Gilbert damping factor of heavy-quark spin polarization in the magnetic field
Phys. Rev. D 113, 043007 – Published 4 February, 2026Erratum Phys. Rev. D 113, 129901 (2026)
DOI: https://doi.org/10.1103/c1sy-7f3g
Abstract
The spin dynamics of fermions in a fermionic system under the influence of a magnetic field have been extensively studied using the Landau-Lifshitz-Gilbert (LLG) equation, where spin polarization and dissipation terms result from the combined effects of spin-magnetic-field interactions and spin-spin interactions between fermions in the medium. In this work, we extend the LLG equation to a fermionic system subject to an external field and two-body random collisions for the first time. We derive the corresponding Gilbert damping factor, which characterizes the spin polarization rate, within the framework of linear response theory. The fermionic medium is assumed to consist of quarks governed by strong interactions. We analyze the dependence of the heavy-quark spin polarization rate on the scattering cross section, the magnetic field strength, medium temperature, and heavy-quark mass in detail. This framework provides a foundation for the phenomenological study of spin dynamics in heavy quarks and heavy-flavor hadrons, such as charmonium spin alignment, in relativistic heavy-ion collisions, where both hot quark matter and strong magnetic fields are simultaneously generated.
Physics Subject Headings (PhySH)
Corrections
10 June, 2026
Correction: Appendix C has been removed, along with a reference to it in the text. Subsequent Appendixes have been relabeled. A citation following Eq. (18) has been fixed.
