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.     

Collins and Sivers asymmetries on the deuteron from COMPASS

COMPASS, a fixed target experiment on the SPS M2 beamline at CERN, has started to collect physics data from Autumn 2002 on a polarized ⁶LiD target. This target can be both longitudinally and transversely polarized with respect to the polarized 160 GeV/c μ⁺ beam. In 2002, 2003 and 2004, 20% of the beam-time was spent in the transverse configuration, allowing the measurement of transverse spin effects. Here the results for the Collins and Sivers asymmetries for charged hadrons, extracted from the 2003–2004 data are presented. on behalf of the COMPASS collaboration     

Transverse spin and momentum correlations in quantum chromodynamics

The naive time reversal odd (‘T-odd’) parton distribution and fragmentation functions are explored. We use the spectator model framework to study flavour dependence of the Boer-Mulders (h ₁^⊥ ) and Sivers (f _1T^⊥) functions as well as the ‘T-even’ but chiral odd function h _1L^⊥. These transverse momentum-dependent parton distribution functions are of significance for the analysis of azimuthal asymmetries in semi-inclusive deep inelastic scattering, as well as for the overall physical understanding of the distribution of transversely polarized quarks in unpolarized hadrons. In this context we also consider the Collins mechanism and the fragmentation function H ₁^⊥. As a by-product of this analysis we calculate the leading twist unpolarized cos(2ϕ) asymmetry, and sin(2ϕ) single spin asymmetry for a longitudinally polarized target in semi-inclusive deep inelastic scattering.      

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     

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.     

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.     

Study of TMDs with polarized beam and/or targets

A Fourier analysis of single- and double-spin azimuthal asymmetries measured at HERMES in semi-inclusive deep-inelastic scattering of unpolarized or longitudinally polarized leptons off tranversely polarized protons is presented for pions and charged kaons. The extracted amplitudes can be interpreted as convolutions of transverse momentum-dependent distribution and fragmentation functions. In particular, the measured double-spin asymmetries are sensitive to the poorly known worm-gear quark distribution g _1T ^⊥      

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.     

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.     

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     

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.     

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.     

Single-spin asymmetries in the Bethe-Heitler process e − + p → e − + γ + p induced by loop corrections

The single-spin beam and target asymmetries in the hard electroproduction process e ⁻ + p → e ⁻ + γ + p induced by the loop radiative corrections to the vertex part of lepton interaction are considered. The physical reason for the appearance of such asymmetries is the nonzero imaginary part of the amplitude (on the level of radiative corrections) caused by diagrams with photon radiation from the outgoing electron. We calculate the single-spin beam and target asymmetries at a longitudinally polarized electron beam or at arbitrary polarizations of the target proton for the CLAS and HERMES experimental conditions. The text was submitted by the authors in English.     

First measurement of the transverse spin asymmetries of the deuteron in semi-inclusive deep inelastic scattering

First measurements of the Collins and Sivers asymmetries of charged hadrons produced in deep-inelastic scattering of muons on a transversely polarized 6LiD target are presented. The data were taken in 2002 with the COMPASS spectrometer using the muon beam of the CERN SPS at 160 GeV/c. The Collins asymmetry turns out to be compatible with zero, as does the measured Sivers asymmetry within the present statistical errors.     

Duality between different mechanisms of QCD factorization in <Emphasis Type="Italic">γ</Emphasis><Superscript>*</Superscript><Emphasis Type="Italic">γ</Emphasis> collisions

We study the phenomenon of duality in hard exclusive reactions to which QCD factorization applies. Considering “two-photon”-like processes in the scalar φ _E ³ model and also two-hadron (pion) production from the collisions of a real (transversely polarized) and a highly-virtual, longitudinally polarized photon in QCD, we identify two regimes of factorization, each of them associated with a distinct nonperturbative mechanism. One mechanism involves twist-3 Generalized Distribution Amplitudes, whereas the other one employs leading-twist Transition Distribution Amplitudes. In the case of the scalar φ _E ³ model, we find duality in that kinematical region where the two mechanisms overlap. In the QCD case, the appearance of duality is sensitive to the particular nonperturbative model applied and can, therefore, be used as an additional adjudicator.     

Contribution of superstring <Emphasis Type="Italic">Z</Emphasis>′ boson on the polarization effects in proton proton collisions

In this work we investigate the single- and the double-spin asymmetries at the collisions of polarized protons pp → (γ ^*, Z ⁰, Z′) + X within the scope of QCD, the electroweak interaction and superstring E ₆ theory. The helicity amplitude method is used. Analytical expressions for the single- and the double-spin asymmetries are obtained and their dependence on the transverse momentum of the lepton pair is investigated at the three different values of invariant masses of the lepton pair. The pure contribution coming from the superstring Z′ boson on the single- and double- spin asymmetries has been extracted. The results obtained allow investigation of the spin structure of the proton.     

The E166 experiment: Development of an undulator-based polarized positron source for the international linear collider

A longitudinal polarized positron beam is foreseen for the international linear collider (ILC). A proof-of-principle experiment has been performed in the final focus test beam at SLAC to demonstrate the production of polarized positrons for implementation at the ILC. The E166 experiment uses a 1 m long helical undulator in a 46.6 GeV electron beam to produce a few MeV photons with a high degree of circular polarization. These photons are then converted in a thin target to generate longitudinally polarized e ⁺ and e ⁻. The positron polarization is measured using a Compton transmission polarimeter. The data analysis has shown asymmetries in the expected vicinity of 3.4% and ∼1% for photons and positrons respectively and the expected positron longitudinal polarization is covering a range from 50% to 90%.      

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.     

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.     

Imaging the Transverse (Spin) Structure of Hadrons

Parton distributions in impact parameter space, which are obtained by Fourier transforming GPDs, exhibit a significant deviation from axial symmetry when the target and/or quark are transversely polarized. Connections between this deformation and transverse single-spin asymmetries as well as with quark–gluon correlations are discussed. The sign of transverse deformation of impact parameter dependent parton distributions in a transversely polarized target can be related to the sign of the contribution from that quark flavor to the nucleon anomalous magnetic moment. Therefore, the signs of the Sivers function for u and d quarks, as well as the signs of quark–gluon correlations embodied in the polarized structure function g ₂ can be understood in terms of the proton and neutron anomalous magnetic moments.