Electromagnetic corrections to the dominant two-pion exchange nucleon-nucleon potential

Abstract

We calculate at two-loop order in chiral perturbation theory the electromagnetic corrections to the dominant two-pion exchange nucleon-nucleon interaction that is generated by the isoscalar $\ensuremath{\pi}N$ contact-vertex proportional to the large low-energy constant ${c}_{3}$. We find that the respective $2\ensuremath{\pi}\ensuremath{\gamma}$-exchange potential contains sizable isospin-breaking components which amount to about $\ensuremath{-}1%$ of the strongly attractive isoscalar central $2\ensuremath{\pi}$-exchange potential. The typical value of these novel charge-independence and charge-symmetry breaking central potentials is 0.3 MeV at a nucleon distance of $r={m}_{\ensuremath{\pi}}^{\ensuremath{-}1}=1.4$ fm. Our analytical result for this dominant $2\ensuremath{\pi}\ensuremath{\gamma}$-exchange interaction is in a form such that it can be easily implemented into phase-shift analyses and few-body calculations.