Transversity Distribution Research Articles

Generalized quark transversity distribution of the pion in chiral quark models

The transversity generalized parton distributions (tGPDs) of the the pion, involving matrix elements of the tensor bilocal quark current, are analyzed in chiral quark models. We apply the nonlocal chiral models involving a momentum-dependent quark mass, as well as the local Nambu--Jona-Lasinio with the Pauli-Villars regularization to calculate the pion tGPDs, as well as related quantities following from restrained kinematics, evaluation of moments, or taking the Fourier-Bessel transforms to the impact-parameter space. The obtained distributions satisfy the formal requirements, such as proper support and polynomiality, following from Lorentz covariance. We carry out the leading-order QCD evolution from the low quark-model scale to higher lattice scales, applying the method of Kivel and Mankiewicz. We evaluate several lowest-order generalized transversity form factors, accessible from the recent lattice QCD calculations. These form factors, after evolution, agree properly with the lattice data, in support of the fact that the spontaneously broken chiral symmetry is the key element also in the evaluation of the transversity observables.

Transverse target spin asymmetries at COMPASS

COMPASS is a fixed target experiment at the CERN M2 beamline where the nucleon spin structure is investigated using a 160 GeV/c polarized μ+ beam and polarized solid state targets. After taking data in the years 2002–2004 using a transversely polarized 6LiD (deuteron) target, in 2007 and 2010 additional data were collected on a transversely polarized NH3 (proton) target. The measurements of single spin asymmetries in semi-inclusive deep inelastic scattering (SIDIS) on a transversely polarized target are an important part of the COMPASS physics program. They allow to investigate the transversity distribution functions, e.g. coupled to the Collins fragmentation function, as well as transverse momentum dependent distribution functions, like the Sivers distribution function, by measuring azimuthal asymmetries in hadron production.

Forward Transverse Single Spin Asymmetries at PHENIX

Recent measurements of single transverse spin asymmetries in proton-proton collisions measured by the PHENIX experiment at RHIC are presented. The focus is on the single particle left-right asymmetry AN for π0 at √s = 200 GeV and √s = 62.4 GeV and the measurement of di-hadron correlations at √s = 200 GeV which are produced by the fragmentation of a transversely polarized quark via the Interference Fragmentation Function (IFF) H1< and thus provide a probe for the quark transversity distribution function.

Sin2ϕazimuthal asymmetry in single longitudinally polarizedπNDrell-Yan process

We study the $\sin2\phi$ azimuthal asymmetry in the $\pi N$ Drell-Yan process, when the nucleon is longitudinally polarized. The asymmetry is contributed by the combination of the Boer-Mulders function and the longitudinal transversity distribution function. We consider the Drell-Yan processes by $\pi^\pm$ beams colliding on the proton and deuteron targets, respectively. We calculate the $\sin2\phi$ azimuthal asymmetries in these processes using the Boer-Mulders function and the longitudinal transversity from spectator models. We show that the study on single polarized $\pi N$ Drell-Yan processes can not only give the information on the new 3-dimensional parton distribution functions in momentum space, but also shed light on the chiral-odd structure of the longitudinally polarized nucleon.

First Glances at the Transversity Parton Distribution through Dihadron Fragmentation Functions

We present first observations of the transversity parton distribution based on an analysis of pion-pair production in deep-inelastic scattering off transversely polarized targets. The extraction of transversity relies on the knowledge of dihadron fragmentation functions, which we take from electron-positron annihilation measurements. This is the first attempt to determine the transversity distribution in the framework of collinear factorization.

Transverse Target Moments of SIDIS Vector Meson Production at HERMES

The on-going analysis of the transverse target (AUT) moments of the non-collinear cross section for SIDIS dihadron production at Hermes is discussed. These moments access the transversity (h1), pretzelocity (h⊥1T), and Sivers (f⊥1T) distribution functions convoluted with the unpolarized (D1) and Collins (H1) dihadron fragmentation functions. This measurement allows greater insight into the flavor decomposition and factorization of these functions. Additionally, the results will test the Lund/Artru fragmentation model, which predicts a sign change in the Collins function between pseudo-scalar mesons and certain partial waves of vector mesons. In preparation for this analysis, a new Monte Carlo generator has been written, and non-collinear fragmentation functions have been computed in a spectator model. Additionally, an alternate partial wave expansion is presented, providing a complementary interpretation of the fragmentation functions and allowing computation of the next-to-leading twist cross section.

Dihadron fragmentation functions and their relevance for transverse spin studies

Dihadron fragmentation functions describe the probability that a quark fragments into two hadrons plus other undetected hadrons. In particular, the so-called interference fragmentation functions describe the azimuthal asymmetry of the dihadron distribution when the quark is transversely polarized. They can be used as tools to probe the quark transversity distribution in the nucleon. Recent studies on unpolarized and polarized dihadron fragmentation functions are presented, and we discuss their role in giving insights into transverse spin distributions.

Transverse spin dependent azimuthal asymmetries at COMPASS

In the semi-inclusive deep inelastic scattering of polarized leptons on a transversely polarized target eight target transverse spin-dependent azimuthal modulations are allowed. In the QCD parton model half of these asymmetries can be interpreted within the leading order approach and the other four are twist-three contributions. The first two leading twist asymmetries extracted by HERMES and COMPASS experiments are related: one to the transversity distribution and the Collins effect, the other to the Sivers distribution function. These results triggered a lot of interest in the past few years and allowed the first extractions of the transversity and the Sivers distribution functions of nucleon. The remaining six asymmetries were obtained by the COMPASS experiment using a 160 GeV/c longitudinally polarized muon beam and transversely polarized deuteron and proton targets. Here we review preliminary results from COMPASS proton data of 2007.

Single spin asymmetry in πp Drell–Yan process

We study the single spin asymmetries for the πp↑→μ+μ−X process. We consider the asymmetries contributed by the coupling of the Boer–Mulders function with the transversity distribution and the pretzelosity distribution, characterized by the sin(ϕ+ϕS) and sin(3ϕ−ϕS) azimuthal angular dependence, respectively. We estimate the magnitude of these asymmetries at COMPASS by using proper weighting functions. We find that the sin(ϕ+ϕS) asymmetry is of the size of a few percent and can be measured through the experiment. The sin(3ϕ−ϕS) asymmetry is smaller than the sin(ϕ+ϕS) asymmetry. After a cut on qT, we succeed in enhancing the asymmetry.

Transverse Spin Physics at COMPASS

The investigation of transverse spin and transverse momentum effects in deep inelastic scattering is one of the key physics programs of the COMPASS collaboration. Three channels have been analyzed at COMPASS to access the transversity distribution function: The azimuthal distribution of single hadrons, involving the Collins fragmentation function, the azimuthal dependence of the plane containing hadron pairs, involving the two-hadron interference fragmentation function, and the measurement of the transverse polarization of Lambda hyperons in the final state. Azimuthal asymmetries in unpolarized semi-inclusive deep-inelastic scattering give important information on the inner structure of the nucleon as well, and can be used to estimate both the quark transverse momentum k_T in an unpolarized nucleon and to access the so-far unmeasured Boer-Mulders function. COMPASS has measured these asymmetries using spin-averaged 6LiD data.

Effects of transversity in deep-inelastic scattering by polarized protons

Single-spin asymmetries for pions and charged kaons are measured in semi-inclusive deep-inelastic scattering of positrons and electrons off a transversely nuclear-polarized hydrogen target. The dependence of the cross section on the azimuthal angles of the target polarization (ϕS) and the produced hadron (ϕ) is found to have a substantial sin(ϕ+ϕS) modulation for the production of π+, π− and K+. This Fourier component can be interpreted in terms of non-zero transversity distribution functions and non-zero favored and disfavored Collins fragmentation functions with opposite sign. For π0 and K− production the amplitude of this Fourier component is consistent with zero.

Nucleon transversity study using a polarized 3He target in Hall A at JLab

A first measurement of Single target Spin Asymmetry (SSA) from semi-inclusive electro-production of charged pions from a transversely polarized 3He target in Deep-Inelastic-Scattering kinematics was completed in Hall A at Jefferson Lab in early 2009. 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. Future 11 GeV measurements at Jefferson Lab in Hall A using a solenoid magnetic detector system is being planned.

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.

Transverse spin effects at COMPASS

The investigation of transverse spin and transverse momentum effects in deep inelastic scattering is one of the key physics programs of the COMPASS collaboration. In the years 2002–2004 COMPASS took data scattering 160 GeV muons on a transversely polarized 6 LiD target. In 2007, a transversely polarized NH 3 target was used. Three different channels to access the transversity distribution function have been analyzed: The azimuthal distribution of single hadrons, involving the Collins fragmentation function, the azimuthal dependence of the plane containing hadron pairs, involving the two-hadron interference fragmentation function, and the measurement of the transverse polarization of λ hyperons in the final state. Transverse quark momentum effects in a transversely polarized nucleon have been investigated by measuring the Sivers distribution function. Azimuthal asymmetries in unpolarized semi-inclusive deep-inelastic scattering give important information on the inner structure of the nucleon as well, and can be used to estimate both the quark transverse momentum k T in an unpolarized nucleon and to access the so-far unmeasured Boer-Mulders function. COMPASS has measured these asymmetries using spin-averaged 6 LiD data.

O(αs2)andO(αs3)heavy flavor contributions to transversity atQ2≫m2

In deep-inelastic processes the heavy flavor Wilson coefficients factorize for ${Q}^{2}\ensuremath{\gg}{m}^{2}$ into the light-flavor Wilson coefficients of the corresponding process and the massive operator matrix elements (OMEs). We calculate the $O({\ensuremath{\alpha}}_{s}^{2})$ and $O({\ensuremath{\alpha}}_{s}^{3})$ massive OME for the flavor nonsinglet transversity distribution. At $O({\ensuremath{\alpha}}_{s}^{2})$ the OME is obtained for general values of the Mellin variable $N$, while at $O({\ensuremath{\alpha}}_{s}^{3})$ the moments $N=1$ to 13 are computed. The terms $\ensuremath{\propto}{T}_{F}$ of the 3-loop transversity anomalous dimension are obtained and results in the literature are confirmed. We discuss the relation of these contributions to the Soffer bound for transversity.

HOW IS TRANSVERSITY RELATED TO HELICITY FOR QUARKS AND ANTIQUARKS INSIDE THE PROTON?

We consider the quark and antiquark transversity distributions inside a polarized proton and study how they are expected to be related to the corresponding helicity distributions, both in sign and magnitude. Our considerations lead to simple predictions in good agreement with their first determination for light quarks from experimental data. We also give our predictions for the light antiquarks transversity distributions, so far unknown.

Update on transversity and Collins functions from SIDIS and [formula omitted] data

We present an update of a previous global analysis of the experimental data on azimuthal asymmetries in semi-inclusive deep inelastic scattering (SIDIS), from the HERMES and COMPASS Collaborations, and in e+ e- -> h1 h2 X processes, from the Belle Collaboration. Compared to the first extraction, a more precise determination of the Collins fragmentation function and the transversity distribution function for u and d quarks is obtained.

Asymmetries involving dihadron fragmentation functions: From DIS toe+e−annihilation

Using a model calculation of dihadron fragmentation functions, we fit the spin asymmetry recently extracted by HERMES for the semi-inclusive pion pair production in deep-inelastic scattering on a transversely polarized proton target. By evolving the obtained dihadron fragmentation functions, we make predictions for the correlation of the angular distributions of two pion pairs produced in electron-positron annihilations at BELLE kinematics. Our study shows that the combination of two-hadron inclusive deep-inelastic scattering and electron-positron annihilation measurements can provide a valid alternative to Collins effect for the extraction of the quark transversity distribution in the nucleon.

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.

ERBL and DGLAP kernels for transversity distributions. Two-loop calculations in covariant gauge

The results of a two-loop calculation in the Feynman gauge of both the DGLAP and the ERBL evolution kernels for transversely polarized distributions are presented. The structure of these evolution kernels is discussed in detail. In addition, the effect of the two-loop evolution on the distribution amplitude of a twist-2 transversely polarized meson is explored.