Quantum kinetic theory for spin transport of quarks with background chromo-electromagnetic fields

TL;DR

This paper develops quantum kinetic equations for quark spin and charge transport in background chromo-electromagnetic fields, revealing how color fields influence spin polarization and axial charge currents in quark-gluon plasmas.

Contribution

It derives coupled color-singlet and color-octet kinetic equations for quarks, incorporating spin and charge dynamics, and explores their implications in weakly coupled quark-gluon plasma environments.

Findings

Derived kinetic equations for massive and massless quarks with spin and charge transport.

Identified source terms leading to dynamical spin polarization.

Obtained axial Ward identities and pseudo-scalar condensate at finite temperature.

Abstract

We derive the quantum kinetic equations for massive and massless quarks coupled with the background chromo-electromagnetic fields from the Wigner-function approach with the $\hbar$ expansion and effective power-counting scheme. For each case, one obtains coupled color-singlet and color-octet kinetic equations, which also involve the scalar and axial-vector components for the charge and spin transport. These kinetic equations delineate entangled evolution of the corresponding distribution functions decomposed in color space. At weak coupling, we derive the close form of the color-singlet kinetic equations for spin transport, which incorporates the diffusion term and the source term that triggers dynamical spin polarization led by correlation functions of color fields. Also, the non-dynamical source term is found in the axial Wigner function. The induced spin polarization and axial charge currents by these source terms are discussed under physical assumptions for color-field correlators in near-equilibrium quark gluon plasmas. In the constant-field limit, we further obtain non-vanishing axial Ward identities, from which we extract the pseudo-scalar condensate for massive quarks at finite temperature.