Single-spin asymmetries in semi-inclusive deep-inelastic scattering on a transversely polarized hydrogen target

Single-spin asymmetries for semi-inclusive electroproduction of charged pions in deep-inelastic scattering of positrons are measured for the first time with transverse target polarization. The asymmetry depends on the azimuthal angles of both the pion (phi) and the target spin axis (phi(S)) about the virtual-photon direction and relative to the lepton scattering plane. The extracted Fourier component sin((phi+phi(S))(pi)(UT) is a signal of the previously unmeasured quark transversity distribution, in conjunction with the Collins fragmentation function, also unknown. The component sin((phi-phi(S)(pi)(UT) arises from a correlation between the transverse polarization of the target nucleon and the intrinsic transverse momentum of quarks, as represented by the previously unmeasured Sivers distribution function. Evidence for both signals is observed, but the Sivers asymmetry may be affected by exclusive vector meson production.     

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.Received: 25 April 2005, Published online: 27 July 2005     

Transversity decomposition of quark angular momentum

We express the correlation between quark transversity and (total) quark angular momentum in terms of the second moment of chirally odd generalized parton distributions. The resulting relation allows to determine how much quarks of a given transversity contribute to the total angular momentum of the nucleon.     

Latest HERMES results on transverse spin effects in hadron structure and formation⋆

Transverse target single-spin asymmetries in semi-inclusive deep inelastic scattering allow to study the so-called Collins and Sivers mechanisms. The first one connects the poorly known fundamental transversity distribution function, describing the transverse spin-polarization of quarks in a transversely polarized proton, to the Collins fragmentation function, describing spin-orbit correlations in the hadron formation process. The second one is sensitive to the Sivers function, which correlates the intrinsic transverse momentum of quarks with the proton’s spin orientation and is related to the orbital angular momentum of quarks. Preliminary results on azimuthal single target-spin asymmetries in semi-inclusive electro-production of pions and kaons at the HERMES experiment are presented. The full data set collected with a transversely polarized hydrogen target was analyzed providing the HERMES most precise results on the Collins and Sivers azimuthal moments. Original article based on material presented at HADRON 2007.     

Transversity GPD in photoproduction and electroproduction of two vector mesons

The chiral-odd generalized parton distribution (GPD), or transversity GPD, of the nucleon can be accessed experimentally through the photoproduction or electroproduction of two vector mesons on a polarized nucleon target, γ^(*)N→ρ₁ρ₂N’, where ρ₁ is produced at large transverse momentum, ρ₂ is transversely polarized, and the mesons are separated by a large rapidity gap. We predict the cross section for this process for both transverse and longitudinal ρ₂ production. To this end, we propose a model for the transversity GPD H_T(x,ξ,t) and give an estimate of the relative sizes of the transverse and longitudinal ρ₂ cross sections. We show that a dedicated experiment at high energy should be able to measure the transversity content of the proton.     

Final-state interactions and single-spin asymmetries in semi-inclusive deep inelastic scattering

Recent measurements from the HERMES and SMC Collaborations show a remarkably large azimuthal single-spin asymmetries A_UL and A_UT of the proton in semi-inclusive pion leptoproduction γ^*(q)p→πX. We show that final-state interactions from gluon exchange between the outgoing quark and the target spectator system lead to single-spin asymmetries in deep inelastic lepton–proton scattering at leading twist in perturbative QCD; i.e., the rescattering corrections are not power-law suppressed at large photon virtuality Q² at fixed x_bj. The existence of such single-spin asymmetries requires a phase difference between two amplitudes coupling the proton target with J^z_p=±1/2 to the same final-state, the same amplitudes which are necessary to produce a nonzero proton anomalous magnetic moment. We show that the exchange of gauge particles between the outgoing quark and the proton spectators produces a Coulomb-like complex phase which depends on the angular momentum L^z of the proton's constituents and is thus distinct for different proton spin amplitudes. The single-spin asymmetry which arises from such final-state interactions does not factorize into a product of distribution function and fragmentation function, and it is not related to the transversity distribution δq(x,Q) which correlates transversely polarized quarks with the spin of the transversely polarized target nucleon.     

How could the proton transversity be measured

The perspectives of two new nonstandard methods of transverse quark polarisation measurement are considered: the jet handedness and the so-called “Collins effect” due to spin dependent T-odd fragmentation function responsible for the left-right asymmetry in fragmenting of transversely polarised quarks. Recent experimental indications in favour of the latter is observed. This makes us hope to use these effects in polarised DIS experiments for transversity measurement. The first estimation of transversity was done by using the azimuthal asymmetry in semi-inclusive DIS recently measured by HERMES and SMC.     

Transverse spin structure of the nucleon from lattice-QCD simulations

We present the first calculation in lattice QCD of the lowest two moments of transverse spin densities of quarks in the nucleon. They encode correlations between quark spin and orbital angular momentum. Our dynamical simulations are based on two flavors of clover-improved Wilson fermions and Wilson gluons. We find significant contributions from certain quark helicity flip generalized parton distributions, leading to strongly distorted densities of transversely polarized quarks in the nucleon. In particular, based on our results and recent arguments by Burkardt [Phys. Rev. D 72, 094020 (2005)], we predict that the Boer-Mulders function h(1/1), describing correlations of transverse quark spin and intrinsic transverse momentum of quarks, is large and negative for both up and down quarks.     

Measuring the transverse polarization of quarks in the proton

The transverse spin polarization distribution of quarks in a proton contributes at leading twist to the angular distribution of lepton pair production in doubly polarized proton-proton collisions. Although this distribution is straightforward to define in the QCD-improved parton model and represents a fundamental quark degree of freedom, it has never been measured. Moreover, deeply inelastic electroproduction experiments are only sensitive to this distribution at the higher twist level, and then mix this contribution with others, including the one coming from multiparton initial states. Reviewing this, we conclude that the Drell-Yan process is the best way to measure the quark transverse spin polarization distribution.Unité propre du CNRS     

On contribution of instantons to nucleon sum rules

The contribution of instantons to nucleon QCD sum rules is obtained. It is shown that this contribution does provide stabilization of the sum rules and leads to formation of a nucleon as a bound state of quarks in the instanton field.     

核环境中部分子演化与重组效应下的核内胶子分布

在既考虑到泄漏在束缚核子外的海夸克与胶子间的重组,又考虑到仍束缚在核子内的部分子由于其禁闭空间的变化而发生的演化的基础上,给出了核内胶子分布函数的普遍形式,并具体计算了锡梭与碳核的胶子分布比,结果与NMC实验合作组的最新实验相一致.     

Polarization effects in Drell-Yan processes

Effects of polarization of hadrons and constituent quarks in Drell-Yan processes are considered; they are one of the most efficient tools for investigation of the quark structure of hadrons. Special attention is paid to such important parton distribution functions as the transversity and T-odd Sivers and Boer—Mulders functions whose study is necessary for understanding the effects connected with the nonzero transverse component of the quark momentum. An original method for direct extraction of transversity and Boer—Mulders function in the proton from the data on Drell—Yan processes, in which a maximum of one hadron in the initial state is transversely polarized, is presented. This method possesses a number of important advantages. The method is applied both to Drell—Yan processes with a valence antiquark (antiproton-proton and pion-proton collisions) and with a sea antiquark (proton-proton, proton-deuteron, and deuteron-deuteron collisions). Theoretical estimates of asymmetries and cross sections for setups at RHIC (BNL, US), NICA (JINR, Russia), COMPASS (CERN, Switzerland), PAX (GSI, Germany), and J-PARC (Japan) are presented for evaluation of the measurability of transversity and T-odd distributions. These theoretical estimates are accompanied by calculations of statistical uncertainties for measured asymmetries using the new Monte Carlo generator of Drell—Yan events. The duality of Drell—Yan processes and those of production of J/Φ resonance is studied, and it may allow one to considerably reduce statistical uncertainties of parton distributions. Kinematical conditions, for which this duality can be observed, are evaluated.     

Quark exchange effects on 3He and 3H charge densities

The exchange of quarks between nucleons bound in a nucleus leads to a definite and evaluable contribution to the nuclear charge density distribution. Although this exchange contribution is a consequence of finite nucleon size, it cannot be included by the conventional procedure of folding nucleon charge distributions with the density of point nucleons. For the A = 3 nuclei investigated here, the effects of quark exchange were found to be of significance for small distances away from the nuclear centre-of-mass.     

Transverse spin structure of hadrons from lattice QCD

This paper presents recent lattice QCD calculations of transverse spin densities of quarks in hadrons.² Based on our simulation results for the tensor generalized form factors, we find substantial correlations between spin and coordinate degrees of freedom in the nucleon and the pion. They lead to strongly distorted transverse spin densities of quarks in the nucleon and a surprisingly non-trivial transverse spin structure of the pion. Following recent arguments by Burkardt [M. Burkardt, Phys. Rev. D 72 (2005) 094020], our results imply that the Boer-Mulders function , describing correlations of the transverse spin and intrinsic transverse momentum of quarks, is large and negative for up-quarks in the proton and the π⁺. This supports the recent hypothesis that all Boer-Mulders functions are alike [arXiv:0705.1573], and also provides additional motivation for future studies of azimuthal asymmetries in πp Drell-Yan production at, e.g., COMPASS.     

Structure functions of bound nucleons: From the EMC effect to nuclear shadowing

We describe the nuclear structure functions in the whole range of the Bjorken variablex, by combining various effects in a many-step procedure. First, we present a QCD motivated model of nucleons, treated, in the limit of vanishingQ ², as bound states of three relativistic constituent quarks. Gluons and sea quarks are generated radiatively from the input valence quarks. All parton distributions are described in terms of the confinement (or nucleon's) radius. The results for free nucleons are in agreement with the experimental determinations. The structure functions of bound nucleons are calculated by assuming that the main effect of nucleon binding is stretching of nucleons. The larger size of bound nucleons lowers the valence momentum and enhances the radiatively generated glue and sea densities. In the small-x region the competitive mechanism of nuclear shadowing takes place. It also depends on the size of the nucleons. By combining stretching, shadowing and Fermi motion effects (the latter confined to very largex), the structure function ratio is well reproduced. Results are also presented for theA-dependence of the momentum integral of charged partons, the nuclear gluon distribution and the hadron-nuclei cross sections.     

夸克的横向性分布与核子张量荷

夸克的横向性分布的一次矩定义了核子张量荷. 核子张量荷也可用张量流算符在核子态的矩阵元定义,由此用量子色动力学求和规则、有效理论和模型计算了核子张量荷. 对研究核子性质及强子物理的自洽非微扰途径问题也作了简要讨论. The first moment of quark transversity distribution defines the tensor charge of nucleon. The tensor charge of nucleon can also be defined as the forward matrix element of the tensor current in the nucleon state，which is used to study the nucleon’s tensor charge in terms of quantum color dynamics(QCD) sum rule approach， the effective theory and model. A consistent nonperturbative approach to study nucleon property and hadronic physics is also discussed.     

EMC and polarized EMC effects in nuclei

We determine nuclear structure functions and quark distributions for ⁷Li, ¹¹B, ¹⁵N and ²⁷Al. For the nucleon bound state we solve the covariant quark–diquark equations in a confining Nambu–Jona-Lasinio model, which yields excellent results for the free nucleon structure functions. The nucleus is described using a relativistic shell model, including mean scalar and vector fields that couple to the quarks in the nucleon. The nuclear structure functions are then obtained as a convolution of the structure function of the bound nucleon with the light-cone nucleon distributions. We find that we are readily able to reproduce the EMC effect in finite nuclei and confirm earlier nuclear matter studies that found a large polarized EMC effect.     

Three-dimensional parton distribution functions g1T and $h_{1L}^{\perp}$ in the polarized proton–antiproton Drell–Yan process

We present predictions of the unweighted and weighted double spin asymmetries related to the transversal helicity distribution g _1T and the longitudinal transversity distribution h_1L^{^}h_{1L}^{\perp}, two of eight leading-twist transverse momentum dependent parton distributions (TMDs) or three-dimensional parton distribution functions (3dPDFs), in the polarized proton–antiproton Drell–Yan process at typical kinematics on the Facility for Antiproton and Ion Research (FAIR). We conclude that FAIR is ideal to access the new 3dPDFs toward a detailed picture of the nucleon structure.     

Spin structure of the pion

We present the first calculation of the transverse spin structure of the pion in lattice QCD. Our simulations are based on two flavors of nonperturbatively improved Wilson fermions, with pion masses as low as 400 MeV in volumes up to (2.1 fm)(3) and lattice spacings below 0.1 fm. We find a characteristic asymmetry in the spatial distribution of transversely polarized quarks. This asymmetry is very similar in magnitude to the analogous asymmetry we previously obtained for quarks in the nucleon. Our results support the hypothesis that all Boer-Mulders functions are alike.     

Spin-Dependent Forces and Current Quark Masses

The J = (3/2) , J = 1/2 Nucleon mass difference shows the quark energies can be spin dependent. It is natural to expect that the quark wave functions also depend on spin. A spin-dependent quark force is fitted to the proton and neutron magnetic moments, axial charge, and spin content using a (1/2⁺)³ configuration for the quarks and assuming only zero mass u and d quarks are in the nucleon. In the octet, such spin-dependent forces lead to different wave functions for quarks with spin parallel or antiparallel to the nucleon spin. The eigen-energy of this potential is 0.15 GeV higher for quark spin parallel than for the quark spin antiparallel to the proton spin. This potential predicts a single quark energy of 0.37 GeV for mass-less quarks in the Delta. Assuming the quark forces are flavor independent, this potential predicts magnetic moments of a bound strange quark to be very close to those determined empirically from the octet magnetic moments.