We calculate at two-loop order in chiral perturbation theory the electromagnetic corrections to the two-pion exchange nucleon-nucleon interaction that is generated by the isovector spin-flip $\pi \pi \mathit{NN}$ contact-vertex proportional to the large low-energy constant $c_4\simeq 3.4{\mathrm{GeV}}^{-1}$. We find that the respective $2\pi \gamma$-exchange potentials contain sizable isospin-breaking components which reach up to −4% of corresponding isovector $2\pi$-exchange potentials. The typical values of these novel charge-independence breaking spin-spin and tensor potentials are −0.11 and 0.09 MeV, at a nucleon distance of $r=m_{\pi }^{-1}=1.4$ fm. The charge-symmetry breaking spin-spin and tensor potentials come out a factor of $2.4$ smaller. Our analytical results for these presumably dominant isospin-violating spin-spin and tensor $\mathit{NN}$-forces are in a form such that they can be easily implemented into phase-shift analyses and few-body calculations.

• Received 14 September 2006

DOI:https://doi.org/10.1103/PhysRevC.74.067001