Rotational Brownian Motion and $\mathrm{J/ψ}$ Spin Alignment in Heavy-Ion Collisions

Abstract: The heavy-quark polarization in ultra-relativistic heavy-ion collisions (HICs) serves as a probe for unfolding the characteristics of deconfined QCD. The present study explores the spin alignment of $\mathrm{J/ψ}$ in the HICs by employing the rotational Brownian motion of charm quarks in the presence of a strong magnetic field. We derive an analytical expression for the polarization of the $c$-$\bar{c}$ pair based on the Fokker-Planck equation under the consideration of spin-vorticity coupling. These polarized $c$-$\bar{c}$ pairs lead to the formation of the $\mathrm{J}/ψ$ at the hadronization surface via the coalescence and fragmentation mechanisms. Correspondingly, we obtain the $m=0$ diagonal element $ρ_{00}$ of the $\mathrm{J}/ψ$ spin-density matrix, which quantifies its spin alignment along the chosen quantization axis. Our study provides a microscopic description of heavy-quark spin transport and suggests rotational diffusion as a possible mechanism underlying the observed $\mathrm{J}/ψ$ spin alignment.