Electromagnetic Currents and Magnetic Moments in $\chi$EFT

Abstract

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.

v2: references added; corrections to text and abstract suggested by referee added

References in corpus (4)

• Covariant spectator theory of np scattering: Phase shifts obtained from precision fits to data below 350 MeV
• Improving the convergence of the chiral expansion for nuclear forces II: low phases and the deuteron
• Electromagnetic two-body currents of one- and two-pion range
• Effective field theory approach for the M1 properties of A=2 and 3 nuclei

Cited by in corpus (1)

• Two-pion exchange electromagnetic current in chiral effective field theory using the method of unitary transformation