Sivers Asymmetry Research Articles

Overview of the COMPASS results on the nucleon spin

The COMPASS experiment [COMPASS, P. Abbon et al., The COMPASS experiment at CERN, Nucl. Inst. Meth. A577, 455 (2007)] at CERN is one of the leading experiments studying the nucleon spin. These studies are being carried on since 2002, by measuring hadrons produced in deep inelastic scattering (DIS) of 160 GeV/c and 200 GeV/c polarised muons off different polarised targets (NH3 for polarised protons and 6LiD for polarised deuterons). One of the main goals is to determine how the total longitudinal spin projection of the nucleon, 1/2, is distributed among its constituents, quarks and gluons. We review here the recent results on the quark and gluon helicities obtained by COMPASS. The other major goal, whose fulfilment is needed for a complete understanding of the nucleon spin, is the determination of the transverse momentum dependent parton distributions (TMDs). Regarding this topic, the latest results on the Collins and Sivers asymmetries will be shown. The former is sensitive to the transverse spin structure of the nucleon, while the latter reflects the correlations between the quarks transverse momentum and the nucleon spin. This overview will conclude with a summary of the approved plans of COMPASS for the near future: the study of TMDs with a pioneering polarised Drell-Yan experiment and the measurement of generalised parton distributions (GPDs).

Sivers Asymmetry in J/ψ Production in COMPASS 2010 Proton Data

The Sivers asymmetry in J/ψ production in scattering of muons off transversely polarized protons μ+ + p↑→μ+ + J/ψ + X is measured in two z-bins (inclusive and exclusive production) in the COMPASS 2010 data. Only J/ψ’s decaying into muons are detected. About 2 230 and 4450 J/ψ events in the lower and the higher z-bins are found. The Sivers asymmetry is extracted using a simple double-ratio method and is found to be compatible with zero in the lower z bin and to have a slight preference for negative values in the higher z bin.

The Gluon Contribution to the Sivers Effect COMPASS results

The Sivers effect describes the correlation between the spin of the nucleon and the orbital motion of partons. It can be measured via Semi-Inclusive Deep Inelastic Scattering of lepton on a transversely polarised proton and deuteron targets by determining the azimuthal asymmetry related to the modulation in the Sivers angle ϕSiv. In the paper a method of obtaining the Sivers asymmetry for gluons is presented. It is based on the model of lepton nucleon interactions via three single-photon-exchange processes: photon-gluon fusion (PGF), QCD Compton (QCDC) and leading process (LP). A method of simultaneous extraction of the Sivers asymmetries of the three processes with the use of Monte Carlo (MC) and neural networks (NN) approach is presented. The method has been applied to COMPASS data taken with 160GeV/c muon beam scattered off transversely polarised deuteron and transversely polarised proton target. For each target a data sample of events containing at least two hadrons with large transverse momentum has been selected. Finally the results for gluon Sivers asymmetry were obtained to be: Adg = −0.14 ± 0.15(stat.) ± 0.06(syst.) at 〈xg〉 = 0.13 and Apg = −0.26 ± 0.09(stat.) ± 0.08(syst.) at 〈xg〉 = 0.15.

Sivers, Boer-Mulders and transversity distributions in the difference cross sections in SIDIS

A major experimental program is presently underway to determine the Sivers, Boer-Mulders and transversity distributions, vital for understanding the internal structure of the nucleon. To this end we consider the Sivers, Boer-Mulders and transversity azimuthal asymmetries of the difference cross sections of hadrons with opposite charges in SIDIS reactions with unpolarized and transversely polarized target l + N → l' + h + X, h = π±, K±, h±. We show that on deuteron target these asymmetries are particularly simple and determine the sum of the valence-quark Qv = uv + dv transverse momentum dependent distributions without any contributions from the strange or other sea-quark functions.At present, data on these asymmetries are presented for the integrated asymmetries i.e. the xB- and zh-dependent asymmetries. If data are available in small bins in Q2, so that Q2-dependence can be neglected, these expressions simplify dramatically leading to remarkably simple and powerful tests of the simplifying assumptions used in extracting these functions from the data.

Transverse Single Spin Asymmetries of Forward π0 and Jet-like Events in s = 500 GeV Polarized Proton Collisions at STAR

The large transverse single spin asymmetries (SSA) of high [Formula: see text] inclusive hadrons produced in polarized proton collisions are usually explained by means of collinear twist-3 multi-parton correlations. In this picture these asymmetries can originate from initial-state twist-3 parton distributions in the polarized proton and/or through the coupling between proton transversity and twist-3 fragmentation functions. The measurement of SSA for forward inclusive hadrons produced in [Formula: see text] collisions out to high transverse momentum helps to examine the validity and interplay of these initial- and final-state models. These models can be further explored by investigating the dependence of the SSA on event topologies. We present our latest status on the measurement of SSA for forward inclusive [Formula: see text] detected within [Formula: see text] in [Formula: see text] = 500 GeV [Formula: see text] collisions as well as its dependence on event topologies. We will also present our analysis of Sivers and Collins asymmetries for forward jet-like events consisting of multi-photon final states. The measurements are based on the data taken in 2011 with integrated luminosity [Formula: see text] 22 [Formula: see text].

Next-to-leading order transverse momentum-weighted Sivers asymmetry in semi-inclusive deep inelastic scattering: The role of the three-gluon correlator

We study the Sivers asymmetry in semi-inclusive hadron production in deep inelastic scattering. We concentrate on the contribution from the photon-gluon fusion channel at ${\cal O}(\alpha_{em}^2 \alpha_s)$, where three-gluon correlation functions play a major role within the twist-3 collinear factorization formalism. We establish the correspondence between such a formalism with three gluon correlation functions and the usual transverse momentum dependent (TMD) factorization formalism at moderate hadron transverse momenta. We derive the coefficient functions used in the usual TMD evolution formalism related to the quark Sivers function expansion in terms of the three-gluon correlation functions. We further perform the next-to-leading order calculation for the transverse-momentum-weighted spin-dependent differential cross section, and identify the off-diagonal contribution from the three-gluon correlation functions to the QCD collinear evolution of the twist-3 Qiu-Sterman function.

Tests of the extraction of the Sivers, Boer-Mulders, and transversity distributions in SIDIS reactions

A major experimental program is presently underway worldwide to determine the fundamental non-perturbative functions, the Sivers, Boer-Mulders and transversity distributions, which are vital for an understanding of the internal structure of the nucleon. However, at present, many simplifying assumptions are used in extracting these functions from the data. We demonstrate that if the binning of the data in Q^2 is small enough so that Q^2-evolution can be neglected inside a bin, then one can obtain stringent tests of these assumptions. Failure to satisfy these tests implies that the presently extracted non-perturbative functions are unreliable. To this end we consider the measurement of the Sivers, Boer-Mulders and transversity difference asymmetries for hadrons with opposite charges in SIDIS reactions with unpolarized and transversely polarized deuteron and proton targets: l+N\to l'+h+X, h=\pi^\pm ,K^\pm ,h^\pm. Utilizing only charge and isospin invariance, and applying the above mentioned simplifying assumptions we obtain several testable relations amongst the measured asymmetries. If these tests are satisfied then the measured asymmetries determine two different combinations of the valence-quark transverse momentum dependent distributions, which can be determined separately without any contributions from the strange and other sea-quarks.

Collins and Sivers asymmetries in muonproduction of pions and kaons off transversely polarised protons

Measurements of the Collins and Sivers asymmetries for charged pions and charged and neutral kaons produced in semi-inclusive deep-inelastic scattering of high energy muons off transversely polarised protons are presented. The results were obtained using all the available COMPASS proton data, which were taken in the years 2007 and 2010. The Collins asymmetries exhibit in the valence region a non-zero signal for pions and there are hints of non-zero signal also for kaons. The Sivers asymmetries are found to be positive for positive pions and kaons and compatible with zero otherwise.

Sivers Asymmetry with QCD Evolution

We analyze the Sivers asymmetry in both Drell-Yan (DY) production and semi-inclusive deep inelastic scattering (SIDIS), while considering properly defined transverse momentum dependent parton distribution and fragmentation functions and their QCD evolution. After finding a universal non-perturbative spin-independent Sudakov factor that can describe reasonably well the world's data of SIDIS, DY lepton pair and W/Z production in unpolarized scatterings, we perform a global fitting of all the experimental data on the Sivers asymmetry in SIDIS from HERMES, COMPASS and Jefferson Lab. Then we make predictions for the asymmetry in DY lepton pair and W boson production, which could be compared to the future experimental data in order to test the sign change of the Sivers function.

Measuring the Sea Quark Sivers Asymmetry: The E1039 Experiment at Fermilab

One of the continuing puzzles in QCD is the origin of the nucleon spin. All of the existing experimental data suggest that the contributions from the quark and gluon spins account only for about 50% of the nucleon spin. In order to account for the remaining 50%, one has to include the orbital angular momentum of the quarks and gluons. One way to establish if quarks carry significant angular momentum, is to perform a measurement of the Sivers function, which describes the correlation of the spin direction of the nucleon with the transverse momentum of the quark. We will describe the E1039 experiment at Fermilab, which will measure the Sivers asymmetry of the sea quarks via the Drell-Yan process, using a 120 GeV unpolarized proton beam on a transversely polarized NH 3 target.

Single Spin Asymmetry in Electroproduction of J/ψ and QCD-evolved TMD's

We estimate Sivers asymmetry in low virtuality photoproduction of J/ψ using color evaporation model and taking into account Q2- evolution of transverse momentum dependent PDF's and Sivers function. There is a substantial reduction in asymmetry as compared to our previous analysis wherein the Q2-dependence came only from DGLAP evolution of collinear part of TMDs. The estimates of asymmetry are comparable to our earlier estimates in which we had used analytical solution of only an approximated form of the evolution equations. We have also estimated asymmetry using the latest parametrization by Echevarria et al. which are based on an evolution kernel in which the perturbative part is resummed to NLL accuracy.

QCD evolution of the Sivers asymmetry

We study the QCD evolution of the Sivers effect in both semi-inclusive deep inelastic scattering (SIDIS) and Drell-Yan production (DY). We pay close attention to the non-perturbative spin-independent Sudakov factor in the evolution formalism and find a universal form which can describe reasonably well the experimental data on the transverse momentum distributions in SIDIS, DY lepton pair and $W/Z$ production. With this Sudakov factor at hand, we perform a global fitting of all the experimental data on the Sivers asymmetry in SIDIS from HERMES, COMPASS and Jefferson Lab. We then make predictions for the Sivers asymmetry in DY lepton pair and $W$ production that can be compared to the future experimental measurements to test the sign change of the Sivers functions between SIDIS and DY processes and constrain the sea quark Sivers functions.

Six “beyond Collins and Sivers” transverse spin asymmetries at COMPASS

COMPASS is a fixed-target high energy physics experiment at the SPS at CERN \cite{Abbon:2007pq}. 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 $NH_3$ (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 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 \cite{Parsamyan:2007ju},\cite{Kotzinian:2007uv} and "proton-2007" data \cite{Parsamyan:2010se}. In this contribution we review the results obtained with the last "proton-2010" data sample.

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. The new results for charged pions and kaons obtained from the 2010 run with a transversely polarised proton target are presented.

Overview of the nucleon spin studies at COMPASS

The COMPASS experiment (1) at CERN is one of the leading experiments studying the spin structure of the nucleon. These studies are being carried on since 2002, by measuring hadrons produced in deep inelastic scattering (DIS) of 160 GeV/c polarised muons off different polarised targets (NH3 for polarised protons and 6 LiD for polarised deuterons). One of the main goals is to determine how the total longitudinal spin pro- jection of the nucleon, 1/2, is distributed among its constituents, quarks and gluons. We review here the recent results on the quark and gluon helicities obtained by COMPASS, using a longitudinally polarised target. However, the understanding of the nucleon (spin) structure based only on the parton helicities is not in any way complete. It basically provides us with a one-dimensional picture in a longitudinal momentum space. There- fore, COMPASS also studies the transverse momentum dependent parton distributions (TMDs) with a transversely polarised target. Concerning the TMDs, the latest results on the Collins and Sivers asymmetries will be shown. The former is sensitive to the trans- verse spin structure of the nucleon, while the latter reflects the correlations between the quarks transverse momentum and the nucleon spin.

ASPECTS OF TMD EVOLUTION OF AZIMUTHAL ASYMMETRIES

In this contribution TMD evolution of azimuthal asymmetries, in particular of the Sivers and double Collins asymmetries, is addressed. A comparison of the scale dependence is made between asymmetries described with TMD factorization at low transverse momentum and those described with collinear factorization at high transverse momentum. Finally, the advantages of Bessel weighting are discussed: convergence of transverse momentum integrals, suppression of large transverse momentum contributions, and well-defined lattice QCD evaluations of Bessel-weighted TMDs including proper gauge links.

PROCESS DEPENDENCE AND THE SIVERS EFFECT IN INCLUSIVE AND SEMI-INCLUSIVE REACTIONS

We perform an analysis of the the spin asymmetry for single inclusive jet production in proton-proton collisions collected by AnDY experiment and the Sivers asymmetry data from semi-inclusive deep inelastic scattering experiments. In particular, we consider the role color gauge invariance plays in determining the process-dependence of the Sivers effect. We find that after carefully taking into account the initial-state and final-state interactions between the active parton and the remnant of the polarized hadron, the calculated jet spin asymmetry based on the Sivers functions extracted from HERMES and COMPASS experiments is consistent with the AnDY experimental data. This provides a first indication for the process-dependence of the Sivers effect in different processes. We also make predictions for both direct photon and Drell-Yan spin asymmetry, to further test the process-dependence of the Sivers effect in future experiments.

TRANSVERSE MOMENTUM-WEIGHTED SIVERS ASYMMETRY IN SEMI-INCLUSIVE DEEP INELASTIC SCATTERING AT NEXT-TO-LEADING ORDER

We summarize the results of a recent study of next-to-leading order perturbative QCD corrections to the transverse momentum-weighted Sivers asymmetry in semi-inclusive hadron production in lepton-proton deep inelastic scattering. The corresponding differential cross section is evaluated as a convolution of a twist-three quark-gluon correlation function, often referred to as Qiu-Sterman function, the usual unpolarized fragmentation function, and a hard coefficient function. By studying the collinear divergence structure, we identify the evolution kernel for the Qiu-Sterman function. The hard coefficient function, which is finite and free of any divergence, is evaluated at one-loop order.

Transverse spin and transverse momentum structure of the nucleon from the COMPASS experiment

COMPASS is a fixed target experiment at the CERN SPS M2 beam line, taking data since year 2002. Part of the physics programme is dedicated to the study of the transverse spin and transverse momentum structure of the nucleon, by means of semi-inclusive deeply inelastic lepton scattering (SIDIS). For these measurements, data have been collected using transversely polarised proton (NH 3 ) and deuteron ( 6 LiD) targets. A selection of the results on the azimuthal asymmetries measured is presented, with particular focus on the most recent measurements from the data collected in 2007 and 2010 with the proton target. These results exhibit clear signals for the Collins asymmetry, interpreted as a convolution of a non-zero transversity PDF and Collins fragmentation function, and for the Sivers asymmetry which is related to the Sivers function, the most famous and discussed of the TMD PDFs. The data collected with the 6 LiD target, have also been recently analysed to search for the azimuthal modulations in the production of hadrons which are expected to be present in the unpolarised part of the SIDIS cross-section. The azimuthal hadron asymmetries, which are related to the Boer-Mulders TMD PDF, show strong and somewhat puzzling kinematical dependencies.

Transverse momentum dependent evolution: Matching semi-inclusive deep inelastic scattering processes to Drell-Yan andW/Zboson production

We examine the QCD evolution for the transverse momentum dependent observables in hard processes of semi-inclusive hadron production in deep inelastic scattering and Drell-Yan lepton pair production in $pp$ collisions, including the spin-average cross sections and Sivers single transverse spin asymmetries. We show that the evolution equations derived by a direct integral of the Collins-Soper-Sterman evolution kernel from low to high Q can describe well the transverse momentum distribution of the unpolarized cross sections in the Q^2 range from 2 to 100 GeV^2. In addition, the matching is established between our evolution and the Collins-Soper-Sterman resummation with b*-prescription and Konychev-Nodalsky parameterization of the non-perturbative form factors, which are formulated to describe the Drell-Yan lepton pair and W/Z boson production in hadronic collisions. With these results, we present the predictions for the Sivers single transverse spin asymmetries in Drell-Yan lepton pair production and $W^\pm$ boson production in polarized pp and $\pi^- p$ collisions for several proposed experiments. We emphasize that these experiments will not only provide crucial test of the sign change of the Sivers asymmetry, but also provide important opportunities to study the QCD evolution effects.