Dynamical equation for quark spin polarization in the rotating medium

TL;DR

This paper derives a phenomenological dynamical equation for heavy quark spin polarization in a rotating quark-gluon plasma, inspired by the Landau-Lifshitz equation, to understand spin behavior in relativistic heavy-ion collisions.

Contribution

It introduces a novel equation modeling heavy quark spin dynamics in rotating media, incorporating spin-angular momentum coupling and spin-spin interactions.

Findings

Provides a detailed balance of heavy quark spin distributions.

Offers insights into quark and quarkonium spin polarization in rotating QGP.

Extends the Landau-Lifshitz framework to rotating relativistic media.

Abstract

In non-central relativistic heavy-ion collisions, the produced quark-gluon plasma (QGP) behaves approximately as a rotating fluid due to the system's initial angular momentum. In this rotating fluid, the spins of quarks become polarized due to the coupling between spin and angular momentum, as well as random spin-spin interactions. Since the Landau-Lifshitz (LL) equation effectively describes the spin polarization of fermions in a medium with a magnetic field, we derive a phenomenological equation analogous to the LL equation for heavy quark spin dynamics in the rotating medium. The spin-angular momentum coupling and random spin-spin interactions are incorporated, leading to a detailed balance of heavy quark spin distributions. This equation provides insight into the spin dynamics of heavy quarks and quarkonium in relativistic heavy-ion collisions.