Parity-violating three-nucleon interactions at low energies and large NC

The parity-violating (PV) nucleon-nucleon (NN) interaction in the three-nucleon system is investigated using pionless effective field theory (EFT((sic))). This work shows that a next-to-leading order (NLO) PV three-body force is necessary in contradiction with a previous claim [H. W. Griesshammer and M. R. Schindler in Eur. Phys. J. A 46, 73 (2010)]. Including three-body P- to D-wave transitions PV three-nucleon observables are calculated to higher energies than previously considered. Using the recent large-N-C analysis of the PV NN interaction in EFT((sic)) the current understanding of low energy PV few-body measurements is reassessed. The recent measurement of the asymmetry A gamma in (n) over right arrow p -> d gamma from the NPDGamma collaboration [D. Blyth et al. (NPDGamma), Phys. Rev. Lett. 121, 242002 (2018)], gives the value g(4)((NC-1)) = [-1.4 +/- 0.63(stat.) +/- 0.09(syst.)] x 10(-10) MeV-1 for a next-to-next-to-leading order ((NLO)-L-2) in large-N-C low energy constant (LEC). Using the large-N-C hierarchy of LECs the sizes of the leading order (LO) in large-N-C LECs are estimated using an experimental bound on a parity violating asymmetry in (p) over right arrowd scattering at E-lab = 15 MeV and a measurement of (p) over right arrowp scattering at E-lab = 13.6 MeV. Comparing the size of the resulting LO(O(N-C)) in large-N-C LECs to the (NLO)-L-2(O(N-C(-1))) in large-N-C LEC g(4)((NC-1)) shows they are roughly the same size in contradiction with current large-N-C counting.