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We address the typical strengths of hadronic parity-violating three-nucleoninteractions in "pion-less" Effective Field Theory in the nucleon-deuteron(iso-doublet) system. By analysing the superficial degree of divergence of loopdiagrams, we conclude that no such interactions are needed at leading order.The only two linearly independent parity-violating three-nucleon structureswith one derivative mix two-S and two-P-half waves with iso-spin transitionsDelta I = 0 or 1. Due to their structure, they cannot absorb any divergenceostensibly appearing at next-to-leading order. This observation is based on theapproximate realisation of Wigner's combined SU(4) spin-isospin symmetry in thetwo-nucleon system, even when effective-range corrections are included.Parity-violating three-nucleon interactions thus only appear beyondnext-to-leading order. This guarantees renormalisability of the theory to thatorder without introducing new, unknown coupling constants and allows the directextraction of parity-violating two-nucleon interactions from three-nucleonexperiments.

On Parity-Violating Three-Nucleon Interactions and the Predictive Power of Few-Nucleon EFT at Very Low Energies