Neutrinoless double beta decay and chiral $SU(3)$

Abstract

TeV-scale lepton number violation can affect neutrinoless double beta decay through dimension-9 $\Delta L=\Delta I=2$ operators involving two electrons and four quarks. Since the dominant effects within a nucleus are expected to arise from pion exchange, the ${\pi }^{-}\to {\pi }^{+}ee$ matrix elements of the dimension-9 operators are a key hadronic input. In this letter we provide estimates for the ${\pi }^{-}\to {\pi }^{+}$ matrix elements of all Lorentz scalar $\Delta I=2$ four-quark operators relevant to the study of TeV-scale lepton number violation. The analysis is based on chiral $SU(3)$ symmetry, which relates the ${\pi }^{-}\to {\pi }^{+}$ matrix elements of the $\Delta I=2$ operators to the $K^0\to {\bar{K}}^0$ and $K\to \pi \pi$ matrix elements of their $\Delta S=2$ and $\Delta S=1$ chiral partners, for which lattice QCD input is available. The inclusion of next-to-leading order chiral loop corrections to all symmetry relations used in the analysis makes our results robust at the $30\%$ level or better, depending on the operator.

9 pages

References in corpus (5)

• Big-Bang Nucleosynthesis
• Leptogenesis
• Limit on Neutrinoless ββ Decay of Xe-136 from the First Phase of KamLAND-Zen and Comparison with the Positive Claim in Ge-76
• $K\to \pi \pi$ $\Delta I=3/2$ decay amplitude in the continuum limit
• Neutral kaon mixing beyond the standard model with nf=2+1 chiral fermions

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