Polarized quarks and antiquarks in high-energy heavy-ion collisions can lead to the spin alignment of vector mesons formed by quark coalescence. Using the relativistic spin Boltzmann equation for vector mesons derived from Kadanoff-Baym equations with an effective quark-meson model for strong interaction and quark coalescence model for hadronizaton, we calculate the spin density matrix element ${\rho }_{00}$ for $\varphi$ mesons and show that anisotropies of local field correlations with respect to the spin quantization direction lead to $\varphi$ meson’s spin alignment. We propose that the local correlation or fluctuation of $\varphi$ fields is the dominant mechanism for the observed $\varphi$ meson’s spin alignment and its strength can be extracted from experimental data as functions of collision energies. The calculated transverse momentum dependence of ${\rho }_{00}$ agrees with STAR’s data. We further predict the azimuthal angle dependence of ${\rho }_{00}$ which can be tested in future experiments.

• Received 17 June 2022
• Revised 4 February 2023
• Accepted 10 July 2023

DOI:https://doi.org/10.1103/PhysRevLett.131.042304