Transversity of quarks in a nucleon

The transversity distribution of quarks in a nucleon is one of the three fundamental distributions, that characterize nucleon's properties in hard scattering processes at leading twist (twist 2). It measures the distribution of quark transverse spin in a nucleon polarized transverse to its (infinite) momentum. It is a chiral-odd twist-two distribution function — gluons do not couple to it. Quarks in a nucleon/hadron are relativistically bound and transversity is a measure of the relativistic nature of bound quarks in a nucleon. In this work, we review some important aspects of this less familiar distribution function which has not been measured experimentally so far.     

Spin physics through unpolarized processes

This article presents a review of our present understanding of the spin structure of the unpolarized hadron. Particular attention is paid to the quark sector at leading twist, namely, the quark Boer–Mulders function, which describes the transverse polarization of the quark inside an unpolarized hadron. After introducing the operator definition of the Boer–Mulders function, a detailed treatment of different non-perturbative calculations of the Boer–Mulders functions is provided. The phenomenology in Drell–Yan processes and semi-inclusive leptoproduction, including the extraction of the quark and antiquark Boer–Mulders functions from experimental data, is presented comprehensively. Finally, prospects for future theoretical studies and experimental measurements are presented in brief.     

Spin densities in the transverse plane and generalized transversity distributions

We show how generalized quark distributions in the nucleon describe the density of polarized quarks in the impact parameter plane, both for longitudinal and transverse polarization of the quark and the nucleon. This density representation entails positivity bounds including chiral-odd distributions, which tighten the known bounds in the chiral-even sector. Using the quark equations of motion, we derive relations between the moments of chiral-odd generalized parton distributions of twist two and twist three. We exhibit the analogy between polarized quark distributions in impact parameter space and transverse momentum dependent distribution functions.Received: 25 April 2005, Published online: 27 July 2005     

Transversely polarized parton densities,their evolution and their measurement

The transverse spin asymmetry of a quark in a baryon and the linear polarization of a gluon in a vector meson are studied from thet-channel point of view. Using the Altarelli-Parisi approach, they are shown to obey independent evolution equations and to decrease with increasingQ ². We investigate the possibility to measure them at leading twist, to leading order in α and α_s and without analyzing the final polarizations. This requires simultaneous polarization of the beam and the target; the observable effect is in the azimuthal distribution of the highP _T particle or jet. Assuming a simple (quark+scalar diquark) model for the baryon, a large asymmetry is expected inp \(\bar p\) Drell-Yan collisions, a smaller one in highP _T pp collisions, from the interference term in the scattering of two identical quarks.     

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.     

Polarized coincidence electroproduction scaling laws for the final state

We study the inclusive electroproduction of single hadrons off a polarized target. Bjorken scaling laws and the hadron azimuthal distribution are derived from the quark parton model.The polarization asymmetries scale when the target spin is along the direction of the virtual photon, and (apart from one significant exception) vanish for transverse spin. These results have a simple explanation; emphasis is given both to the general mathematical formalism and to intuitive physical reasoning.Through this framework we consider other cases: quarks with anomalous magnetic moment; renormalization group effects and asymptotic freedom; production of vector mesons (whose spin state is analysed by their decay); relation to large transverse momentum hadron production; and a covariant parton model calculation. We also look into spin-0 partons and Regge singularities.All of these cases (apart from the last two) modify the pattern of conclusions. Vector meson production shows polarization enhancements in the density matrix element ?₀₊; the renormalization group approach does not lead to any significant suppressions. They are also less severe in parton models for large p_T hadrons, and are not supported by the covariantly formulated calculation. The origins of these differences are isolated and used to exemplify the sensitivity that polarized hadron electroproduction has to delicate detail that is otherwise concealed.     

Spin physics in the high energy hadron productions. A systematic study of the spin asymmetries induced by <Emphasis Type="Italic">pp, γp,ep</Emphasis> and λ<Emphasis Type="Italic">p</Emphasis> collisions

The spin polarizations of hadrons inclusively produced by pp, γp and λp collisions are studied by the quark rearrangement model. The present model is a phenomenological one based on the relativistic spin equations of motion and using the quark distribution functions in hadrons and photon. A general success of the model is demonstrated. We find usefulness of the present formulation for studying the dynamics producing spin asymmetry distributions and the statics determining signs and magnitudes of the spin polarization by reflecting the characteristic quark structure in hadrons.     

Spin physics at HERMES

The primary goal of the HERMES experiment is the study of the spin structure of the nucleon. Results on the measured inclusive and semi-inclusive hadron asymmetries using a polarized positron beam on polarized ³He, hydrogen and deuterium targets are here presented. In the covered kinematic range, 0.023<x _Bj <0.6 and 1 GeV²<Q ²<10GeV² the polarized quark distribution were determined for all up (u+?u) and down (d+?) quarks, and separately for valence and sea quarks. The up quark polarization is positive, and the down quark polarization is negative. The polarization of the sea is consistent with zero in the measured range. A first indication of a positive gluon polarization is presented, based on the measured spin asymmetry in the photo-production of hadron pairs with high transverse momentum p _T . This asymmetry is negative, which is in contrast to the measured positive asymmetry for inclusive experiments.     

On Gravitational Form Factors and Transverse Spin Sum Rule

Using the light front wave functions of the scalar quark–diquark model for nucleon predicted by the soft-wall AdS/QCD, we calculate the flavor dependent gravitational form factors. We evaluate the matrix element of Pauli–Lubanski operator in this model and show that the intrinsic spin sum rule involves the higher twist form factor \({\bar{C}}\). The longitudinal momentum densities in the transverse impact parameter space are also discussed for both unpolarized and transversely polarized nucleons.     

Evidence for a single-spin azimuthal asymmetry in semi-inclusive pion electroproduction

Single-spin asymmetries for semi-inclusive pion production in deep-inelastic scattering have been measured for the first time. A significant target-spin asymmetry of the distribution in the azimuthal angle straight phi of the pion relative to the lepton scattering plane was formed for pi(+) electroproduction on a longitudinally polarized hydrogen target. The corresponding analyzing power in the sinstraight phi moment of the cross section is 0.022+/-0.005+/-0.003. This result can be interpreted as the effect of terms in the cross section involving chiral-odd spin distribution functions in combination with a chiral-odd fragmentation function that is sensitive to the transverse polarization of the fragmenting quark.     

Measurement of azimuthal asymmetries in inclusive production of hadron pairs in e(+)e(-) annihilation at Belle

The Collins effect connects transverse quark spin with a measurable azimuthal dependence in the yield of hadronic fragments around the quark's momentum vector. Using two different reconstruction methods, we find evidence of statistically significant azimuthal asymmetries for charged pion pairs in e(+)e(-) annihilation at a center-of-mass energy of 10.52 GeV, which can be attributed to a transverse polarization of the primordial quarks. The measurement was performed using a sample of 79 x 10(6) hadronic events collected with the Belle detector.     

Quantitative study of the violation of kperpendicular factorization in hadroproduction of quarks at collider energies

We demonstrate the violation of kperpendicular factorization for quark production in high energy hadronic collisions. This violation is quantified in the color glass condensate framework and studied as a function of the quark mass, the quark transverse momentum, and the saturation scale Q(s), which is a measure of large parton densities. At x values where parton densities are large but leading twist shadowing effects are still small, violations of kperpendicularkfactorization can be significant--especially for lighter quarks. At very small x, where leading twist shadowing is large, we show that violations of kperpendicular factorization are relatively weaker.     

Polarization of Λ0 hyperons as a signature for the quark-gluon plasma

The momentum distribution of Λ⁰ hyperons produced from the quark-gluon plasma (QGP) in ultra-relativistic heavy-ion collisions is calculated in dependence on their polarization. The momentum distribution of Λ⁰ hyperons is defined by matrix elements of relativistic quark Wigner operators, which are calculated within the effective quark model with chiral U(3)×U(3) symmetry and the quark-gluon transport theory. We show that the polarization of the Λ⁰ hyperon depends on the spin of the strange quark that agrees well with the DeGrand-Miettinen model. We show that Λ⁰ hyperons, produced from the QGP, are fully unpolarized. This means that a detection of unpolarized Λ⁰ hyperons, produced in ultra-relativistic heavy-ion collisions, should serve as one of the signatures for the existence of the QGP in intermediate states of ultra-relativistic heavy-ion collisions.     

Transverse spin structure of the nucleon from lattice-QCD simulations

We present the first calculation in lattice QCD of the lowest two moments of transverse spin densities of quarks in the nucleon. They encode correlations between quark spin and orbital angular momentum. Our dynamical simulations are based on two flavors of clover-improved Wilson fermions and Wilson gluons. We find significant contributions from certain quark helicity flip generalized parton distributions, leading to strongly distorted densities of transversely polarized quarks in the nucleon. In particular, based on our results and recent arguments by Burkardt [Phys. Rev. D 72, 094020 (2005)], we predict that the Boer-Mulders function h(1/1), describing correlations of transverse quark spin and intrinsic transverse momentum of quarks, is large and negative for both up and down quarks.     

Top Quark Polarization and Spin Correlation in the Littlest Higgs Model with T-Parity at the ILC

In the framework of the littlest Higgs model with T-parity(LHT),we study the top quark spin correlation and polarization at the International Linear Collider(ILC).We find that the top quark polarization asymmetry δP t and the left-right asymmetry δA LR can respectively reach-35% and-37.5% for s～(1/2)=500 GeV and s～(1/2)=1000 GeV via e+e-collision,which can reach the observable level at the ILC.By contrast,the spin correlation δC is smaller.The correlation behaviors of these observables at the e+e-collision and the γγ collision will be helpful to distinguish different models and test the LHT model at the ILC.     

Top quark production asymmetries A(FB)t and A(FB)ℓ

A large forward-backward asymmetry is seen in both the top quark rapidity distribution A(FB)(t) and in the rapidity distribution of charged leptons A(FB)(?) from top quarks produced at the Tevatron. We study the kinematic and dynamic aspects of the relationship of the two observables arising from the spin correlation between the charged lepton and the top quark with different polarization states. We emphasize the value of both measurements, and we conclude that a new physics model which produces more right-handed than left-handed top quarks is favored by the present data.     

Spin Transfer in High-Energy Hadronization Processes and Polarization of Hyperon in the Lepton-Induced Reactions

We show that measuring the polarization of hyperon in the lepton induced reactions is an ideal way to study the spin transfer in high energy hadronization processes. After a brief summary of the polarization of the initial quark or antiquark in these reactions,we give the calculation method of the polarization of hyperon. As an example,we calculate polarizations of different hyperons in e⁺e^－ annihilation at LEP energys and compare these results with the available data. The results show that measurements of such polarizations should provide important information about the question of which picture of spin structure of baryon is more suitable in describing the spin effects in the high energy fragmentation processes.     

PHENIX spin program,recent results

Acceleration of polarized protons in Relativistic Heavy Ion Collider (RHIC) provides unique tool to study the spin structure of the nucleon. We give a brief overview of the PHENIX program to investigate poorly known gluon and flavor decomposed see quark polarization in the proton, utilizing polarized proton collisions at RHIC. We report PHENIX first results on transverse single-spin asymmetry inπ ⁰ and charged hadron production and longitudinal double-spin asymmetry inπ ⁰ production at mid-rapidity.     

Color sextet scalars in early LHC experiments

We explore the potential for discovery of an exotic color sextet scalar in same-sign top quark pair production in early running at the LHC. We present the first phenomenological analysis at colliders of color sextet scalars with full top quark spin correlations included. We demonstrate that one can measure the scalar mass, the top quark polarization, and confirm the scalar resonance with 1 fb?1 of integrated luminosity. The top quark polarization can distinguish gauge triplet and singlet scalars.