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

TL;DR

This paper calculates the Gilbert damping factor for heavy quark spin polarization in hot QCD matter under strong magnetic fields, using linear response theory and the LLG equation, to understand spin dynamics in relativistic heavy-ion collisions.

Contribution

It introduces a novel calculation of the Gilbert damping factor for heavy quarks in hot QCD matter, linking condensed matter spin dynamics models to high-energy physics.

Findings

The spin polarization rate depends on magnetic field strength, quark mass, temperature, and chemical potential.

The Gilbert damping factor quantifies the dissipation of heavy quark spin polarization.

The model provides insights into quark spin behavior in extreme conditions.

Abstract

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.