How to interpret a discovery or null result of the 0ν2β0\nu 2\beta decay

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.Comment: 13 pages, 6 figures, Figures and references update

[(1S,2S,3R,4R)-3-Hydr­oxy-4,7,7-tri­methyl­bicyclo­[2.2.1]heptan-2-yl]methyl[(E)-3-(trimethyl­silyl)prop-2-enyl]selen­onium bromide

The title compound, a seleno­nium bromide, C17H33OSeSi+·Br−, was obtained from the reaction of enanti­omerically pure 4,7,7-trimethyl-2-methyl­selanylbicyclo­[2.2.1]heptan-3-ol and (3-bromopropen­yl)trimethyl­silane in acetone. Due to the chiral bicyclic substituent, the crystal structure is not centrosymmetric and has no symmetry plane, with four chiral C atoms in the cation. The asymmetric unit contains one seleno­nium cation and one bromide anion. C–H⋯Br and O–H⋯Br hydrogen bonds link the ions, forming a one-dimensional R-helical chain-like supra­molecular structure