Sivers Asymmetry Research Articles

Sivers asymmetries for inclusive pion and kaon production in deep-inelastic scattering

We calculate the Sivers distribution functions induced by the final-state interaction due to one-gluon exchange in diquark models of a nucleon structure, treating the cases of scalar and axial-vector diquarks with both dipole and Gaussian form factors. We use these distribution functions to calculate the Sivers single-spin asymmetries for inclusive pion and kaon production in deep-inelastic scattering. We compare our calculations with the results of HERMES and COMPASS, finding good agreement for ${\ensuremath{\pi}}^{+}$ production at HERMES, and qualitative agreement for ${\ensuremath{\pi}}^{0}$ and ${K}^{+}$ production. Our predictions for pion and kaon production at COMPASS could be probed with increased statistics. The successful comparison of our calculations with the HERMES data constitutes prima facie evidence that the quarks in the nucleon have some orbital angular momentum in the infinite-momentum frame.

Sivers effect in Drell-Yan processes

The Sivers distributions recently extracted from semi-inclusive deep inelastic scattering data [M. Anselmino et al., Eur. Phys. J. A 39, 89 (2009)] are used to compute estimates for Sivers asymmetries in Drell-Yan processes which are being planned at several facilities (RHIC, COMPASS, J-PARC, PAX, PANDA, NICA (JINR) and SPASCHARM (IHEP)). Most of these asymmetries turn out to be large and could allow a clear test of the predicted sign change of the Sivers distributions when active in SIDIS and Drell-Yan processes. This is regarded as a fundamental test of our understanding, within QCD and the factorization scheme, of single spin asymmetries.

Collins and Sivers asymmetries for pions and kaons in muon–deuteron DIS

The measurements of the Collins and Sivers asymmetries of identified hadrons produced in deep-inelastic scattering of 160 GeV/c muons on a transversely polarised 6LiD target at COMPASS are presented. The results for charged pions and charged and neutral kaons correspond to all data available, which were collected from 2002 to 2004. For all final state particles both, the Collins and Sivers asymmetries turn out to be small, compatible with zero within the statistical errors, in line with the previously published results for not identified charged hadrons, and with the expected cancellation between the u- and d-quark contributions.

Transverse Spin Structure of the Nucleon from COMPASS

The measurement of transverse spin effects in semi-inclusive deep-inelastic scattering is an important part of the COMPASS physics program. In the years 2002-2004 data were taken by scattering a 160 GeV muon beam on a transversely polarized deuteron target. In 2007, additional data were collected on a transversely polarized proton target. New results for the Collins and Sivers asymmetries from the analysis of the proton data are presented.

Extraction of finite-energy contributions to the Sivers asymmetry from the analysis of exclusive proton–proton scattering

I study the effect of scalar and spin–orbit rescattering terms, in the production of a nonzero Sivers-like asymmetry in proton–proton collisions (inclusive production and Drell-Yan) at moderate center of mass energies 15 GeV and transverse momentum up to 3 GeV/c. An ultrarelativistic generalization of the Glauber formalism is used here to (i) fit the scalar and spin–orbit interaction terms on proton–proton elastic scattering data, including analyzing power, (ii) transfer such information to inclusive proton–proton scattering. It is shown that the phenomenological interactions responsible for the nonzero analyzing power in proton–proton elastic scattering produce a relevant nonzero analyzing power in inclusive processes associated with proton–proton collisions. This could represent a relevant (possibly higher-twist) contribution to the Sivers asymmetry.

Sivers and Collins single spin asymmetries

The Sivers and Collins asymmetries are the most prominent Single Spin Asymmetries (SSA) in Semi-Inclusive Deeply Inelastic Scattering (SIDIS) with transverse target polarization. In this talk we present our understanding of these phenomena.

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.

HERMES measurement of the collins and sivers asymmetries from a transversely polarized hydrogen target

In 2005 the HERMES collaboration published first evidence for azimuthal single-spin asymmetries in semi-inclusive production of charged pions on a transversely polarised hydrogen target. The distinctive Fourier components of the measured asymmetries caused by both the Collins and the Sivers mechanisms provide signals for previously unmeasured quantities: the transversity quark distribution in conjunction with the Collins fragmentation function (Collins mechanism) and the Sivers parton distribution (Sivers mechanism). The transversity distribution will provide a detailed insight into the relativistic nature of the quarks inside the nucleon. Recent theoretical work demonstrated a relation between the Sivers function and the contribution of the orbital angular momentum of quarks within the nucleon. The results presented for charged pions have a much higher statistical significance than the published data. In addition the Collins and Sivers asymmetries for neutral pions and charged kaons are provided.

Neutron transversity measurement at Jefferson Lab with a polarized 3He target

A first measurement of single target spin asymmetry (SSA) from semi-inclusive electroproduction of charged pions from a transversely polarized 3He target in deep-inelastic-scattering kinematics will take data in Hall A at Jefferson Lab in 2008. Such SSA will allow for an extraction of the much desired information on the Collins and Sivers asymmetry from the “neutron” in order to probe the quark transversity distributions. The experiment will be a coincidence measurement with the BigBite spectrometer detecting the scattered electrons and the left-arm HRS spectrometer detecting the charged pions. The prospect of future 11 GeV measurements at Jefferson Lab in Hall A using a solenoid magnetic detector system is also discussed in this talk.

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.

A new measurement of the Collins and Sivers asymmetries on a transversely polarised deuteron target

New high precision measurements of the Collins and Sivers asymmetries of charged hadrons produced in deep-inelastic scattering of muons on a transversely polarised 6LiD target are presented. The data were taken in 2003 and 2004 with the COMPASS spectrometer using the muon beam of the CERN SPS at 160 GeV / c . Both the Collins and Sivers asymmetries turn out to be compatible with zero, within the present statistical errors, which are more than a factor of 2 smaller than those of the published COMPASS results from the 2002 data. The final results from the 2002, 2003 and 2004 runs are compared with naive expectations and with existing model calculations.

First measurements of Collins and Sivers asymmetries at COMPASS

COMPASS is a fixed-target experiment on the SPS M2 beamline at CERN. Its 6LiD target can be polarised both longitudinally and transversally with respect to the longitudinally polarised 160GeV/c μ+ beam. Approximately 20% of the beam-time in 2002, 2003 and 2004 was spent in the transverse configuration, allowing the first measurement of both the Collins and Sivers asymmetries on a deuterium target. First results from the the transverse data of the COMPASS run in 2002 are reported here.

Measurement of Transverse Target-spin Asymmetries at Hermes

Azimuthal asymmetries are observed in the cross section of semi-inclusive charged pion electroproduction from a transversely polarized hydrogen target at Hermes. Their si- multaneous dependence on the azimuthal angles of both the pion and the target spin axis allows the extraction of two Fourier components that are interpreted in terms of Collins and Sivers effects. For π + -production both components are found to be positive, while for π − -production the Sivers asymmetry vanishes and the Collins asymmetry is found to be negative and surprisingly large in magnitude.

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.

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.

Sivers function in light-cone quark model and azimuthal spin asymmetries in pion electroproduction

We perform a calculation of Sivers function in a light-cone SU(6) quark–diquark model with both scalar diquark and vector diquark spectators. We derive the transverse momentum dependent light-cone wave function of the proton by taking into account the Melosh–Wigner rotation. By adopting one-gluon exchange, we obtain a non-vanishing Sivers function of down quark from interference of proton spin amplitudes. We analyze the |P h⊥| M weighted Sivers asymmetries in π +, π − and π 0 electroproduction off transverse polarized proton target, averaged and not averaged by the kinematics of HERMES experiment.

Sivers effect and generalized parton distributions in impact parameter space

Recently, it has been pointed out that there exists a connection between the generalized parton distribution $E(x,0,t)$ and the Sivers asymmetry. For transversely polarized nucleon targets, generalized parton distributions are asymmetric in impact parameter space. This impact parameter space asymmetry, together with the final state interaction of the active quark, gives rise to the Sivers asymmetry in momentum space. We demonstrate this phenomenon explicitly in the scalar diquark model. This result also illustrates the physics that underlies the correlation between the anomalous magnetic moment and the Sivers asymmetry for a given quark flavor.

Quark correlations and single spin asymmetries

We analyze the Sivers asymmetry in light-cone gauge. The average transverse momentum of the quark distribution is related to the correlation between the quark distribution and the transverse component of the gauge field at $x^-\pm \infty$. We then use finiteness conditions for the light-cone Hamiltonian to relate the transverse gauge field at $x^-=\pm \infty$ to the color density integrated over $x^-$. This result allows us to relate the average transverse momentum of the active quark to color charge correlations in the transverse plane.

Chromodynamic lensing and transverse single spin asymmetries

We illustrate, in a simple physical picture, how an axial asymmetry in impact parameter dependent parton distributions, in combination with final state interactions, can give rise to an axial asymmetry for the transverse momentum of the leading quark in the photo-production of hadrons. The effect is related to the asymmetry originating from the Wilson-line phase factor in gauge invariant Sivers distributions. We also explain the correlation between the sign of the anomalous magnetic moment and the sign of the Sivers asymmetry.

Universality of T-odd effects in single spin and azimuthal asymmetries

We analyze the transverse-momentum-dependent distribution and fragmentation functions in space-like and time-like hard processes involving at least two hadrons, in particular, 1-particle inclusive leptoproduction, the Drell–Yan process and two-particle inclusive hadron production in electron–positron annihilation. As is well known, transverse momentum dependence allows for the appearance of unsuppressed single spin azimuthal asymmetries, such as Sivers and Collins asymmetries. Recently, Belitsky, Ji and Yuan obtained fully color-gauge-invariant expressions for the relevant matrix elements appearing in these asymmetries at leading order in an expansion in the inverse hard scale. We rederive these results and extend them to observables at the next order in this expansion. We observe that at leading order one retains a probability interpretation, contrary to a claim in the literature and show the direct relation between the Sivers effect in single spin asymmetries and the Qiu–Sterman mechanism. We also study fragmentation functions, where the process-dependent gauge link structure of the correlators is not the only source of T-odd observables and discuss the implications for universality.