On parity-violating three-nucleon interactions and the predictive power of few-nucleon EFT at very low energies |
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Authors: | H?W?Grie?hammer M?R?Schindler |
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Institution: | 1.Center for Nuclear Studies, Department of Physics,The George Washington University,Washington,USA |
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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, O(eQ-1)\ensuremath {O}(\epsilon Q^{-1}) . The only two distinct parity-violating three-nucleon structures with one derivative mix
2S\frac12\ensuremath ^2S_{\frac{1}{2}} and
2P\frac12\ensuremath ^2P_{\frac{1}{2}} waves with iso-spin transitions D \Delta
I = 0 or 1. Due to their structure, they cannot absorb any divergence ostensibly appearing at next-to-leading order, O(eQ0)\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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Keywords: | |
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