Electromagnetic Currents and Magnetic Moments in $\chi$EFT

A two-nucleon potential and consistent electromagnetic currents are derived in chiral effective field theory ($\chi$EFT) at, respectively, $Q^2$ (or N${}^2$LO) and $eQ$ (or N${}^3$LO), 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 (LEC’s) entering the N${}^2$LO potential are fixed by fits to the $np$ S- and P-wave phase shifts up to 100 MeV lab energies.