Role of $\Sigma^*(1385)$ on $\Lambda$ hyperon polarization in relativistic heavy ion collisions

The effect of $\Sigma^*(1385)$ baryon resonance on the time evolution of the $\Lambda$ hyperon polarization in hadronic matter is studied using a kinetic approach. This approach explicitly includes the production of the $\Sigma^*$ resonance from the $\Lambda-\pi$ and $\Sigma(1192)-\pi$ scatterings as well as its decay into $\Lambda+\pi$ or $\Sigma+\pi$. The resulting coupled kinetic equations governing the time evolution of $\Lambda$, $\Sigma$ and $\Sigma^*$ 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 $\Lambda$ polarization is found to increase slightly during early times and then decreases very slowly afterwards, while the $\Sigma$ polarization remains nearly constant and the $\Sigma^*$ polarization continuously decreases. Including feed-down contributions to the $\Lambda$ polarization from the decays of partially polarized $\Sigma^0$, $\Sigma^*$, and $\Xi(1322)$ hyperons, where the $\Xi$ polarization is obtained by solving coupled kinetic equations for the $\Xi$ and $\Xi^*(1532)$ system, the resulting $\Lambda$ polarization becomes smaller and decreases over time. In both cases, however, the time variation of the $\Lambda$ polarization is sufficiently small to support the assumption of an early freeze-out of $\Lambda$ spin degree of freedom in relativistic heavy ion collisions.