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

Abstract

The effect of ${\Sigma }^{\ast }(1385)$ 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 ${\Sigma }^{\ast }$ 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 ${\Sigma }^{\ast }$ 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 ${\Sigma }^{\ast }$ polarization continuously decreases. Including feed-down contributions to the $\Lambda$ polarization from the decays of partially polarized ${\Sigma }^0$, ${\Sigma }^{\ast }$, and $\Xi (1322)$ hyperons, where the $\Xi$ polarization is obtained by solving coupled kinetic equations for the $\Xi$ and ${\Xi }^{\ast }(1532)$ 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.

Comments: 8 pages, 6 figures