Mass correction to chiral kinetic equations

Ziyue Wang,Shuzhe Shi,Xingyu Guo,Pengfei Zhuang

doi:10.1103/physrevd.100.014015

Ziyue Wang, Shuzhe Shi + Show 2 more

Open Access

https://doi.org/10.1103/physrevd.100.014015

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Abstract

We study fermion mass correction to chiral kinetic equations in electromagnetic fields. Different from the chiral limit where fermion number density is the only independent distribution, the number and spin densities are coupled to each other for massive fermion systems. To the first order in $\ensuremath{\hbar}$, we derived the quantum correction to the classical on-shell condition and the Boltzmann-type transport equations. To the linear order in the fermion mass, the mass correction does not change the structure of the chiral kinetic equations and behaves like additional collision terms. While the mass correction exists already at classical level in general electromagnetic fields, it is only a first-order quantum correction in the study of the chiral magnetic effect.

Highlights

The chiral anomaly of QCD or QED has been recently widely discussed both theoretically and experimentally
When we turn off the electric field E and keep only the magnetic field B, corresponding to the physics of chiral magnetic effect, the effective collision term with F1 which is coupled to g3 vanishes, and the other collision term is only related to the classical distribution gð30Þ, which can be solved through the csiloasnsitcearml trħanmsFpo21⁄2rgt ð3e0qÞu=aptiffiGoffiffinffi before
While the quantum chiral anomaly and related phenomena in fermion systems are widely discussed in chiral limit, the mass correction in real case should be seriously considered

Summary

INTRODUCTION

The chiral anomaly of QCD or QED has been recently widely discussed both theoretically and experimentally. To check the degree of the chiral anomaly in a real fermion system, it is necessary to study the fermion mass effect on the chiral magnetic effect. By applying the semiclassical expansion method to the kinetic equations, to the first order in ħ, the chiral anomaly related effects are incorporated into the transport equation for the chiral fermion distribution function [23,24,25]. We generally study the fermion mass correction to the chiral kinetic equations in external electromagnetic fields in equal-time Wigner function formalism.

EQUAL-TIME KINETIC EQUATIONS

TRANSPORT EQUATIONS FOR CHIRAL COMPONENTS

SOLUTION TO THE MASS CORRECTION

Gp4 ðp

SUMMARY