Investigating $J/ψ$ spin alignment in heavy-ion collisions within a two-component transport model

We investigate the spin alignment of $J/\psi$ mesons in relativistic heavy-ion collisions within a two-component Boltzmann transport model. Starting from the relativistic spin Boltzmann equation, we derive the spin density matrix element $\rho_{00}$ under a non-relativistic approximation for heavy quarks. To interpret the recent ALICE measurements in Pb+Pb collisions, the observed $\rho_{00}$ is described as a $p_T$-dependent mixture of contributions from primordial production and the coalescence process. At forward rapidity, the $p_T$ dependence of charmonium $\rho_{00}$ is well reproduced by this two-component mechanism: at low $p_T$, charmonium production is dominated by the coalescence of partially polarized charm quarks induced by thermal vorticity; with increasing $p_T$, primordially produced charmonia become dominant, causing $\rho_{00}$ to approach $1/3$. To further test this spin alignment mechanism, we provide predictions for the $J/\psi$ $\rho_{00}$ in the mid-rapidity region, which exhibits a distinct $p_T$ trend due to the kinematic suppression of the thermal vorticity contribution. This study elucidates the underlying mechanism of $J/\psi$ spin alignment and advances our understanding of heavy quarkonium spin dynamics in strongly interacting matter.