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

TL;DR

This paper demonstrates that parity-violating three-nucleon interactions are absent at leading order in pion-less EFT for nucleon-deuteron systems and only appear at higher orders, simplifying the theory's predictive power.

Contribution

It shows that parity-violating three-nucleon interactions are not needed at leading order in pion-less EFT, ensuring renormalizability and enabling extraction of two-nucleon interactions from three-nucleon data.

Findings

No parity-violating three-nucleon interactions at leading order.

Such interactions only appear beyond next-to-leading order.

The theory remains renormalizable without additional couplings.

Abstract

We address the typical strengths of hadronic parity-violating three-nucleon interactions in "pion-less" Effective Field Theory 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. The only two linearly independent parity-violating three-nucleon structures with one derivative mix two-S and two-P-half 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. 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.