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

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• Relativistic heavy-ion collisions
• Polarization