Electric dipole moment induced by a QCD instanton in an external magnetic field

TL;DR

This paper investigates how a QCD instanton in an external magnetic field influences the Dirac equation's zero modes and the resulting electric dipole moment, combining analytical and lattice QCD approaches.

Contribution

It provides an analytical study of zero modes of the Dirac equation with both a magnetic field and an instanton, connecting to lattice QCD results and implications for electric dipole moments.

Findings

Zero modes are analytically characterized in various limits.

Comparison with lattice QCD results confirms theoretical predictions.

Implications for the electric dipole moment are discussed.

Abstract

In the chiral magnetic effect, there is a competition between a strong magnetic field, which tends to project positively charged particles to have spin aligned along the magnetic field, and a chirality imbalance which may be produced locally by a topologically nontrivial gauge field such as an instanton. We study the properties of the Euclidean Dirac equation for a light fermion in the presence of both a constant abelian magnetic field and an SU(2) instanton. In particular, we analyze the zero modes analytically in various limits, both on R^4 and on the four-torus, in order to compare with recent lattice QCD results, and study the implications for the electric dipole moment.