Analysis of Two-Nucleon Magnetic and Axial Currents in a Combined Large-$N_c$ and Pionless Effective Field Theory Expansion

The combined large-$N_c$ and pionless effective field theory (EFT$_{\pi\hskip-0.40em /}$) expansion places theoretical constraints on low energy coefficients that accompany the operators of the effective theory. We obtain constraints from this framework for magnetic and axial two-nucleon contact terms. These operators contribute to a variety of electroweak processes such as the deuteron magnetic moment, radiative neutron capture, and proton-proton fusion. The large-$N_c$ expansion indicates that the isoscalar magnetic coupling is suppressed relative to the isovector coupling, which offers a partial explanation of the suppression found in data. A similar result holds for the general two-nucleon axial current which adds support for the previous omission of the isoscalar operator in processes such as neutrino-deuteron scattering. The results also imply that naturalness assumptions may be hidden depending on the choice of basis.