Single-spin Azimuthal Asymmetries Research Articles

Single-Spin Asymmetry of Neutrons in Polarized pA Collisions

Absorptive corrections, which are known to suppress proton-neutron transitions with a large fractional momentum z→1 in pp collisions, become dramatically strong on a nuclear target, and they push the partial cross sections of leading neutron production to the very periphery of the nucleus. The mechanism of the pion π and axial vector meson a1 interference, which successfully explains the observed single-spin asymmetry in a polarized pp→nX, is extended to the collisions of polarized protons with nuclei. When corrected for nuclear effects, it explains the observed single-spin azimuthal asymmetry of neutrons that is produced in inelastic events, which is where the nucleus violently breaks up. This single-spin asymmetry is found to be negative and nearly atomic mass number A-independent.

Azimuthal Single-Spin Asymmetries of Charged Pions in Jets in s = 200 GeV p↑p Collisions at STAR

Single spin asymmetry measurements ([Formula: see text]) of the azimuthal distribution of charged pions inside jets produced in transversely polarized proton collisions are sensitive to the transversity distribution and the Collins fragmentation function. The STAR Detector at the Relativistic Heavy Ion Collider is well suited for these types of measurements as it is capable of full jet reconstruction and charged pion identification in the mid-rapidity region ([Formula: see text][Formula: see text][Formula: see text][Formula: see text]). We report here the first observation of Collins [Formula: see text] asymmetries in [Formula: see text] GeV [Formula: see text] collisions.

Operator analysis of pT -widths of TMDs

Transverse momentum dependent (TMD) parton distribution functions (PDFs), TMDs for short, are defined as the Fourier transform of matrix elements of nonlocal combinations of quark and gluon fields. The nonlocality is bridged by gauge links, which for TMDs have characteristic paths (future or past pointing), giving rise to a process dependence that breaks universality. It is possible, however, to construct sets of universal TMDs of which in a given process particular combinations are needed with calculable, process-dependent, coefficients. This occurs for both T-odd and T-even TMDs, including also the {\it unpolarized} quark and gluon TMDs. This extends the by now well-known example of T-odd TMDs that appear with opposite sign in single-spin azimuthal asymmetries in semi-inclusive deep inelastic scattering or in the Drell-Yan process. In this paper we analyze the cases where TMDs enter multiplied by products of two transverse momenta, which includes besides the $p_T$-broadening observable, also instances with rank two structures. To experimentally demonstrate the process dependence of the latter cases requires measurements of second harmonic azimuthal asymmetries, while the $p_T$-broadening will require measurements of processes beyond semi-inclusive deep inelastic scattering or the Drell-Yan process. Furthermore, we propose specific quantities that will allow for theoretical studies of the process dependence of TMDs using lattice QCD calculations.

Single transverse spin asymmetries in semi-inclusive deep inelastic scattering in a spin-1 diquark model

The observed results for the azimuthal single spin asymmetries (SSAs) of the proton, measured in the semi-inclusive deep inelastic scattering (SIDIS), can be explained by the final-state interaction (FSI) from the gluon exchange between the outgoing quark and the target spectator system. SSAs require a phase difference between two amplitudes coupling the target with opposite spins to the same final state. We have used the model of light front wave functions (LFWFs) consisting of a spin- $ \frac{1}{2}$ system as a composite of a spin- $ \frac{1}{2}$ fermion and a spin-1 vector boson to estimate the SSAs. The implications of such a model have been investigated in detail by considering different coupling constants. The FSIs also produce a complex phase which can be included in the LFWFs to calculate the Sivers and Boer-Mulders distribution functions of the nucleon.

Azimuthal correlations in the structure functions of polarized dihadron semi-inclusive deep inelastic scattering

Azimuthal correlations in two hadron production in deep inelastic scattering of unpolarized leptons off transversely polarized nucleon are discussed. Specifically, a simple approach for accessing ratios of structure functions corresponding to Sivers effect and transversity induced single spin azimuthal asymmetries to unpolarized structure functions is presented. This approach is then applied to a sample pseudo-data generated by a modified version of the LEPTO Monte Carlo event generator that includes the Sivers effect. Using this data it is shown, that the azimuthal correlations in the Sivers-like structure functions and the unpolarized structure functions are significantly different. Collins-like single hadron asymmetries in a dihadron sample are also discussed, for which experimental results were recently presented by the COMPASS collaboration.

Recent results on TMDs from the HERMES experiment

Single-spin azimuthal asymmetries were extracted at HERMES in inclusive electroproduction of charged hadrons from transversely polarized protons. The asymmetries were studied as a function of the transverse hadron momentum P T relative to the beam direction, and the Feynman variable x F . The asymmetry amplitudes are positive for π+ and K + , slightly negative for π− and consistent with zero for K − . Especially large asymmetries are observed for two small subsamples of events, where also the scattered electron was recorded, revealing important contributions from TMDs.

SINGLE-SPIN AZIMUTHAL ASYMMETRY IN EXCLUSIVE ELECTROPRODUCTION OF ɸ AND ω VECTOR MESONS ON TRANSVERSELY POLARIZED PROTONS

The hard exclusive electro-production of ɸ and ω vector mesons was studied with the HERMES spectrometer at the DESY laboratory by scattering 27.6 GeV positron and electron beams off a transversely polarized hydrogen target. The single-spin azimuthal asymmetry with respect to the transverse proton polarization was measured.

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.

Single-spin azimuthal asymmetry in exclusive electroproduction of [formula omitted] mesons on transversely polarized protons

Exclusive electroproduction of π+ mesons was studied by scattering 27.6 GeV positrons or electrons off a transversely polarized hydrogen target. The single-spin azimuthal asymmetry with respect to target polarization was measured as a function of the Mandelstam variable t, the Bjorken scaling variable xB, and the virtuality Q2 of the exchanged photon. The extracted Fourier components of the asymmetry were found to be consistent with zero, except one that was found to be large and that involves interference of contributions from longitudinal and transverse virtual photons.

Observation of the Naive-T-Odd Sivers Effect in Deep-Inelastic Scattering

Azimuthal single-spin asymmetries of leptoproduced pions and charged kaons were measured on a transversely polarized hydrogen target. Evidence for a naive-T-odd, transverse-momentum-dependent parton distribution function is deduced from nonvanishing Sivers effects for pi(+), pi(0), and K(+/-), as well as in the difference of the pi(+) and pi(-) cross sections.

Transverse momentum dependent distribution functionh1T⊥and the single spin asymmetryAUTsin(3ϕ−3S)

The leading twist transverse momentum dependent parton distribution function h_1T^perp, which is sometimes called ``pretzelosity,'' is studied. We review the theoretical properties of this function, and present bag model predictions. We observe an interesting relation valid in a large class of relativistic models: The difference between helicity and transversity distributions, which is often said to be a 'measure of relativistic effects' in nucleon, is nothing but the pretzelosity distribution. Pretzelosity is chirally odd and can be accessed in combination with the Collins effect in semi-inclusive deep inelastic scattering, where it gives rise to an azimuthal single spin asymmetry proportional to sin(3phi-phi_S). We discuss the preliminary deuteron target data from COMPASS, on that observable and make predictions for future experiments on various targets at JLab, COMPASS and HERMES.

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 single spin asymmetries from semi-inclusive deep inelastic scattering off transversely polarizedHe3

A study of semi-inclusive deep inelastic scattering off transversely polarized $^{3}\mathrm{He}$ is presented. The formal expressions of the Collins and Sivers contributions to the azimuthal single spin asymmetry for the production of leading pions are derived, in impulse approximation, and estimated in the kinematics of forth-coming experiments at JLab. The AV18 interaction has been used for a realistic description of the nuclear dynamics; the nucleon structure has been described by proper parametrizations of data or suitable model calculations. The initial transverse momentum of the struck quark has been properly included in the calculation. The crucial issue of extracting the neutron information from $^{3}\mathrm{He}$ data, planned to shed some light on the puzzling experimental scenario arisen from recent measurements for the proton and the deuteron, is thoroughly discussed. It is found that a model independent procedure, widely used in inclusive deep inelastic scattering to take into account the momentum and energy distributions of the bound nucleons in $^{3}\mathrm{He}$, can be applied also in the kinematics of the planned JLab experiments, although fragmentation functions, not only parton distributions, are involved. The possible role played by final state interactions in the process under investigation is addressed.

Collins effect in semiinclusive deeply inelastic scattering and in electron-positron-annihilation

The Collins fragmentation function is extracted from HERMES data on azimuthal single spin asymmetries in semi-inclusive deeply inelastic scattering, and BELLE data on azimuthal asymmetries in electron positron annihilations. A Gaussian model is assumed for the distribution of transverse parton momenta and predictions are used from the chiral quark-soliton model for the transversity distribution function. We find that the HERMES and BELLE data yield a consistent picture of the Collins fragmentation function which is compatible with COMPASS data and the information previously obtained from an analysis of DELPHI data. Estimates for future experiments are made.

Single spin asymmetries in hadron-hadron collisions

We study weighted azimuthal single spin asymmetries in hadron-hadron scattering using the diagrammatic approach at leading order and assuming factorization. The effects of the intrinsic transverse momenta of the partons are taken into account. We show that the way in which $T$-odd functions, such as the Sivers function, appear in these processes does not merely involve a sign flip when compared with semi-inclusive deep inelastic scattering, such as in the case of the Drell-Yan process. Expressions for the weighted scattering cross sections in terms of distribution and fragmentation functions folded with hard cross sections are obtained by introducing modified hard cross sections, referred to as gluonic pole cross sections.

Survey of [formula omitted] asymmetries in semi-exclusive electron scattering on 4He and 12C

Single spin azimuthal asymmetries A L T ′ were measured at Jefferson Lab using 2.2 and 4.4 GeV longitudinally polarised electrons incident on 4He and 12C targets in the CLAS detector. A L T ′ is related to the imaginary part of the longitudinal-transverse interference and in quasifree nucleon knockout it provides an unambiguous signature for final state interactions (FSI). Experimental values of A L T ′ were found to be below 5%, typically | A L T ′ | ⩽ 3 % for data with good statistical precision. Optical model in eikonal approximation (OMEA) and relativistic multiple-scattering Glauber approximation (RMSGA) calculations are shown to be consistent with the measured asymmetries.

MEASUREMENTS WITH POLARIZED HADRONS

Recent progress in physics with polarized hadrons is described with the emphasis on the spin structure of the nucleon. The nucleon spin problem, which was discovered by EMC in 1988, is now being studied in various experiments. Flavor separation of the quark helicity distributions has been made. Recent observations of asymmetries in deeply virtual Compton scattering (DVCS) and exclusive meson productions provide possibilities to access the total angluar momentum carried by quarks in the framework of generalized parton distributions. Single spin azimuthal asymmetries observed in semi-inclusive measurements provide a new handle to determine the transverse quark distributions which are basic but have never been measured so far.

Transversity measurement at HERMES

Abstract Polarised deep-inelastic lepton scattering has been the main experimental basis for our understanding of the spin structure of the nucleon. In addition to inclusive and semi-inclusive measurements, recently single-spin azimuthal asymmetries in semi-inclusive scattering have been recognized as a powerful tool to access further information about the spin structure of the nucleon. The appearance of non-zero single-spin asymmetries can be explained in terms of a non-zero transversity distribution combined with a non-zero Collins fragmentation function. Results from the HERMES experiment are presented on single-spin asymmetries in semi-inclusive hadron production from longitudinally polarised hydrogen and deuterium targets. The azimuthal dependence of the asymmetries is discussed in relation to the transversity distribution and the data are compared with a number of theoretical calculations.

Azimuthal single spin asymmetries in SIDIS in the light of chiral symmetry breaking

An attempt is made to understand the z-dependence of the azimuthal single spin asymmetries observed by the HERMES Collaboration in terms of chiral models based on effective quark and Goldstone boson degrees of freedom. The effects of respectively neglecting and considering Gaussian intrinsic parton transverse momenta and the Sivers effect are explored. Predictions for the transverse target polarization experiment at HERMES are presented.

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 partons into account by using transverse momentum dependent parton distributions, while another is to take asymmetries as a twist-3 effect. The nonperturbative 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 nonperturbative matrix elements in 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 Drell-Yan process is predicted differently in different approaches.