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 sizable 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 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.

• Received 29 March 2006

DOI:https://doi.org/10.1103/PhysRevC.73.064003