Chiral kinetic theory with small mass corrections and quantum coherent states

TL;DR

This paper extends the chiral kinetic theory to include small fermion mass effects, incorporating quantum coherence states and analyzing their impact on dispersion, transport, and anomalies.

Contribution

It introduces a systematic way to include small mass corrections and quantum coherent states into the chiral kinetic theory framework.

Findings

Tensorial components are needed with mass corrections, while scalar components vanish.

Vectorial and tensorial components are decoupled up to second order, sharing the same dispersion law.

The framework accounts for mass modifications to the chiral anomaly equation.

Abstract

We study the effect of a small fermion mass in the formulation of the on-shell effective field theory (OSEFT). This is our starting point to derive small mass corrections to the chiral kinetic theory. In the massless case, only four Wigner functions are needed to describe positive and negative energy fermions of left and right chirality, corresponding to the vectorial components of a fermionic two-point Green's function. As soon as mass correction are introduced, tensorial components are also needed, while the scalar components strictly vanish in the OSEFT. The tensorial components are conveniently parametrized in the so-called spin coherence function, which describe quantum coherent mixtures of left-right and right-left chiral fermions, of either positive or negative energy. We show that, up to second order in the energy expansion, vectorial and tensorial components are decoupled, and obey the same dispersion law and transport equation, depending on their respective chirality. We study the mass modifications of the reparametrization invariance of the OSEFT, and check that vector and tensorial components are related by the associated symmetry transformations. We study how the macroscopic properties of the system are described in terms of the whole set of Wigner functions, and check that our framework allows to account for the mass modifications to the chiral anomaly equation.