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

Combining the large-$N_c$ expansion with the pionless effective field theory (EFT$_{\pi\hskip-0.40em /}$) expansion provides theoretical constraints on the low energy coefficients that accompany each operator in the effective theory. In EFT$_{\pi\hskip-0.40em /}$, magnetic and axial two-nucleon contact terms 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. We find a similar result for a general two-nucleon axial current that justifies the omission of one of the terms in processes such as neutrino-deuteron scattering.