# Chiral kinetic theory from the on-shell effective theory: derivation of collision terms

## TL;DR

This paper derives collision terms in chiral kinetic theory from the on-shell effective theory, clarifying quantum effects and spin interactions for massless fermions, with applications to chiral imbalances in plasma.

## Contribution

It provides a detailed derivation of collision terms in chiral kinetic theory using OSEFT, including spin and polarization effects up to order 1/E, linking quantum field theory with semiclassical transport.

## Key findings

- Collision terms depend on fermion spin tensor.
- Results reproduce fermion decay rates in chiral imbalanced plasma.
- Collision interactions differ for helicities and photon polarizations.

## Abstract

We show that the on-shell effective theory (OSEFT) is the quantum field theory counterpart of a Foldy-Wouthuysen diagonalization of relativistic quantum mechanics for massless fermions. Thus, it is free of the Zitterbewegung oscillations that would yield an ill-defined meaning to the semiclassical transport approach at short distances if derived from the pure Dirac picture. We present a detailed derivation of the collision terms in the chiral kinetic theory using the OSEFT. Collision integrals are derived up to order 1/E, where E is the energy of an on-shell fermion. At this order, the collision terms depends on the spin tensor of the fermion, and in the presence of chiral imbalance, it describes how a massless fermion of a given helicity interacts differently with the transverse photons of different circular polarization. In order to back up our results, we check that they allow us to reproduce the fermion decay rate in an ultradegenerate plasma with a chiral imbalance computed directly from QED.