Global quark polarization in noncentral A+A collisions

Partons produced in the early stage of noncentral heavy-ion collisions can develop a longitudinal fluid shear because of the unequal local number densities of participant target and projectile nucleons. Under such fluid shear, local parton pairs with nonvanishing impact parameters have finite local relative orbital angular momentum along the direction opposite to the reaction plane. Such a finite relative orbital angular momentum among locally interacting quark pairs can lead to global quark polarization along the same direction because of spin-orbital coupling. Local longitudinal fluid shear is estimated within both the Landau fireball and the Bjorken scaling model of initial parton production. Quark polarization through quark-quark scatterings with the exchange of a thermal gluon is calculated beyond the small-angle scattering approximation in a quark-gluon plasma. The polarization is shown to have a nonmonotonic dependence on the local relative orbital angular momentum dictated by the interplay between electric and magnetic interactions. It peaks at a value of relative orbital angular momentum which scales with the magnetic mass of the exchanged gluons. With the estimated small longitudinal fluid shear in semiperipheral Au+Au collisions at energies currently available at the BNL Relativistic Heavy Ion Collider (RHIC), the final quark polarization is found to be small |P-q|< 0.04 in the weak coupling limit. Possible behavior of the quark polarization in the strong coupling limit and implications on the experimental detection of such global quark polarization at RHIC and CERN Large Hadron Collider (LHC) are also discussed.