Spin alignment of vector mesons from quark dynamics in a rotating medium

Vorticities in heavy-ion collisions (HICs) are supposed to induce spin alignment and polarization phenomena of quarks and mesons. In this work, we analyze the spin alignment of vector mesons $\phi$ and $\rho$ induced by rotation from quark dynamics in the framework of the Nambu-Jona-Lasinio (NJL) model. The rotating angular velocity induces mass splitting of spin components for vector $\phi,\rho$ mesons $M_{\phi,\rho}(\Omega)\simeq M_{\phi,\rho}(\Omega=0)-s_{z}\Omega$. This behavior contributes to the spin alignment of vector mesons $\phi,\rho$ in an equilibrium medium and naturally explains the negative deviation of $\rho_{00}-1/3$ for vector mesons. Incidentally, the positive deviation of $\rho_{00}-1/3$ under the magnetic field can also be easily understood from quark dynamics.