Electromagnetic Currents and Magnetic Moments in $\chi$EFT

TL;DR

This paper develops a chiral effective field theory framework for two-nucleon potentials and electromagnetic currents, including pion-loop corrections and low-energy constants fitted to nucleon scattering data.

Contribution

It provides a consistent derivation of electromagnetic currents and potentials in $hi$EFT at N$^2$LO and N$^3$LO, with explicit expressions for magnetic dipole operators and renormalization details.

Findings

Derived simple expressions for M1 operators with pion loops

Fixed low-energy constants by fitting to np scattering data

Renormalized pion-loop corrections using dimensional regularization

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 $e Q$ (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.