Transversity Properties of Quarks and Hadrons in SIDIS and Drell-Yan

We consider the leading twist T -odd contributions as the dominant source of the azimuthal and transverse single spin asymmetries in SIDIS and dilepton production in Drell-Yan Scattering. These asymmetries contain information on the distribution of quark transverse spin in (un)polarized protons. In the spectator framework we estimate these asymmetries at HERMES kinematics and at 50 GeV for the proposed experiments at GSI, where an anti-proton beam is ideal for studying the transversity properties of quarks due to the dominance of valence quark effects. One of the persistent challenges confronting the QCD parton model is to provide a theoretical basis for the experimentally significant azimuthal and transverse spin asymmetries that emerge in inclusive and semi-inclusive processes. Generally speaking, the spin dependent amplitudes for the scattering will contribute to non-zero transverse single spin asymmetries (SSA) if there are imaginary parts of bilinear products of those amplitudes that have overall helicity change. In perturbative QCD (PQCD), applicable to the hard scattering region, to obtain an imaginary contribution to quark and/or gluon scattering processes demands introducing higher order corrections to tree level processes. One approach incorporates the requisite phases through interference of tree level and one-loop contributions in PQCD in an attempt to explain up-down polarization asymmetry in Λ production [1]. On general grounds the helicity conservation property of massless QCD predicts that such contributions are small, going like αsm/Q, where αs is the strong coupling, m represents a non-zero quark mass and Q represents the hard QCD scale [1, 2]. Such contributions have failed to account for the large SSA observed in Λ production [3]. However, considering the soft contributions to hadronic processes opens up the possibility that there are non-trivial transversity parton distributions that can contribute to transverse spin asymmetries [4]. For transverse SSA in SIDIS, transverse momentum must be acquired to lead to appropriate helicity changes at leading twist. In describing transverse asymmetries this is particularly relevant when the transverse momentum can arise from intrinsic quark momenta. Here the effects are associated with non-perturbative transverse momentum distribution functions [5] (TMD), where transverse SSAs indicate so called T -odd correlations between transverse spin and longitudinal and intrinsic quark transverse momentum. The T -odd distributions [6, 7] are of importance as they possess both transversity properties and the necessary phases to account for SSA and azimuthal asymmetries [8, 9]. Formally, these phases can be generated from the gauge invariant definitions of the T -odd quark distribution functions [10, 11, 12]. In contrast to the transverse SSAs generated from the interference of tree-level and one loop correction in PQCD, such effects go like αs/M, where now M plays the role of the chiral symmetry breaking scale and k⊥ is characteristic of quark intrinsic motion. Here we consider the leading twist T -odd contributions as the dominant source of the cos2φ azimuthal asymmetry and sin(φ ± φs) transverse SSAs in SIDIS [13] and azimuthal asymmetry ν in dilepton production in Drell-Yan Scattering [14]. Among other interesting properties, these asymmetries contain information on the distribution of quark transverse spin in an unpolarized proton, h1 (x,k⊥) [7]. In a parton-spectator framework we estimate these asymmetries at HERMES kinematics [15] and for DrellYan scattering at 50 GeV center of mass energy. The latter azimuthal asymmetry is interesting in light of proposed experiments at GSI, where an anti-proton beam will ideal for studying the transversity properties of quarks due to the dominance of valence quark effects [16]. The leading twist contributions to the factorized cross-section for a transversely polarized nucleon target in lepton-proton scattering are d6σ lN↑→lπX UT dxHdydzhdφSdPh⊥ = 2α2 Q2y { |ST |(1− y)sin(φh +φS)∑ q eq F [ p⊥ · ĥ Mh h1H ⊥q 1 ] + |ST | ( 1 +(1− y)2 ) 2 sin(φh −φS)∑ q eq F [ k⊥ · ĥ M f 1T D q 1 ]}