Background field approach to electromagnetic properties of baryons

TL;DR

This paper studies how external magnetic fields affect baryon self-energies, highlighting the importance of non-analytic points and finite volume corrections, with implications for lattice QCD and chiral perturbation theory.

Contribution

It introduces a background field approach to compute electromagnetic properties of baryons, including finite volume corrections, within covariant chiral perturbation theory.

Findings

Self-energies depend on magnetic field with non-analytic points.

Finite volume corrections can explain discrepancies in lattice QCD.

Linear energy shift approximation is constrained for resonances.

Abstract

We investigate the self-energies of particles in an external magnetic field $B$. The dependence is generally of the type $\sqrt{P(B)}$ with $P$ a polynomial in $B$ and the participating masses. The non-analytic point depends on the mass and charge constellations, is unproblematic for stable particles but constrains the linear energy shift approximation for resonances. We calculate the $B$ dependent self-energies of the nucleon and $\Delta(1232)$-isobar in the SU(2) covariant chiral perturbation theory and outline a way to obtain finite volume corrections to the nucleon anomalous magnetic moment without using the three point function method. We show that finite volume corrections might explain present discrepancies of lattice QCD and chiral perturbation theory results in the small pion mass region.