Abstract
TeV-scale lepton number violation can affect neutrinoless double beta decay through dimension-9 ΔL=ΔI=2 operators involving two electrons and four quarks. Since the dominant effects within a nucleus are expected to arise from pion exchange, the π−→π+ee matrix elements of the dimension-9 operators are a key hadronic input. In this letter we provide estimates for the π−→π+ matrix elements of all Lorentz scalar ΔI=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 π−→π+ matrix elements of the ΔI=2 operators to the K0→K¯0 and K→ππ matrix elements of their ΔS=2 and ΔS=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.
Highlights
To interpret positive or null 0νββ results in the context of TeV-scale lepton number violation (LNV) dynamics, it is essential to quantify the hadronic and nuclear matrix elements involving the ∆L = 2 dimension9 operators
TeV-scale lepton number violation can affect neutrinoless double beta decay through dimension-9 ∆L = ∆I = 2 operators involving two electrons and four quarks
Since lepton number is conserved in the Standard Model (SM) at the classical level, observation of 0νββ would be direct evidence of new physics, with far reaching implications: it would demonstrate that neutrinos are Majorana fermions [1], shed light on the mechanism of neutrino mass generation, and probe lepton number violation (LNV), a key ingredient needed to generate the matter-antimatter asymmetry in the universe via “leptogenesis” [2]
Summary
To interpret positive or null 0νββ results in the context of TeV-scale LNV dynamics, it is essential to quantify the hadronic and nuclear matrix elements involving the ∆L = 2 dimension9 operators. We provide estimates for the π− → π+ matrix elements of O2,...,5 by relating them to the K0 → K 0 matrix elements of their ∆S = 2 chiral partners, which have been computed by several lattice QCD groups [20,21,22,23,24]. By including the leading chiral loop corrections, we are able to estimate the uncertainty on the symmetry relations, finding that it does not exceed 30%.
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