Role of $Σ^*(1385)$ on $Λ$ hyperon polarization in relativistic heavy ion collisions

The effect of $Σ^*(1385)$ baryon resonance on the time evolution of the $Λ$ hyperon polarization in hadronic matter is studied using a kinetic approach. This approach explicitly includes the production of the $Σ^*$ resonance from the $Λ-π$ and $Σ(1192)-π$ scatterings as well as its decay into $Λ+π$ or $Σ+π$. The resulting coupled kinetic equations governing the time evolution of $Λ$, $Σ$ and $Σ^*$ numbers and polarizations are solved for Au-Au collisions at $\sqrt{s_{NN}}=7.7$ GeV and 20-50\% centrality, using initial values determined by thermal yields and the thermal vorticity at chemical freeze-out temperature. As the hadronic matter expands and cools, the $Λ$ polarization is found to increase slightly during early times and then decreases very slowly afterwards, while the $Σ$ polarization remains nearly constant and the $Σ^*$ polarization continuously decreases. Including feed-down contributions to the $Λ$ polarization from the decays of partially polarized $Σ^0$, $Σ^*$, and $Ξ(1322)$ hyperons, where the $Ξ$ polarization is obtained by solving coupled kinetic equations for the $Ξ$ and $Ξ^*(1532)$ system, the resulting $Λ$ polarization becomes smaller and decreases over time. In both cases, however, the time variation of the $Λ$ polarization is sufficiently small to support the assumption of an early freeze-out of $Λ$ spin degree of freedom in relativistic heavy ion collisions.