Functional renormalization group study of anomalous magnetic moment in a low energy effective theory

TL;DR

This study uses the functional renormalization group approach to analyze the dynamical generation of quark anomalous magnetic moments in a low-energy effective theory under magnetic fields, revealing flavor-dependent behaviors and consistency with experimental nucleon magnetic moments.

Contribution

It introduces a FRG-based method to compute quark AMMs dynamically, including Fierz-complete four-quark interactions, and explores their magnetic field dependence.

Findings

Quark AMMs are generated with chiral symmetry breaking.

Down quark AMM is about four times larger than up quark AMM.

Proton and neutron magnetic moments are close to experimental values at zero magnetic field.

Abstract

The quark anomalous magnetic moments (AMMs) are investigated in a 2-flavor low-energy effective theory within the functional renormalization group (FRG) approach under an external magnetic field. The Schwinger formalism is adopted for quark propagators, and Fierz-complete four-quark scatterings are self-consistently included through the renormalization group flows. We find that the quark AMMs are dynamically generated with the chiral symmetry breaking, and the magnitude of the AMM of the down quark is around 4 times larger than that of the up quark. The transverse AMMs and the longitudinal d-quark AMM monotonically decrease with the magnetic field strength, while the longitudinal u-quark AMM slightly increases with the magnetic field strength. At $B=0$, the magnetic moments of proton and neutron are computed using the constituent quark model, which are close to the experimental values.