How to interpret a discovery or null result of the \(0\nu 2\beta\) decay

Abstract

The Majorana nature of massive neutrinos will be crucially probed in the next-generation experiments of the neutrinoless double-beta (\(0\nu 2\beta\)) decay. The effective mass term of this process, \(\langle m\rangle^{}_{ee}\), may be contaminated by new physics. So how to interpret a discovery or null result of the \(0\nu 2\beta\) decay in the foreseeable future is highly nontrivial. In this paper we introduce a novel three-dimensional description of \(|\langle m\rangle_{ee}^{}|\), which allows us to see its sensitivity to the lightest neutrino mass and two Majorana phases in a transparent way. We take a look at to what extent the free parameters of \(|\langle m\rangle_{ee}^{}|\) can be well constrained provided a signal of the \(0\nu 2\beta\) decay is observed someday. To fully explore lepton number violation, all the six effective Majorana mass terms \(\langle m\rangle_{\alpha\beta}^{}\) (for \(\alpha, \beta = e, \mu, \tau\)) are calculated and their lower bounds are illustrated with the two-dimensional contour figures. The effect of possible new physics on the \(0\nu 2\beta\) decay is also discussed in a model-independent way. We find that the result of \(|\langle m\rangle_{ee}^{}|\) in the normal (or inverted) neutrino mass ordering case modified by the new physics effect may somewhat mimic that in the inverted (or normal) mass ordering case in the standard three-flavor scheme. Hence a proper interpretation of a discovery or null result of the \(0\nu 2\beta\) decay may demand extra information from some other measurements.