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

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 $\pi N$ contact-vertex proportional to the large low-energy constant $c_3$. We find that the respective $2\pi\gamma$-exchange potential contains sizeable isospin-breaking components which amount to about -1% of the strongly attractive isoscalar central $2\pi$-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_\pi^{-1} = 1.4 $fm. Our analytical result for this presumably dominant $2\pi\gamma$-exchange interaction is in a form such that it can be easily implemented into phase-shift analyses and few-body calculations.