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The European Physical Journal A

, Volume 46, Issue 1, pp 73–83 | Cite as

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

  • H. W. Grießhammer
  • M. R. Schindler
Regular Article - Theoretical Physics

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.

Keywords

Strong Sector 
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Copyright information

© SIF, Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • H. W. Grießhammer
    • 1
  • M. R. Schindler
    • 1
  1. 1.Center for Nuclear Studies, Department of PhysicsThe George Washington UniversityWashingtonUSA

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