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

Abstract

The parity-violating (PV) nucleon-nucleon (NN ) interaction in the three-nucleon system is investigated using pionless effective field theory (EFT(/ π)). This work shows that a next-to-leading order (NLO) PV three-body force is necessary in contradiction with a previous claim [1]. 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(/ π) the current understanding of low energy PV few-body measurements is reassessed. The recent measurement of the asymmetry A γ in np → dγ from the NPDGamma collaboration [2] gives the value g (N −1 C ) 4 * jvanasse@stetson.edu arXiv:1809.10740v2 [nucl-th] 12 May 2019 PV PV PV PV PV PC PC PC PC PV FIG. 2. Coupled integral equations for the LO PV scattering amplitude. The green box represents an insertion of a two-body PV LEC and the yellow oval the LO PV scattering amplitude. Some diagrams only exist in certain channels with the LO three-body force only existing if the outgoing partial wave is 2 S1 /2 . the integral equation t PV J L S ,LS 1 2 1 −1 1 1 K PV J L S ,LS (k, p, E) t PV J LS,L S (k, q, E) T ⊗ D NLO (E, q) t PC J LS,LS (k, q, E) + t PC J L S ,L S (k, q, E) T ⊗ D NLO (E, q) t PV J L S ,LS (k, q, E)

Combining the large-$N_{C}$ and low-momentum expansions to describe parity violation in few-nucleon systems

“…current experimental data and the predicted large-N C scaling [37]. This work also shows that a NLO (in EFT(/ π)) PV three-nucleon force is necessary in contradiction with earlier claims [38].…”

Parity- and time-reversal-violating nuclear forces

“…[48,47]. These studies suggest that three out of five PVTC contact interactions are suppressed by a factor of (1/N c ) 2 or by the factor sin 2 θ W ≈ 0.23, see also a related discussion in [49]. If the large-N c scaling persists to the physically relevant case of N c = 3, the pionless potential at LO should be dominated by only 2 LECs [39].…”

Parity- and Time-Reversal-Violating Nuclear Forces

“…The advantage of this framework is related to the fact that the resulting potentials depends on only five LECs. Then, assuming the validity of the large N c analysis [47,49], the number of dominant LECs could be further reduced. This new paradigm is advocated for the PVTC case in Gardner et al [39].…”

“…The large-N c scaling of PVTC NN contact interactions was analyzed in Phillips et al [48] and Schindler et al [47]. These studies suggest that three out of five PVTC contact interactions are suppressed by a factor of (1/N c ) 2 or by the factor (1/N c ) sin 2 θ W ≈ 0.08, see also a related discussion in Vanasse [49]. If the large-N c scaling persists to the physically relevant case of N c = 3, the pionless potential at LO should be dominated by only 2 LECs [39].…”