Polarized Quark Distributions Research Articles

Measurement of longitudinal spin asymmetries for weak boson production in polarized proton-proton collisions at RHIC.

We report measurements of single- and double-spin asymmetries for W^{±} and Z/γ^{*} boson production in longitudinally polarized p+p collisions at sqrt[s]=510 GeV by the STAR experiment at RHIC. The asymmetries for W^{±} were measured as a function of the decay lepton pseudorapidity, which provides a theoretically clean probe of the proton's polarized quark distributions at the scale of the W mass. The results are compared to theoretical predictions, constrained by polarized deep inelastic scattering measurements, and show a preference for a sizable, positive up antiquark polarization in the range 0.05<x<0.2.

Accessing Gluon Polarization in the Proton with Direct Photons at PHENIX

Direct photon production in polarized pp collisions serves as an excellent probe of the spin structure of the proton. Gluon-quark scattering, g + q → γ + q, dominates direct photon production for p + p collisions. This channel is theoretically clean as it requires no fragmentation function for the photon. In addition, the double longitudinal asymmetry ALLis directly proportional to the quark and gluon polarizations, giving access to both the magnitude and sign of the polarized gluon distribution since the polarized quark distributions are known from polarized DIS. The status of the direct photon cross section measurement and ALLfor center of mass energies 200 and 500 GeV at midrapidity (|η| < 0.35) will be presented.

Polarized EMC effect in the Thermodynamical Bag Model

We determine the polarized quark distributions and structure functions for nuclear media such as Li7 and Al27 by using a phenomenological model known as Thermodynamical Bag Model. The evaluation of nuclear medium modifications to single nucleon structure function discusses the predictions of the polarized EMC effect. The deviation of polarized EMC from unpolarized case shows quenching of polarized quark distributions and proves the significance of this study as adding the spin observables will explore more about medium modification of nuclear structure and the nature of the strong interaction.

Spin Structure of the Nucleon

HERMES is a second generation experiment to study the spin structure of the nucleon, in which measurements of the spin dependent properties of semi-inclusive deep-inelastic lepton scattering are emphasized. The first experimental results from measurements of single-spin asymmetries for pions and kaons in deep-inelastic scattering with transverse target polarization are discussed. Longitudinally polarized beam and target data provide information on the flavor decomposition of the polarized quark distributions in the nucleon and a first glimpse of the gluon polarization. Moreover, first preliminary results for the unpolarized ep → enπ + total cross section are presented and compared to Generalized Parton Distribution calculations.

Hadronization in polarized semi-inclusive DIS: the question of independent fragmentation

The new formalism for description of (un)polarized semi-inclusive DIS at moderate energies is developed. Hadron production is modeled as a product of distribution functions and hadronization functions (HFs) weighted by the hard scattering cross sections, as it is done in the {\tt LEPTO} event generator. The correct treatment of polarization effects shows that description of semi-inclusive DIS within this formalism includes a new nonperturbative input -- {\it polarized} HFs. It is shown that this approach does not correspond to the commonly adopted one with the independent quark fragmentation. The purity method used by the HERMES collaboration mixes up the two approaches and ignores the contributions from polarized HFs. This method cannot be considered a precise tool for the extraction of polarized quark distributions from measured SIDIS asymmetries.

Spin densities in the transverse plane and generalized transversity distributions

We show how generalized quark distributions in the nucleon describe the density of polarized quarks in the impact parameter plane, both for longitudinal and transverse polarization of the quark and the nucleon. This density representation entails positivity bounds including chiral-odd distributions, which tighten the known bounds in the chiral-even sector. Using the quark equations of motion, we derive relations between the moments of chiral-odd generalized parton distributions of twist two and twist three. We exhibit the analogy between polarized quark distributions in impact parameter space and transverse momentum dependent distribution functions.

Spin structure of the nucleon

HERMES is a second generation experiment to study the spin structure of the nucleon, in which measurements of the spin dependent properties of semi-inclusive deep-inelastic lepton scattering are emphasized. The first experimental results from measurements of single-spin asymmetries for pions and kaons in deep-inelastic scattering with transverse target polarization are discussed. Longitudinally polarized beam and target data provide information on the flavor decomposition of the polarized quark distributions in the nucleon and a first glimpse of the gluon polarization. Moreover, first preliminary results for the unpolarized e p→ e n π+ total cross section are presented and compared to Generalized Parton Distribution calculations. PACS: 13.87.Fh – 13.60.-r – 13.88.+e

Precision measurement of the neutron spin asymmetryA(n)(1) and spin-flavor decomposition in the valence quark region.

We have measured the neutron spin asymmetry A(n)(1) with high precision at three kinematics in the deep inelastic region at x=0.33, 0.47, and 0.60, and Q(2)=2.7, 3.5, and 4.8 (GeV/c)(2), respectively. Our results unambiguously show, for the first time, that A(n)(1) crosses zero around x=0.47 and becomes significantly positive at x=0.60. Combined with the world proton data, polarized quark distributions were extracted. Our results, in general, agree with relativistic constituent quark models and with perturbative quantum chromodynamics (PQCD) analyses based on the earlier data. However they deviate from PQCD predictions based on hadron helicity conservation.

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 Bjorken-x 0.023 < x < 0.06 and 1 GeV2 < 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.

Remarks on polarized quark distributions extracted from SIDIS experiments

The results of SIDIS experiments concerning the first moments of the polarized quark distributions are considered. The possible reasons of the deviation from the fundamental restrictions such as the Bjorken sum rule and the ways to properly improve the analysis of measured SIDIS asymmetries are discussed. The possibility of broken polarized sea scenario is analysed.

MEASUREMENT OF POLARIZED QUARK DISTRIBUTIONS AT HERMES

The HERMES experiment has measured double spin asymmetries in the cross section for deep–inelastic scattering of longitudinally polarized positrons on longitudinally polarized 3 He (1995), 1 H (1996/97), and 2 D (1998) targets. A kinematic range of 0.023 &lt; x &lt; 0.6, and 1 GeV 2 &lt; Q2 &lt; 15 GeV 2 has been covered. From these asymmetries, based on inclusive and semi–inclusive measurements, polarized quark distributions are extracted as a function of x for up [Formula: see text] and down [Formula: see text] flavors as well as for valence and sea quarks. In the measured range, the up quark polarization is positive while the down quark polarization is negative. The sea quark polarization is compatible with zero. In this analysis all sea quark polarizations have been assumed to be flavor symmetric. Presently HERMES is analyzing a high statistics 2 D data sample taken in 1999-2000. For these data it is possible to identify pions and kaons with a RICH detector which was installed in 1998. This will enable an extraction of the individual sea quark flavors [Formula: see text], [Formula: see text], and [Formula: see text] without any symmetry assumptions.

Polarized SIDIS: comment on purity method for extraction of polarized quark distributions

The role of hadronization mechanism in polarization phenomena in semi inclusive deep inelastic scattering (SIDIS) and a purity method for extraction of polarized distribution functions are discussed. According to the Monte Carlo (MC) event generator, on which this method is based, hadrons can be produced via quark (diquark) fragmentation or light cluster decays. In contrast, the purity method assumes that only quark fragmentation gives contribution to hadron production in the current fragmentation region. The ignorance of contributions from diquark fragmentation and cluster decays to asymmetry can be source of incorrect values of polarized quark distributions extracted by the purity method.

HERMES AND THE SPIN OF THE PROTON

HERMES is a second generation experiment to study the spin structure of the nucleon, in which measurements of the spin dependent properties of semi-inclusive deep-inelastic lepton scattering are emphasized. Data have been accumulated for semi-inclusive pion, kaon, and proton double-spin asymmetries, as well as for high-pT hadron pairs, and single-spin azimuthal asymmetries for pion electroproduction and deep virtual Compton scattering. These results provide information on the flavor decomposition of the polarized quark distributions in the nucleon and a first glimpse of the gluon polarization, while the observation of the azimuthal asymmetries show promise for probing the tensor spin of the nucleon and isolating the total angular momentum carried by the quarks.

Polarized parton distributions from charged-current deep-inelastic scattering and future neutrino factories

We discuss the determination of polarized parton distributions from charged-current deep-inelastic scattering experiments. We summarize the next-to-leading order treatment of charged-current polarized structure functions, their relation to polarized parton distributions and scale dependence, and discuss their description by means of a next-to-leading order evolution code. We discuss current theoretical expectations and positivity constraints on the unmeasured C-odd combinations Delta q-Delta qbar of polarized quark distributions, and their determination in charged-current deep-inelastic scattering experiments. We give estimates of the expected errors on charged-current structure functions at a future neutrino factory, and perform a study of the accuracy in the determination of polarized parton distributions that would be possible at such a facility. We show that these measurements have the potential to distinguish between different theoretical scenarios for the proton spin structure.

Recent spin physics results from the HERMES experiment

The HERMES experiment at HERA/DESY studies the spin structure of the nucleon through deep inelastic scattering of longitudinally polarised positrons off polarised H̄, D̄ and 3 He targets. In addition to inclusive measurements which aim at a precise determination of the spin structure functions g 1 and g 2 of the proton and the neutron, HERMES focuses on semi-inclusive measurements, taking advantage of the unique capability of the experiment to reconstruct and identify final state hadrons. A selection of recent results from measurements with longitudinally polarised targets are presented, including polarised quark distributions and a first extraction of the polarisation of gluons. Also presented are results from single-spin asymmetries which allow to complete the investigation of the nucleon spin structure at and beyond leading twist level. Finally, first evidence is presented for (double-)spin asymmetries in the diffractive production of vector mesons.

Spin physics by the SMC

The Spin Muon Collaboration at CERN has covered a wide range of spin physics. The main aim of the collaboration was the measurement of the g 1 spin structure functions of the proton and the neutron (using deuteron targets) in the range 0.003 < x < 0.7 for Q 2 ≥ 1 GeV 2. This was accompanied by a QCD analysis of all published g 1 data. The spin structure functions g 2 were also measured, which allowed for a reduction on the error in g 1. Semi inclusive data were analyzed in order to produce the first polarized quark distributions. Data obtained with a dedicated low x trigger extend down to x = 6 × 10 −5 for Q 2 ≥ 0.01 GeV 2. Some more specifics channels are still being analyzed, they include asymmetry in diffractive ϱ production, hadron azimuthal asymmetry with a transversely polarized target, measurement of the longitudinal Λ polarization, and the asymmetry in high P t hadron pair production. This last asymmetry is related to the gluon polarization in the nucleon, and this topic will be discussed in some details after a brief review of the main inclusive results.

Physics results from HERMES

The Hermes experiment at the Desy laboratory in Hamburg, Germany, studies the spin structure of the nucleon. Its unique feature is the combination of a polarized internal gas target with the longitudinally polarized 27.5 GeV electron/positron beam of the Hera accelerator. Recent Hermes measurements include the proton spin structure function g1p, the flavor decomposition of the polarized quark distributions in the nucleon, the DIS contribution to the generalized GDH sum rule, the first observation of a spin asymmetry in exclusive vector meson production and the first observation of a single-spin azimuthal asymmetry in semi-inclusive pion production. Additionally, the possibility of using various unpolarized gases as target material broadens the spectrum of physics measurements with Hermes.

Flavour decomposition of the polarised quark distributions from semi-inclusive data

Spin asymmetries of the semi-inclusive cross section for the production of charged hadrons have been measured in deep-inelastic scattering of polarised leptons from polarised nuclei by the SMC experiment in the kinematic range 0.003 < x < 0.7 and 1 GeV 2 < Q 2 < 56 GeV 2 and by the HERMES experiment in the kinematic range 0.023 < x < 0.6 and 1 GeV 2 < Q 2 < 10GeV 2. Recent results from HERMES on the extraction of polarised quark distributions from the measured spin asymmetries were presented at this conference for the first time. Polarised quark distributions were extracted as a function of x for up ( u + u ) and down ( d + d ) flavours, and for valence and sea quarks. The up quark polarisation is positive and the down quark polarisation is negative in the measured range. The polarisation of the sea is compatible with zero. The moments of the polarised quark distributions are presented. All HERMES results are preliminary.

Flavor decomposition of the polarized quark distributions in the nucleon from inclusive and semi-inclusive deep-inelastic scattering

Spin asymmetries of semi-inclusive cross sections for the production of positively and negatively charged hadrons have been measured in deep-inelastic scattering of polarized positrons on polarized hydrogen and 3 He targets, in the kinematic range 0.023< x<0.6 and 1 GeV 2< Q 2<10 GeV 2. Polarized quark distributions are extracted as a function of x for up (u+ u ̄ ) and down ( d+ d ̄ ) flavors. The up quark polarization is positive and the down quark polarization is negative in the measured range. The polarization of the sea is compatible with zero. The first moments of the polarized quark distributions are presented. The isospin non-singlet combination Δq 3 is consistent with the prediction based on the Bjorken sum rule. The moments of the polarized quark distributions are compared to predictions based on SU(3) f flavor symmetry and to a prediction from lattice QCD.

Hard exclusive electroproduction of pions

We investigate the exclusive electroproduction of pi^+ mesons from nucleons. To leading twist, leading order alpha_s accuracy the corresponding production amplitude can be decomposed into pseudovector and pseudoscalar parts. Both can be expressed in terms of quark double distribution functions of the nucleon. While the pseudovector contribution is connected to ordinary polarized quark distributions, the pseudoscalar part can be related to one pion t-channel exchange. We observe that the pseudovector part of the production amplitude is important at x < 0.1. On the other hand, for 0.1 < x < 0.4 contributions from one pion exchange dominate.