Abstract.
We address the typical strengths of hadronic parity-violating three-nucleon interactions in “pion-less” 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, \(\ensuremath {O}(\epsilon Q^{-1})\) . The only two distinct parity-violating three-nucleon structures with one derivative mix \(\ensuremath ^2S_{\frac{1}{2}}\) and \(\ensuremath ^2P_{\frac{1}{2}}\) 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, \(\ensuremath {O}(\epsilon Q^0)\) . 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.
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Grießhammer, H.W., Schindler, M.R. On parity-violating three-nucleon interactions and the predictive power of few-nucleon EFT at very low energies. Eur. Phys. J. A 46, 73–83 (2010). https://doi.org/10.1140/epja/i2010-11017-x
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DOI: https://doi.org/10.1140/epja/i2010-11017-x