Charge-dependent nucleon-nucleon potential from chiral effective field   theory
  We discuss charge symmetry and charge independence breaking in a chiral effective field theory approach for few-nucleon systems based on a modified Weinberg power counting. We construct a two-nucleon potential with bound and scattering states generated by means of a properly regularized Lippmann-Schwinger equation. We systematically introduce strong isospin-violating and electromagnetic operators in the theory. We use standard procedures to treat the Coulomb potential between two protons in momentum space. We present results for phase shifts in the proton-proton, the neutron-proton and the neutron-neutron systems. We discuss the various contributions to charge dependence and charge symmetry breaking observed in the nucleon-nucleon scattering lengths. 
Markus Walzl, Ulf-G. Mei{\ss}ner, Evgeny Epelbaum