Background field approach to electromagnetic properties of baryons

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 $Δ(1232)$-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.

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