic processes) - 13.88. + e Polarization in interactions and scattering - 14.20.Dh Protons and neutrons - 24.85. + p Quarks, gluons, and QCD in nuclei and nuclear processesG. van der Steenhoven: For the HERMES Collaboration     

Spin physics and more with HERMES

A review of recent results obtained by the HERMES experiment is given. Inclusive measurements on polarized and unpolarized targets provide precise information on the polarized structure functions g₁^d and g₁^p and the isoscalar unpolarized structure function ratio F₂^A/F₂^d. The geometrical acceptance of the HERMES detector and the good particle identification capabilities allow the study of semi-inclusive reactions as well. Using polarized targets, the polarized quark distribution functions can be extracted as well as a first indication of the transversity distributions . On unpolarized heavy targets, hadron formation in a nuclear environment is studied. Finally, data on Deeply Virtual Compton Scattering, the hard exclusive electroproduction of real photons, are presented, which are closely linked to the novel framework of Generalised Parton Distributions. For this reaction HERMES has measured the asymmetry main beam charge as well as in-beam spin.Received: 1 November 2002, Published online: 15 July 2003PACS: 13.60.Hb Total and inclusive cross-sections (including deep-inelastic processes) - 13.60.Le Meson production - 24.85.+p Quarks, gluons, and QCD in nuclei and nuclear processes - 25.30.Mr Muon scattering (including the EMC effect)B. Seitz: For the HERMES Collaboration     

Decoupling of the Leading Order DGLAP Evolution Equation with Spin Dependent Structure Functions

We propose an analytical solution for DGLAP evolution equations with polarized splitting functions at the Leading Order (LO) approximation based on the Laplace transform method. It is shown that the DGLAP evolution equations can be decoupled completely into two second order differential equations which then are solved analytically by using the initial conditions \(\delta F^{\mathrm {S}}(x,Q^{2})=\mathcal {F}[\partial \delta F^{\mathrm {S}}_{0}(x), \delta F^{\mathrm {S}}_{0}(x)]\) and \({\delta G}(x,Q^{2})=\mathcal {G}[\partial \delta G_{0}(x), \delta G_{0}(x)]\). We used this method to obtain the polarized structure function of the proton as well as the polarized gluon distribution function inside the proton and compared the numerical results with experimental data of COMPASS, HERMES, and AAC’08 Collaborations. It was found that there is a good agreement between our predictions and the experiments.     

Predictions for azimuthal asymmetries in pion and kaon production in SIDIS off a longitudinally polarized deuterium target at HERMES

Predictions are made for azimuthal asymmetries in pion and kaon production from SIDIS off a longitudinally polarized deuterium target for HERMES kinematics, based on information on the “Collins fragmentation function” from DELPHI data and on predictions for the transversity distribution function from non-perturbative calculations in the chiral quark-soliton model. There are no free parameters in the approach, which has already been successfully applied to explain the azimuthal asymmetries from SIDIS off polarized proton targets observed by HERMES and SMC. Received: 8 January 2002 / Revised version: 25 January 2002 / Published online: 26 April 2002     

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.