Electromagnetic currents and magnetic moments in chiral effective field theory (χEFT)

A two-nucleon potential and consistent electromagnetic currents are derived in chiral effective field theory (χEFT) at, respectively, Q² (or N²LO) and eQ (or N³LO), where Q generically denotes the low-momentum scale and e is the electric charge. Dimensional regularization is used to renormalize the pion-loop corrections. A simple expression is derived for the magnetic dipole (M1) operator associated with pion loops, consisting of two terms, one of which is determined, uniquely, by the isospin-dependent part of the two-pion-exchange potential. This decomposition is also carried out for the M1 operator arising from contact currents, in which the unique term is determined by the contact potential. Finally, the low-energy constants entering the N²LO potential are fixed by fits to the np S- and P-wave phase shifts up to 100 MeV laboratory energies.