The QED Radiative Corrections to Chiral Magnetic Effect

TL;DR

This paper investigates the radiative corrections to the chiral magnetic effect in massless QED at zero and nonzero temperatures, clarifying the role of infrared effects and Ward identities in these corrections.

Contribution

It provides a simplified approach to calculating radiative corrections to the chiral magnetic current and discusses their behavior at different temperatures and potential extensions to QED and QCD.

Findings

Radiative corrections at zero temperature are derived from a three-loop diagram.

Infrared subtleties affect the corrections at zero temperature but vanish at nonzero temperature.

The three-loop diagram does not contribute to the current at nonzero temperature in a static magnetic field.

Abstract

We study in this paper the radiative corrections to chiral magnetic current at both zero and nonzero temperature. Our motivation is a radiative correction to the matrix element of the anomalous Ward identity in massless QED stemming from a three-loop diagram where the two photons coming from the one-loop anomalous triangle are re-scattered. Through the interplay between the Ward identity and the infrared subtlety of the fermion loop integral, we are able to reproduce the corrections known in literature in a simpler approach and obtain its contribution to the chiral magnetic current at zero temperature. At a nonzero temperature, the infrared subtlety disappeared in a static magnetic field and the three-loop diagram does not contribute to the chiral magnetic current any more. The generalization to all orders of the massless QED and the QCD corrections are discussed.