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.     

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.     

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.     

Recent results from the HERMES experiment

Results are presented from the Hermes experiment which uses semi-inclusive deep inelastic lepton scattering to study the flavor structure of the nucleon. Data have been accumulated for pion and kaon double spin asymmetries, single-spin azimuthal asymmetries for meson electroproduction, deep virtual Compton scattering (DVCS), and meson multiplicities. These results provide information on the properties of the strange sea in the proton, constraints on transverse momentum dependent quark parton distributions, and demonstrate the promise of DVCS for isolating the total angular momentum carried by the quarks in the proton.     

COMPASS results on collins and sivers asymmetries for charged hadrons

The study of transverse spin and transverse momentum effects is an important part of the scientific program of COMPASS, a fixed target experiment at the CERN SPS taking data since 2002. The studies are carried on by measuring the hadrons produced in deep inelastic scattering (DIS) of 160 GeV/c muons off different targets. Among the possible asymmetries in the hadron azimuthal distributions, particularly interesting are the Collins and Sivers asymmetries which the COMPASS Collaboration has measured using transversely polarised deuteron and proton targets. Here new results for charged pions and kaons obtained from the 2010 run with a transversely polarised proton target are presented for the first time.     

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.     

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.     

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.     

Longitudinal and transverse target-spin asymmetries associated with DVCS on the proton at HERMES

Measurements of azimuthal cross-section asymmetries from deeply virtual Compton scattering on transversely and longitudinally polarized hydrogen and longitudinally polarized deuterium targets at HERMES are reported. By comparing the HERMES results on the transverse target-spin asymmetry with theoretical calculations based on a phenomenological model of generalized parton distributions, a model-dependent constraint on the total angular momentum carried by quarks in the nucleon is obtained.     

Recent HERMES Results on DVCS from Proton and Nuclear Targets

Spin structure is one of the fundamental subjects in the study of nucleon structure.Recently it is found that Generalized Parton Distributions(GPDs) are related to the total angular momentum carried by partons,which offers a possible solution to the spin puzzle in the first time.We get access to certain GPDs by looking at the azimuthal angle asymmetries attributed to the interference between Deeply Virtual Compton Scattering (DVCS) and Bethe-Heilter processes in HERMES experiment.By measuring the asymmetry with respect to transverse target polarization from proton target,a model-dependent constraint on J_u vs J_d is obtained.Another worldwide unique channel is nuclear DVCS.The preliminary results on asymmetries with respect to beam spin and beam charge are reported.     

Spin physics with COMPASS

COMPASS is a fixed target experiment at CERN studying nucleon spin structure in polarised deep inelastic muon nucleon scattering and hadron spectroscopy using hadron beams. The main goal of the COMPASS spin physics program is the measurement of the helicity contribution of the gluons to the nucleon spin, ΔG. This quantity is accessible via the photon-gluon-fusion process which can be selected by open charm production or production of hadron pairs with large transverse momenta. The spin physics program of COMPASS includes also measurements with a transversely polarised target. These allow to measure the transverse structure function.COMPASS has up to now successfully finished three runs with a muon beam of 160 GeV and a longitudinally polarized⁶LiD target in the years 2002, 2003 and 2004. An overview of the physics addressed by the muon program, with an emphasis on the ΔG/G measurement will be presented. The status of the analysis of the highpt hadron pairs, open charm, longitudinal and transverse asymmetries will be reviewed.     

Spin and orbital angular momentum in gauge theories: nucleon spin structure and multipole radiation revisited

We address and solve the long-standing gauge-invariance problem of the nucleon spin structure. Explicitly gauge-invariant spin and orbital angular momentum operators of quarks and gluons are obtained. This was previously thought to be an impossible task and opens a more promising avenue towards the understanding of the nucleon spin. Our research also justifies the traditional use of the canonical, gauge-dependent angular momentum operators of photons and electrons in the multipole-radiation analysis and labeling of atomic states and sheds much light on the related energy-momentum problem in gauge theories, especially in connection with the nucleon momentum.     

Transversity of quarks in a nucleon

The transversity distribution of quarks in a nucleon is one of the three fundamental distributions, that characterize nucleon's properties in hard scattering processes at leading twist (twist 2). It measures the distribution of quark transverse spin in a nucleon polarized transverse to its (infinite) momentum. It is a chiral-odd twist-two distribution function — gluons do not couple to it. Quarks in a nucleon/hadron are relativistically bound and transversity is a measure of the relativistic nature of bound quarks in a nucleon. In this work, we review some important aspects of this less familiar distribution function which has not been measured experimentally so far.     

Flavor dependent azimuthal asymmetries in unpolarized semi-inclusive DIS at HERMES

The azimuthal cos? _h and cos2? _h modulations of the distribution of hadrons produced in unpolarized semi-inclusive deep-inelastic scattering of electrons and positrons off hydrogen and deuterium targets have been measured in the hermes experiment. For the first time these modulations were determined in a 4-Dimensional kinematic space for positively and negatively charged pions and kaons separately, as well as for unidentified hadrons. These azimuthal dependences are sensitive to the transverse motion and polarization of the quarks within the nucleon via, e.g., the Cahn, Boer-Mulders and Collins effects.     

COMPASS-II

On December 1st 2010 the proposal of the COMPASS-II Experiment [1] has been approved by the CERN Research Board. After almost ten years of important results achieved by the COMPASS Collaboration in both nucleon spin physics, with the use of muon beam, and hadron spectroscopy, using hadron beams, this second phase offers now a unique chance to address in the very near future newly opened QCD-related challenges, at very moderate upgrade cost, thanks to the versatility of the COMPASS apparatus [2]. This implies mainly study of chiral perturbation theory (ChPT), by measuring the pion polarizability through Primakoff reaction; generalized parton distributions (GPDs), by measuring exclusive deeply virtual compton scattering (DVCS) and hard exclusive meson production (DVMP); transverse momentum dependent parton distributions (TMDs) in single-polarised pion-induced Drell-Yan muon production and in SIDIS on a liquid hydrogen target (in parallel to DVCS). An overview of the COMPASS-II proposal is presented here, with a main focus on the new upcoming investigation of the nucleon structure via the Drell-Yan and DVCS processes.     

Longitudinal polarisation of Λ and Λ̄ hyperons in lepton–nucleon deep-inelastic scattering

We consider models for the spin transfers to Λ and Λ̄ hyperons produced in lepton–nucleon deep-inelastic scattering. We make predictions for longitudinal Λ and Λ̄ spin transfers for the COMPASS experiment and for HERA, and for the spin transfer to Λ hyperons produced at JLAB. We demonstrate that accurate measurements of the spin transfers to Λ and Λ̄ hyperons with COMPASS kinematics have the potential to probe the intrinsic strangeness in the nucleon. We show that a measurement of Λ̄ polarisation could provide a clean probe of the spin transfer from s̄ quarks and provides a new possibility to measure the antistrange quark distribution function. COMPASS data in a domain of x that has not been studied previously will provide valuable extra information to fix models for the nucleon spin structure. The spin transfer to Λ̄ hyperons, which could be measured by the COMPASS experiment, would provide a new tool to distinguish between the SU(6) and Burkardt–Jaffe (BJ) models for baryon spin structure. In the case of the HERA electron–proton collider experiments with longitudinally-polarised electrons, the separation between the target and current fragmentation mechanisms is more clear. It provides a complementary probe of the strange quark distribution and helps distinguish between the SU(6) and BJ models for the Λ and Λ̄ spin structure. Finally, we show that the spin transfer to Λ hyperons measured in a JLAB experiment would be dominated by the spin transfer of the intrinsic polarised-strangeness in the remnant nucleon, providing an independent way to check our model predictions. PACS 13.60.Rj; 13.87.Fh; 13.88.+e; 14.40.Ev; 14.20.Jn     

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.     

Measurement of azimuthal asymmetries in inclusive production of hadron pairs in e(+)e(-) annihilation at Belle

The Collins effect connects transverse quark spin with a measurable azimuthal dependence in the yield of hadronic fragments around the quark's momentum vector. Using two different reconstruction methods, we find evidence of statistically significant azimuthal asymmetries for charged pion pairs in e(+)e(-) annihilation at a center-of-mass energy of 10.52 GeV, which can be attributed to a transverse polarization of the primordial quarks. The measurement was performed using a sample of 79 x 10(6) hadronic events collected with the Belle detector.     

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.