Explicit calculation on two-loop correction to the chiral magnetic effect with NJL model

TL;DR

This paper explicitly calculates two-loop corrections to the Chiral Magnetic Effect within the NJL model and confirms that these higher-order corrections vanish, supporting the non-renormalization property of CME conductivity.

Contribution

The study provides a detailed two-loop calculation of CME corrections within the NJL model, clarifying the non-renormalization of CME conductivity beyond one-loop.

Findings

Two-loop corrections to CME conductivity are zero.

Supports the non-renormalization of CME in quantum field theory.

Highlights the importance of infrared effects in CME calculations.

Abstract

Chiral Magnetic Effect(CME) is usually believed not receiving higher order corrections due to the non-renormalization of AVV triangle diagram in the framework of quantum field theory. However, the CME-relevant triangle, which is obtained by expanding the current-current correlation requires zero momentum on the axial vertex, is not equivalent to the general AVV triangle when taking the zero-momentum limit owing to the infrared problem on the axial vertex. Therefore, it is still significant to check if there exists perturbative higher order corrections to the current-current correlation. In this paper, we explicitly calculate the two-loop corrections of CME within NJL model with Chern-Simons term which ensures a consistent $\mu_5$. The result shows the two-loop corrections to the CME conductivity are zero, which confirms the non-renomalization of CME conductivity.