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

Abstract

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