On the Ambiguity of the Definition of Shear and Spin-Hall Contributions to the Λ Polarization in Heavy-Ion Collisions

Abstract

Recently proposed thermal-shear and spin-Hall contributions to the particle polarization in heavy-ion collisions are discussed. Alternative definitions of the thermal-shear contribution, i.e., those of Becattini–Buzzegoli–Palermo on the one hand and Liu–Yin on the other, are very similar in the midrapidity region while quite different at forward-backward rapidities, which are measured in fixed-target experiments. It is shown that the thermal-shear contribution to the global polarization with momentum averaging extended to all momenta is very different within these alternative definitions. The spin-Hall contribution to the global polarization, defined similarly to the Liu–Yin shear one, is identically zero, if averaging runs over all momenta. Only application of restrictive momentum acceptance and the boost (to Λ rest frame) correction result in nonzero global spin-Hall polarization. If the spin-Hall contribution were defined similarly to Becattini–Buzzegoli–Palermo shear one, the global spin-Hall polarization would be nonzero even without any acceptance and the boost correction.