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

TL;DR

This work addresses the origin and time evolution of Λ polarization in relativistic heavy-ion collisions by explicitly treating the Σ^*(1385) resonance as a dynamical degree of freedom through Λ+π↔Σ^*↔Σ+π, and by incorporating feed-down from Σ^0, Σ^*, and Ξ decays. The authors derive spin-dependent, coupled kinetic equations for the numbers and polarizations of Λ, Σ, and Σ^* (and similarly for Ξ/Ξ^*) and compute thermally averaged cross sections and decay rates to drive the evolution during the hadronic stage of Au-Au collisions at √s_{NN}=7.7 GeV. They find that Λ polarization exhibits only a small time dependence, increasing slightly in the early hadronic phase, but being reduced when feed-down is included; Σ^* polarization continuously decreases, and Σ polarization remains nearly constant. Overall, the time variation of P_Λ is small, supporting the common assumption of early Λ spin freeze-out at chemical freeze-out, with feed-down contributing a modest additional reduction, and the framework provides a basis for extending the analysis to other hyperons such as Ξ and Ω.

Abstract

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.

Figures (6)

• Figure 1: Temperature dependence of the thermal averages of the spin-averaged $\Lambda+\pi\rightarrow \Sigma^*$ (solid line) and $\Sigma+\pi\rightarrow \Sigma^*$ (dashed line) cross sections shown in the inset.
• Figure 2: Time evolution of $\Lambda$ (solid line), $\Sigma$ (dashed line), and $\Sigma^*$ (dotted line) numbers in Au-Au collisions at $\sqrt{s_{NN}}=7.7$ GeV and 20-50% collision centrality.
• Figure 3: Time evolution of $\Lambda$ (solid line), $\Sigma$ (dashed line), and $\Sigma^*(1385)$ (dotted line) polarizations in Au-Au collisions at $\sqrt{s_{NN}}=7.7$ GeV and 20-50% collision centrality, for initial $\Lambda$ and $\Sigma$ polarizations of 0.025 and initial $\Sigma^*$ polarization of 0.042. Also shown (dot-dashed line) is the $\Lambda$ polarization $P_\Lambda^{\rm FD}$ that includes the feed-down contributions described in the text.
• Figure 4: Temperature dependence of the thermal average of the spin-averaged $\Xi+\pi\rightarrow \Xi^*$ cross section shown in inset.
• Figure 5: Time evolution of the $\Xi$ number (solid line) and $\Xi^*$ number (dotted line) in Au-Au collisions at $\sqrt{s_{NN}}=7.7$ GeV and 20-50% collision centrality.