The covariant equations of motion of massive spinning particles in a background Yang-Mills field

TL;DR

This paper develops covariant equations of motion for massive spinning particles in a background Yang-Mills field, improving the modeling of quark dynamics in the early stages of heavy-ion collisions.

Contribution

It extends the classical equations of motion for spinning particles to fully incorporate spin, color charge, and relativistic covariance in non-Abelian fields, addressing limitations of previous models.

Findings

Derived self-consistent equations satisfying all physical constraints.

Provides a comprehensive framework for studying spin and momentum dynamics.

Enhances understanding of quark behavior in glasma fields.

Abstract

A strong classical color field, known as the glasma, is generated in the earliest stage of relativistic heavy-ion collisions and can significantly influence the momentum and spin dynamics of hard probes such as quarks and jets. Most existing studies based on the classical equations of motion in a background Yang-Mills field, such as Wong equations, may not capture the full range of effects, for example, they neglect the Stern-Gerlach force experienced by spinning particles in non-uniform glasma fields. Although several extensions of Wong equations have been proposed to include spin degrees of freedom, they generally fail to satisfy all the required conditions simultaneously, such as Lorentz covariance, allowance for an arbitrary chromomagnetic moment, and respect for the necessary physical constraints. In this work, we extend the framework of a relativistic classical spinning particle in an electromagnetic field to describe spin one-half quarks propagating in a background non-Abelian Yang-Mills field. By systematically applying the Dirac-Bergmann algorithm, we derive self-consistent equations of motion for the particle's coordinates, momenta, spin, and color charge that satisfy all these requirements. This formalism provides a more complete and physically relevant description for studying momentum diffusion and spin polarization phenomena of hard probes in the glasma.