Pion-photon exchange nucleon-nucleon potentials

Abstract

We calculate in chiral perturbation theory the dominant next-to-leading order correction to the $πγ$-exchange NN-potential proportional to the large isovector magnetic moment $κ_v = 4.7$ of the nucleon. The corresponding spin-spin and tensor potentials $\widetilde V_{S,T}(r)$ in coordinate space have a very simple analytical form. At long distances $r \simeq 2$ fm these potentials are of similar size (but opposite in sign) as the leading order $πγ$-exchange potentials. We consider also effects from virtual $Δ$-isobar excitation as well as other isospin-breaking contributions to the $2π$-exchange NN-potential induced by additional one-photon exchange.