QED radiative corrections to chiral magnetic effect

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 rescattered. 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 is discussed.

Figure 1

The photon-photon scattering contributions to chiral anomaly. The dashed and wavy lines represent the axial-vector and vector fields, respectively.

Figure 2

The two-photon reducible AVV diagrams. The shaded box and triangle represent the two-photon irreducible diagrams.

Figure 3

The four-photon box diagrams including all permutations.