Large-Nclimit reduces the number of independent few-body parity-violating low-energy constants in pionless effective field theory

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 (EFT(π-0.5em0ex/)), 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 Nc becomes large reduces the number of independent LECs to two at leading order in the combined EFT(π-0.5em0ex/) and large-Nc expansions. We also find a relation between the two isoscalar LECs in the large-Nc 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 Pγd→np together with the existing result for parity-violating Ppp scattering would constrain all leading-order (in the combined expansion) LECs. This is a considerable improvement on the previous understanding of the system.