A renormalization group approach for QCD in a strong magnetic field

TL;DR

This paper develops a Wilsonian renormalization group method to incorporate higher Landau level effects into the lowest Landau level in QCD under strong magnetic fields, enabling model-independent calculations of quark self-energy.

Contribution

It introduces a renormalization framework that includes higher Landau levels into the LLL effective theory using perturbation theory and form factors, providing new insights into magnetic field effects in QCD.

Findings

Higher Landau levels become negligible at magnetic fields of 0.1-0.3 GeV^2.

The approach allows for perturbative calculations of quark self-energy including all Landau levels.

Most calculations are model-independent thanks to Ritus bases.

Abstract

A Wilsonian renormalization group approach is applied, in order to include effects of the higher Landau levels for quarks into a set of renormalized parameters for the lowest Landau level (LLL), plus a set of operators made of the LLL fields. Most of the calculations can be done in a model-independent way with perturbation theory for hard gluons, thanks to form factors of quark-gluon vertices that arise from the Ritus bases for quark fields. As a part of such renormalization program, we compute the renormalized quark self-energy at 1-loop, including effects from all higher orbital levels. The result indicates that the higher orbital levels cease to strongly affect the LLL at a rather small magnetic field of (0.1 - 0.3) GeV^2.