Spin Hall effect in heavy-ion collisions

Abstract

Spin Hall effect (SHE) is the generation of spin current due to an electric field, and has been observed in a variety of materials. In this work, we use linear response theory to verify that the analogous spin Hall current can be induced by chemical potential and temperature gradient, both of which are present in hot and dense nuclear matter created in heavy-ion collisions. We propose to measure ``directed spin flow'', the first Fourier coefficients of local spin polarization of $\mathrm{\ensuremath{\Lambda}}$ $(\overline{\mathrm{\ensuremath{\Lambda}}})$ hyperon, at central collisions to probe spin Hall current in heavy-ion collision experiments. We benchmark the magnitude of the induced ``directed spin flow'' at two representatively collisions energies, namely ${\sqrt{s}}_{NN}=200\text{ }\text{ }\mathrm{GeV}$ and ${\sqrt{s}}_{NN}=19.6\text{ }\text{ }\mathrm{GeV}$, by employing a phenomenologically motivated freeze-out prescription. At both beam energies, the resulting ``directed spin flow'' ranges from ${10}^{\ensuremath{-}4}$ to ${10}^{\ensuremath{-}3}$, and is very sensitive to the rapidity.