Abstract
We revisit the "interpolating formula" proposed in our previous publication. It allows one to calculate the neutrinoless double beta decay ($0\nu\beta\beta$-decay) half-life for arbitrary neutrino mass without involvement of the complicated results for nuclear matrix elements (NME) obtained within specific nuclear structure models. The formula derives from the finding that the value of a properly normalized ratio of the NMEs for the light and heavy neutrino mass mechanisms weakly depends on isotope. From this fact it follows, in particular, that the light and heavy neutrino mass mechanisms can hardly be distinguished in a model independent way searching for $0\nu\beta\beta$-decay of different nuclei. Here we show that this formula holds for all the known nuclear structure approaches. We give a mathematical justification of our results examining analytical properties of the NMEs. We also consider several simplified benchmark scenarios within left-right symmetric models and analyze the conditions for the dominance of the light or heavy neutrino mass mechanisms in $0\nu\beta\beta$-decay.
Highlights
INTRODUCTIONThere are two sources of leptonnumber violation: Majorana neutrino mass and lepton number–violating (LNV) vertices
Neutrinoless double-beta decay (0νββ) is a lepton number–violating (LNV) process changing the lepton number by two units ΔL 1⁄4 2
The formula derives from the finding that the value of a properly normalized ratio of the nuclear matrix elements (NMEs) for the light and heavy neutrino mass mechanisms weakly depends on the isotope
Summary
There are two sources of leptonnumber violation: Majorana neutrino mass and LNV vertices The latter may emerge from numerous high-scale models giving rise to the corresponding mechanisms of 0νββ decay. Once this process is observed, the question of distinguishing between the dominant mechanisms will arise. The IntF is a simple analytical formula representing with an accuracy of 30% or better the NME as a function of the Majorana neutrino mass. This accuracy is sufficient for practical purposes, taking into account the limited accuracy of the available nuclear structure approaches to the NME calculations. For the sake of concreteness, we consider the neutrino mass mechanism within the left-right symmetric models (LRSMs) [2,3] and extend our analysis toward some more particular scenarios
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