The Gilbert Damping Factor of Heavy Quark Spin Polarization in the Magnetic Field

We employ the linear response theory to calculate the polarization rate of heavy quark spin in the presence of a strong magnetic field and the hot QCD matter, both of which are simultaneously generated in relativistic heavy-ion collisions. The hot QCD medium is simplified as a fermionic system consisting of only quarks. The spin of heavy quarks can be polarized as a result of combined contributions from spin-spin interactions between quarks and spin-magnetic field interactions. This spin dynamics is modeled as consisting of a polarization term and a dissipation term, which is described by the Landau-Lifshitz-Gilbert (LLG) equation and widely studied in condensed matter physics, analogous to the momentum evolution in the Langevin equation. In this study, we calculate the Gilbert damping factor that characterizes the spin polarization rate of heavy quarks, considering a Coulomb potential between two fermions in the medium. The dependence of the heavy quark spin polarization rate on the strength of the magnetic field, the heavy quark mass, temperature, and baryon chemical potential is studied in detail. This analysis contributes to a better understanding of quark spin dynamics in the hot QCD medium and the magnetic field.