# Mass Correction to Chiral Kinetic Equations

## TL;DR

This paper investigates how fermion mass influences chiral kinetic equations, revealing that mass introduces coupling between number and spin densities and acts as a quantum correction in electromagnetic fields, affecting phenomena like the chiral magnetic effect.

## Contribution

It derives the first-order quantum mass correction to chiral kinetic equations, showing it acts as an additional collision term without altering the fundamental structure.

## Key findings

- Mass correction couples number and spin densities in massive fermion systems.
- Mass correction appears as a quantum effect in chiral magnetic phenomena.
- Classical mass correction exists but quantum correction is first order in  in chiral kinetic equations.

## 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 $\hbar$, 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 chiral magnetic effect.