Chiral Magnetic Effect at Weak Coupling with Relaxation Dynamics

TL;DR

This paper resolves a longstanding discrepancy in weak coupling calculations of the Chiral Magnetic Effect by demonstrating that relaxation dynamics and proper limit handling yield consistent results, aligning with hydrodynamic expectations.

Contribution

It shows that non-commutativity of limits in CME calculations is resolved at weak coupling using kinetic theory and diagrammatic methods, incorporating relaxation effects.

Findings

Correct CME current obtained with relaxation dynamics

Non-commutativity of limits resolved in weak coupling

Pinch singularity absent in P-odd correlator

Abstract

We provide a resolution of an old issue in weak coupling computation of the Chiral Magnetic Effect (CME) current, where a free chiral fermion theory gives two different results depending on the order of the two limits, $\omega\rightarrow 0$ (frequency) and $k\rightarrow 0$ (spatial momentum). We first argue based on hydrodynamics that in any reasonable interacting theory of chiral fermions the non-commutativity between the two limits should be absent, and we demonstrate this at weak coupling regime in two different frameworks: kinetic theory in the relaxation time approximation, and diagrammatic computation with resummation of damping rate. In the latter computation, we also show that the "pinch" singularity, which would make the summation of ladder diagrams necessary as in the P-even correlation function, is absent in the relevant P-odd correlation function. The correct value of CME current is reproduced even in the presence of relaxation dynamics in both computations.