Hyperon longitudinal polarization and vector meson spin alignment in a thermal model for heavy-ion collisions

TL;DR

The paper addresses whether a common local spin equilibrium can describe both $\Lambda$ longitudinal polarization and vector-meson spin alignment in heavy-ion collisions at top RHIC energies. It implements a boost-invariant thermal model with anisotropic transverse flow and a projected thermal vorticity $\varpi_{\mu\nu}$, scaled by a factor $\lambda$, to compute spin observables for $\Lambda$, $\phi$, and $K^{*0}$ via $\rho_{00}$ and related quantities. It finds a positive, mass-ordered, $p_T$- and centrality-dependent vector-meson alignment that qualitatively mirrors the $\Lambda$ polarization trends, though the quantitative match to data is incomplete; increasing $\lambda$ improves agreement but does not fully resolve discrepancies. The results reveal a correlation between the magnitude of the $\Lambda$ longitudinal polarization and vector-meson alignment, suggesting a common mechanism and motivating more sophisticated spin-polarization tensor calculations and further refinement of the model.

Abstract

The concept of a common local spin equilibrium for both spin-1/2 and spin-1 particles is incorporated into a thermal model of particle production in heavy-ion collisions at the top RHIC energies. We show that an effective spin polarization tensor leading to a correct description of the longitudinal spin polarization of $Λ$ hyperons simultaneously yields a positive alignment of vector mesons ($φ$ and $K^{*0}$) that grows monotonically with transverse momentum and centrality. Similar trends can be seen in the data, suggesting a possible common mechanism for longitudinal spin polarization and alignment. However, model calculations are insufficient to explain the data in a fully quantitative way. The correlation found between the magnitude of the $Λ$ longitudinal polarization and vector meson alignment suggests further more elaborate investigations of this issue.

Figures (6)

• Figure 1: Longitudinal spin polarization of $\Lambda$ hyperons compared to the experimental data STAR:2019erd. The blue solid (red dashed) line describes the model result with projected thermal vorticity and $\lambda =1$ ($\lambda =3$).
• Figure 2: Transverse-momentum integrated $\rho_{00}$ for $\phi$ and $K^{*0}$ mesons as a function of mass. Experimental data from STAR STAR:2022fan.
• Figure 3: Transverse-momentum dependence of $\rho_{00}$ for $\phi$ mesons. Solid blue and dashed red lines show our results for $\lambda = 1$ and $3$, respectively. Experimental data from STAR STAR:2022fan.
• Figure 4: Same as Fig. \ref{['fig:phi_diff']} but for $K^{*0}$ mesons.
• Figure 5: Centrality dependence of $\rho_{00}$ for $\phi$ mesons. Solid blue and dashed red lines show model results for $\lambda = 1$ and $3$, respectively. Experimental data are from STAR STAR:2022fan.