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, $⟨m{⟩}_{ee}^{}$, 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 $|⟨m{⟩}_{ee}^{}|$, 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 $|⟨m{⟩}_{ee}^{}|$ 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 $⟨m{⟩}_{\alpha \beta }^{}$ (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 $|⟨m{⟩}_{ee}^{}|$ 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.

13 pages, 6 figures, Figures and references updated

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