On parity-violating three-nucleon interactions and the predictive power of few-nucleon EFT at very low energies

We address the typical strengths of hadronic parity-violating three-nucleon interactions in "pionless" Effective Field Theory (EFT) in the nucleon-deuteron (iso-doublet) system. By analysing the superficial degree of divergence of loop diagrams, we conclude that no such interactions are needed at leading order, O(epsilon Q(-1)). The only two distinct parity-violating three-nucleon structures with one derivative mix (2)S(1/2) and (2)P(1/2) waves with iso-spin transitions Delta I = 0 or 1. Due to their structure, they cannot absorb any divergence ostensibly appearing at next-to-leading order, O(epsilon Q(0)). This observation is based on the approximate realisation of Wigner's combined SU(4) spin-isospin symmetry in the two-nucleon system, even when effective-range corrections are included. Parity-violating three-nucleon interactions thus only appear beyond next-to-leading order. This guarantees renormalisability of the theory to that order without introducing new, unknown coupling constants and allows the direct extraction of parity-violating two-nucleon interactions from three-nucleon experiments.