On unique predictions for single spin azimuthal asymmetry

Theoretically there are two approaches to predict single spin azimuthal asymmetries. One is to take transverse momenta of the partons into account by using transverse momentum dependent parton distributions, while another is to take asymmetries as twist-3 effects. The non-perturbative effects in these approaches are parameterized with different matrix elements, and predictions can be different. Recently, gauge invariant definitions of transverse momentum dependent parton distributions were derived. With these definitions it can be shown that there are relations between non-perturbative matrix elements in these two approaches. These relations may enable us to unify two approaches and to have unique predictions for single spin azimuthal asymmetries. In this letter we derive these relations by using time-reversal symmetry and show that even with these relations the single spin azimuthal asymmetry in a Drell-Yan process is predicted differently in different approaches.Received: 2 July 2004, Published online: 24 September 2004     

Collins and sivers effects in p↑p → jet πX: Universality and process dependence

In this paper we briefly review the transverse momentum dependent generalized parton model and its application to the study of azimuthal asymmetries in the distribution of leading hadrons (mainly pions) inside large transverse momentum jets inclusively produced in polarized proton-proton collisions. We put particular emphasis on the phenomenological interest of these observables, in combination with similar asymmetries measured in semi-inclusive deeply inelastic scattering, Drell-Yan processes and e ⁺ e ^? collisions, for the study of the universality properties of the transverse momentum dependent parton distribution and fragmentation functions. We present results for RHIC kinematics at center-of-mass energies √s = 200 and 500 GeV, for central and mainly forward jet rapidities, in particular for the Sivers distribution and the Collins fragmentation function, that are believed to be responsible for many of the largest asymmetries measured in the last years. We also briefly discuss the case of inclusive jet production and recent phenomenological applications of other theoretical approaches, like the colour gauge invariant generalized parton model and the collinear twist-three approach, aiming at clarifying the issues of the universality and process dependence of transverse momentum dependent functions.     

Testing the process dependence of the Sivers function via hadron distributions inside a jet

We study the process dependence of the Sivers function by considering the impact of color-gauge invariant initial and final state interactions on transverse spin asymmetries in proton-proton scattering reactions within the framework of the transverse momentum dependent (TMD), generalized parton model. To this aim, we consider the azimuthal distribution of leading pions inside a fragmenting jet as well as single inclusive jet asymmetry in polarized proton-proton collisions. In contrast to single inclusive pion production, in both cases we can isolate the Sivers contribution and thereby study its process dependence. The predictions for the Sivers asymmetry obtained with and without inclusion of color gauge factors are comparable in size but with opposite signs. We conclude that both processes represent unique opportunities to discriminate among the two approaches and test the universality properties of the Sivers function in hadronic scattering reactions.     

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.     

Measurement of single- and double-spin asymmetries in deep inelastic pion electroproduction with a longitudinally polarized target

We report the first measurement of the transverse momentum dependence of double-spin asymmetries in semi-inclusive production of pions in deep-inelastic scattering off the longitudinally polarized proton. Data have been obtained using a polarized electron beam of 5.7 GeV with the CLAS detector at the Jefferson Lab (JLab). Modulations of single spin asymmetries over the azimuthal angle between lepton scattering and hadron production planes ? have been measured over a wide kinematic range in Bjorken x and virtual photon squared four-momentum Q2. A significant nonzero sin2? single spin asymmetry was observed for the first time indicating strong spin-orbit correlations for transversely polarized quarks in the longitudinally polarized proton.     

Extracting TMDs from CLAS12 data

We present studies of double longitudinal spin asymmetries in semi-inclusive deep inelastic scattering using a new dedicated Monte Carlo generator, which includes quark intrinsic transverse momentum within the generalized parton model based on the fully differential cross section for the process. Additionally we employ Bessel-weighting to the MC events to extract transverse momentum dependent parton distribution functions and also discuss possible uncertainties due to kinematic correlation effects.     

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.     

Non-collinearity in high energy processes

We discuss the treatment of intrinsic transverse momenta in high energy scattering processes. Within the field theoretical framework of QCD, the process is described in terms of correlators containing quark and gluon fields. The correlators, parametrized in terms of distribution and fragmentation functions, contain matrix elements of nonlocal field configurations requiring a careful treatment to assure colour gauge invariance. It leads to nontrivial gauge links connecting the parton fields. For the transverse momentum-dependent correlators the gauge links give rise to time reversal odd phenomena, showing up as single spin and azimuthal asymmetries. The gauge links, arising from multi-gluon initial and final state interactions, depend on the colour flow in the process, challenging universality.      

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.     

Measurement of transverse single-spin asymmetries for Dijet production in proton-proton collisions at sqrt[s]=200 GeV

We report the first measurement of the opening angle distribution between pairs of jets produced in high-energy collisions of transversely polarized protons. The measurement probes (Sivers) correlations between the transverse spin orientation of a proton and the transverse momentum directions of its partons. With both beams polarized, the wide pseudorapidity (-1< or = eta < or = +2) coverage for jets permits separation of Sivers functions for the valence and sea regions. The resulting asymmetries are all consistent with zero and considerably smaller than Sivers effects observed in semi-inclusive deep inelastic scattering. We discuss theoretical attempts to reconcile the new results with the sizable transverse spin effects seen in semi-inclusive deep inelastic scattering and forward hadron production in pp collisions.     

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.     

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.     

Azimuthal and spin asymmetries in DIS

In these lectures I want to discuss how the structure functions in deep inelastic scattering relate to quark and gluon correlation functions. In particular we will consider the issue of intrinsic transverse momenta of quarks, which becomes important in processes like 1-particle inclusive leptoproduction. Some examples of cross sections and asymmetries, in particular in polarized scattering processes are discussed. We also discuss the operator structure for azimuthal asymmetries and their evolution.     

Unpolarized azimuthal asymmetries in SIDIS at COMPASS

The study of the spin structure of the nucleon and of the effects due to the quarks transverse momentum are part of the scientific program of COMPASS, a fixed target experiment at the CERN SPS. The azimuthal modulations which appear in the cross-section of SIDIS off unpolarised targets give insight on the intrinsic momentum structure of the nucleon and on the possible correlation between transverse spin and transverse momentum of the quarks. We present the results for the amplitudes of the cos(?), cos(2?), and sin(?) modulatuions (where ? is the azimuthal hadron angle in the gamma-nucleon system) obtained from the COMPASS data collected with a 160 GeV/c positive muon beam impinging on a deuteron target. The amplitudes are measured for both positive and negative hadrons, and the results on the dependence of the relevant kinematical variables obtained after a multi dimensional analysis are also presented.     

Probing transverse quark polarization via azimuthal asymmetries in leptoproduction

We consider the leading order result for polarized leptoproduction, putting emphasis on transverse momentum dependent effects appearing in azimuthal asymmetries.Measurements of weighted cross sections enable extraction of the distribution of transversely polarized quarks. We focus on the distribution in a longitudinally polarized hadron and estimate the expected asymmetries in leptoproduction.     

TMDs studied in semi-inclusive deep inelastic scattering at HERMES

The HERMES measured azimuthal amplitudes of cross sections and their transverse target single spin asymmetries for hadron productions in semi-inclusive deep inelastic scattering.From the extracted amplitudes,novel patton distribution functions can be studied.The recent results related to Sivers and Boer-Mulders distribution functions are discussed.