The symmetries of the standard model dictate that for very low energies, where nucleon dynamics can be described in terms of a pionless effective field theory $(\text{EFT}\left(\pi /\right))$, the leading-order parity-violating nucleon-nucleon Lagrangian contains five independent unknown low-energy constants (LECs). We find that imposing the approximate symmetry of QCD that appears when the number of colors $N_c$ becomes large reduces the number of independent LECs to two at leading order in the combined $\text{EFT}\left(\pi /\right)$ and large-$N_c$ expansions. We also find a relation between the two isoscalar LECs in the large-$N_c$ limit. This has important implications for the number of experiments and/or lattice calculations necessary to confirm this description of physics. In particular, we find that a future measurement of the parity-violating asymmetry in $\vec{\gamma }d\to np$ together with the existing result for parity-violating $\vec{p}p$ scattering would constrain all leading-order (in the combined expansion) LECs. This is a considerable improvement on the previous understanding of the system.

• Received 30 October 2015

DOI:https://doi.org/10.1103/PhysRevC.93.025502