Transverse Spin Distribution Research Articles

Chiral-even twist-3 GPDs for the proton in a spectator diquark model

We investigate the chiral-even twist-3 generalized parton distributions (GPDs) of valence quarks in the proton at nonzero skewness ξ, using a spectator model with scalar and axial-vector diquarks. We consider the exponential form factor for the nucleon-quark-diquark vertex and the axial-vector diquark with light-cone transverse polarization. We analyze the dependence of GPDs on the longitudinal momentum fraction x at different ξ, and on the square of the transverse momentum transfer ΔT2 at different x. Our numerical results reveal distinct discontinuities in all twist-3 GPDs except G1 and G˜1. By taking the forward limit, we obtain the twist-3 parton distribution function gT, which encodes the transverse spin distribution of quarks. We also compare the kinetic orbital angular momentum and the spin-orbit correlations of quarks defined by the twist-2 and twist-3 GPDs, respectively. Published by the American Physical Society 2024

Kaon generalized parton distributions and light-front wave functions in the Nambu\u2013Jona-Lasinio model

Kaon generalized parton distributions (GPDs) and the leading Fock state light-front wave functions are investigated in the framework of Nambu–Jona-Lasinio model with proper time regularization. In addition, we compared the form factors, parton distribution functions, and generalized form factors obtained from them, respectively. The first Mellin moments of GPDs result in the form factors of local currents. The second Mellin moments of vector GPDs are related to gravitational form factors, the quark mass distribution theta _2 and the quark pressure distribution theta _1. When taking a Fourier transform of GPDs in impact parameter space, we can get the mean-squared impact parameter for the quarks of the kaon: langle {varvec{b}}_{bot }^2rangle _K^u=0.149 fm^2, langle {varvec{b}}_{bot }^2rangle _K^s=0.088 fm^2. This means that the kaon s quark is nearer to the center of transverse momentum than the u quark. We also give the light-cone energy radius for the quarks of the kaon from the mass distribution theta _2: r_{E,LC}^{u,K}=0.187 fm, r_{E,LC}^{s,K}=0.167 fm, and the light-cone charge radius from quark form factors of the kaon: r_{c,LC}^{u,K}=0.390 fm, r_{c,LC}^{s,K}=0.296 fm, which means that the s quark has a smaller extent than the u quark. The light-front transverse-spin distributions rho _u^1left( {varvec{b}}_{bot },{varvec{s}}_{perp }right) and rho _u^2left( {varvec{b}}_{bot },{varvec{s}}_{perp }right) show distortions, the average shift are langle b_{bot }^yrangle _1^u=0.116 fm and langle b_{bot }^yrangle _2^u=0.083 fm. On the kinematic domain associated with the valence-quark dominance, the unpolarized Wigner distribution from light-front wave functions is sharply peaked. It extends as the transverse position variable increases in magnitude and has a domain of negative support. Through the comparison of distributions from the two methods, we find that they give the same multi-dimensional mapping of the kaon in the Nambu–Jona-Lasinio model.

QCD EVOLUTION AND TMD/SPIN EXPERIMENTS

Transverse Spin and Transverse Momemtum Dependent (TMD) distribution study has been one of the main focuses of hadron physics in recent years. The initial exploratory Semi-Incluisve Deep-Inelastic-Scattering (SIDIS) experiments with transversely polarized proton and deuteron from HERMES and COMPASS attracted great attention and lead to very active efforts in both experiments and theory. QCD factorization has been carefully studied. A SIDIS experiment on the neutron with a polarized 3 He target was performed at JLab. Recently published results will be shown. Precision TMD experiments are planned at JLab after the 12 GeV energy upgrade. The approved experiments with a new SoLID spectrometer on both the proton and neutron will be presented. Proper QCD evolution treatments beyond collinear cases become crucial for the precision study of the TMDs. Experimentally, Q2 evolution and higher-twist effects are often closely related. The experience of study higher-twist effects in the cases of moments of the spin structure functions will be discussed.

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.

Azimuthal angle dependence of dijet production in unpolarized hadron scattering

We study the azimuthal angular dependence of back-to-back dijet production in unpolarized hadron scattering H{sub A}+H{sub B}{yields}J{sub 1}+J{sub 2}+X, arising from the product of two Boer-Mulders functions, which describe the transverse spin distribution of quarks inside an unpolarized hadron. We find that when the dijet is of two identical quarks (J{sub q}+J{sub q}) or a quark-antiquark pair (J{sub q}+J{sub q}), there is a cos{delta}{phi} angular dependence of the dijet, with {delta}{phi}={phi}{sub 1}-{phi}{sub 2}, and {phi}{sub 1} and {phi}{sub 2} are the azimuthal angles of the two individual jets. In the case of J{sub q}+J{sub q} production, we find that there is a color factor enhancement in the gluonic cross section, compared with the result from the standard generalized parton model. We estimate the cos{delta}{phi} asymmetry of dijet production at RHIC, showing that the color factor enhancement in the angular dependence of J{sub q}+J{sub q} production will reverse the sign of the asymmetry.

Measurement of transversity signals in two hadron production at COMPASS

The quark structure of the nucleon at the twist two level can be completely described with three quark distribution functions: the spin averaged distribution function q(x), the helicity distribution Δq(x) and the transverse spin distribution ΔTq(x). This last function, referred to as transversity, is chiral-odd and can only be measured in combination with another chiral-odd function. COMPASS is a fixed target experiment at the CERN SPS M2 beamline. Its target (6LiD) can be both longitudinally and transversely polarized with respect to the polarized 160 GeV/c µ+-beam. In transverse configuration ΔTq(x) can be measured in semi-inclusive deep-inelastic scattering (SIDIS), requiring the detection of hadronic products. A rather new probe of the transverse spin distribution function ΔTq(x) is the measurement of two hadron production, introducing the chiral odd interference fragmentation function H1∢(z, Mh2). Results are presented for the years 2003–2004 including particle identification by using the information of the RICH detector. The analysis was performed using all positive/negative charged pairs and z-ordered pairs.

Transversity signals at COMPASS

COMPASS is a fixed target experiment at the CERN SPS, with a rich physics program focused on nucleon spin structure and on hadron spectroscopy. One of the main goals of the spin program is the measurement of the transverse spin distribution function ΔTq(x) in semi-inclusive DIS off transversely polarized nucleons. For this purpose approximately 20% of the running time in the years 2002 to 2004 with the longitudinally polarized muon beam of 160 GeV and with 6LiD polarized target was used to collect data with the target polarized transversely with respect to the beam direction. The 2002 data have been already analysed and published. We present here the preliminary results from the full statistics for the Collins and Sivers single hadron asymmetries and for the transverse spin asymmetry in hadron pair production.

QCD physics at hadron storage rings: From COSY to FAIR

As a result of the rapid rise of the coupling constant αs at low momentum transfers, perturbation theory is not an appropriate method to describe the strong interaction. In this kinematic regime other methods such as lattice QCD or effective field theories are more appropriate to investigate the appearance of a still unsettled phenomena: confinement and chiral symmetry breaking. Furthermore, the confinement of quarks and gluons to hadrons allows crucial tests of fundamental symmetries that are inherent to the QCD Lagrangian but are broken in hadronic systems. Thus, high precision measurements of the production and decay of specific hadronic states provides decisive benchmarks to investigate the properties of QCD in this regime. A new series of experiments are being prepared using nearly full acceptance detectors for neutral and charged particles around internal targets in high intensity, phase-space-cooled hadronic beams. Later this year, it is planned to transfer the WASA detector from the CELSIUS to the COSY ring in order to measure the production and various decay channels of the η and η′ mesons, thereby investigating the violation of P, C, T, and combinations thereof, as well as isospin violation. The experimental and theoretical techniques employed here will provide an important basis to extend these investigations to the static and dynamical properties of hadrons with charm quark content with the high energy storage ring for antiprotons at the new GSI/FAIR facility. Additional related perspectives will be opened at the new facility ranging from the properties of hadrons in dense nuclear matter to measurements of the nucleon’s transverse spin distribution in the valence quark region using polarized antiprotons

Monte Carlo simulation of events with Drell-Yan lepton pairs from antiproton-proton collisions: The fully polarized case

In this paper, we extend the study of Drell-Yan processes with antiproton beams already presented in a previous work. We consider the fully polarized $\bar{p}^\uparrow p^\uparrow \to \mu^+ \mu^- X$ process, because this is the simplest scenario for extracting the transverse spin distribution of quarks, or transversity, which is the missing piece to complete the knowledge of the nucleon spin structure at leading twist. We perform Monte Carlo simulations for transversely polarized antiproton and proton beams colliding at a center-of-mass energy of interest for the future HESR at GSI. The goal is to possibly establish feasibility conditions for an unambiguous extraction of the transversity from data on double spin asymmetries.

THE KINETIC INTERPRETATION OF THE DGLAP EQUATION, ITS KRAMERS–MOYAL EXPANSION AND POSITIVITY OF HELICITY DISTRIBUTIONS

According to a rederivation — due to Collins and Qiu — the DGLAP equation can be reinterpreted (in leading order) in a probabilistic way. This form of the equation has been used indirectly to prove the bound |Δ f(x, Q)| < f(x, Q) between polarized and unpolarized distributions, or positivity of the helicity distributions, for any Q. We reanalyze this issue by performing a detailed numerical study of the positivity bounds of the helicity distributions. To obtain the numerical solution we implement an x-space based algorithm for polarized and unpolarized distributions to next-to-leading order in αs, which we illustrate. We also elaborate on some of the formal properties of the Collins–Qiu form and comment on the underlying regularization, introduce a Kramers–Moyal expansion of the equation and briefly analyze its Fokker–Planck approximation. These follow quite naturally once the master version is given. We illustrate this expansion both for the valence quark distribution qV and for the transverse spin distribution h1.

Azimuthal asymmetries in unpolarized Drell–Yan events on nuclear targets

We show that for Drell–Yan events by unpolarized hadronic projectiles and nuclear targets, azimuthal asymmetries can arise from the nuclear distortion of the hadronic projectile wavefunction, typically a spin–orbit effect occurring on the nuclear surface. The asymmetry depends on quantities that enter also the spin asymmetry in the corresponding Drell–Yan event on polarized free nucleonic targets. Hence, this study can be of help in exploring the spin structure of the nucleon, in particular the transverse spin distribution of partons inside the proton. All arguments can be extended also to antinucleon projectiles and, consequently, apply to possible future measurements involving nuclear targets at the foreseen HESR ring at GSI.

Monte Carlo simulation of events with Drell-Yan lepton pairs from antiproton-proton collisions

The complete knowledge of the nucleon spin structure at leading twist requires also addressing the transverse spin distribution of quarks, or transversity, which is yet unexplored because of its chiral-odd nature. Transversity can be best extracted from single-spin asymmetries in fully polarized Drell-Yan processes with antiprotons, where valence contributions are involved anyway. Alternatively, in single-polarized Drell-Yan the transversity happens convoluted with another chiral-odd function, which is likely to be responsible for the well known (and yet unexplained) violation of the Lam-Tung sum rule in the corresponding unpolarized cross section. We present Monte-Carlo simulations for the unpolarized and single-polarized Drell-Yan $\bar{p} p^{(\uparrow)} \to \mu^+ \mu^- X$ at different center-of-mass energies in both configurations where the antiproton beam hits a fixed proton target or it collides on another proton beam. The goal is to estimate the minimum number of events needed to extract the above chiral-odd distributions from future measurements at the HESR ring at GSI. It is important to study the feasibility of such experiments at HESR in order to demonstrate that interesting spin physics can be explored already using unpolarized antiprotons.

Future directions in studying QCD aspects of Nuclear Physics

Quantum Chromodynamics (QCD) provides the framework for our understanding of the strong interaction, and is therefore at the basis of our understanding of nuclear physics. The difficulty encountered when applying QCD to the length scales appropriate for nucleons, however, is the fact that the perturbative techniques used to solve QCD at high energies cannot be used. Neverthless considerable progress is being made in this domain through a series of very precise experiments that were analysed in a QCD framework. In this way the quark-gluon structure of hadrons has been investigated successfully. In recent years these studies were extended in various directions. Striking results in the areas of hadron spectrospy and hadron form factors revived the interest in the corresponding experiments, while the (theoretical) introduction of the transverse spin distributions and the generalized parton distributions led to a whole set of newly proposed experiments. Initial results obtained in each of these areas of research are used to illustrate likely future directions of experiments aimed at unraveling the QCD structure of the nucleon.

Current-induced spin flip scattering at interfaces in noncollinear magnetic multilayers

We show that when one drives a charge current across noncollinear magnetic layers the two electron Coulomb scattering creates a spin flip potential at interfaces. This scattering is found when the interface potential is updated due to the spin accumulation attendant to charge flow, and it contributes in linear response to the current. With this scattering there is an injection of transverse spin distributions in a layer that propagate, and that in the steady state lead to spin currents transverse to the magnetization.

Azimuthal asymmetry in meson productions in electron-nucleon deep inelastic scattering by HERMES

The spin structure of the nucleon is studied with deep inelastic scattering by HERMES. The electron (positron) beam at 27.6 GeV, polarized internal gas targets, and wide acceptance magnetic spectrometer with a ring imaging Cherenkov counter for the particle identification are the important ingredients of the experiment. The observation of significant azimuthal asymmetry in pion productions is reported. The measurement of the quark transverse spin distribution h 1( x) which is underway is discussed.

Investigation of single spin asymmetries in [formula omitted] electroproduction

The azimuthal single target-spin asymmetries for π + production in semi-inclusive deep inelastic scattering of leptons off longitudinally polarized protons are evaluated using two main approaches available in the literature. It is shown that the approximation where the twist-2 transverse quark spin distribution in the longitudinally polarized nucleon is small enough to be neglected leads to a consistent description of all existing asymmetries observed by the HERMES experiment.

Single-spin azimuthal asymmetries in the “Reduced twist-3 approximation”

We consider the single-spin azimuthal asymmetries recently measured at the HERMES experiment for charged pions produced in semi-inclusive deep inelastic scattering of leptons off longitudinally polarized protons. Guided by the experimental results and assuming a vanishing twist-2 transverse quark spin distribution in the longitudinally polarized nucleon, denoted as “reduced twist-3 approximation”, a self-consistent description of the observed single-spin asymmetries is obtained. In addition, predictions are given for the z dependence of the single target-spin asymmetry.

Transverse spin distribution function of the nucleon in chiral theory

At large N c the nucleon can be viewed as a soliton of the effective chiral lagrangian. This picture of nucleons allows a consistent nonperturbative calculation of the leading-twist parton distributions at a low normalization point. We derive general formulae for the transverse spin quark distribution h 1( x) in the chiral quark-soliton model. We present numerical estimates and compare them to the results obtained in other models.

Soffer positivity bound and a suggestion for measuring valence quark transverse spin distributions at BNL RHIC.

A positivity bound obtained by Soffer severely restricts the magnitude of quark transverse spin distributions for those quark flavors with negative longitudinal polarization. Since the interpretation of lepton scattering data on longitudinally polarized protons suggests a strong negative longitudinal polarization for antiquarks in the sea, a hard-scattering process which depends only on the transverse spin distribution of valence u quarks should be investigated. The large transverse-momentum production processes ${\mathit{A}}_{\mathit{N}\mathit{N}}$d\ensuremath{\sigma}(p\ensuremath{\uparrow}p\ensuremath{\uparrow}\ensuremath{\rightarrow}${\mathrm{\ensuremath{\pi}}}^{+}$X) and ${\mathit{A}}_{\mathit{N}\mathit{N}}$d\ensuremath{\sigma}(p\ensuremath{\uparrow}p\ensuremath{\uparrow}\ensuremath{\rightarrow}${\mathrm{\ensuremath{\pi}}}^{+}$${\mathit{p}}^{+}$X) could be considered a backup to the measurement of ${\mathit{A}}_{\mathit{N}\mathit{N}}$d\ensuremath{\sigma}(p\ensuremath{\uparrow}p\ensuremath{\uparrow}\ensuremath{\rightarrow}\ensuremath{\gamma}(${\mathit{Q}}^{2}$)X) and other production processes involving antiquarks.

Phenomenological theory of impurity-induced spin-lattice relaxation in paramagnetic metals

We have calculated the low-temperature spin-lattice relaxation rate $\frac{1}{{T}_{2}}$ for conduction electrons by using a Boltzmann-like transport equation for the semiclassical density matrix. Collisions with nonmagnetic impurities are described by a collision integral containing a phenomenological rotationally invariant scattering matrix. The scattering matrix contains terms describing both spin-conserving (ordinary potential scattering) and spin-flip (spin-orbit scattering) collisions. The spin-orbit scattering term leads to a coupling of the transport equations for the transverse spin and particle distribution functions. The resulting coupled integral equations are solved self-consistently for $\frac{1}{{T}_{2}}$. Our calculation takes full account of the cyclotron motion of the electrons. We are able to express $\frac{1}{{T}_{2}}$ in terms of only two Legendre coefficients of the spin-dependent part of the scattering matrix and also to show that the relaxation rate is independent of the cyclotron motion without making any assumptions about the magnitude of ${\ensuremath{\omega}}_{c}{\ensuremath{\tau}}_{0}$ (${\ensuremath{\tau}}_{0}$ is an orbital relaxation time). Finally we have calculated the longitudinal spin-lattice relaxation rate $\frac{1}{{T}_{1}}$ and found that it is identical to $\frac{1}{{T}_{2}}$ in our model.