On Ambiguity of Definition of Shear and Spin-Hall Contributions to $\Lambda$ Polarization in Heavy-Ion Collisions

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 $\Lambda$ 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 non-zero even without any acceptance and the boost correction.