Short-baseline neutrino oscillations and neutrinoless double- beta decay in the framework of three neutrino mixing and a mass hierarchy.

Abstract

We have analyzed the results of the latest terrestrial neutrino oscillation experiments in the framework of a model with mixing of three massive neutrinos and a neutrino mass hierarchy (${m}_{1}\ensuremath{\ll}{m}_{2}\ensuremath{\ll}{m}_{3}$). In this model, oscillations of the terrestrial neutrinos are characterized by three parameters, $\ensuremath{\Delta}{m}^{2}\ensuremath{\equiv}{m}_{3}^{2}\ensuremath{-}{m}_{1}^{2}$ and the squared moduli of the two mixing matrix elements ${U}_{e3}$ and ${U}_{\ensuremath{\mu}3}$. Using the results of disappearance experiments and solar neutrino experiments, it is shown that only two regions of possible values of ${|{U}_{e3}|}^{2}$ and ${|{U}_{\ensuremath{\mu}3}|}^{2}$ are allowed: (I) ${|{U}_{e3}|}^{2}$ and ${|{U}_{\ensuremath{\mu}3}|}^{2}$ are both small and (II) ${|{U}_{e3}|}^{2}$ is small and ${|{U}_{\ensuremath{\mu}3}|}^{2}$ is large. If the mixing parameters are in region I, ${\ensuremath{\nu}}_{\ensuremath{\mu}}\ensuremath{\leftrightarrows}{\ensuremath{\nu}}_{e}$ oscillations are suppressed. In this case the LSND indication in favor of ${\ensuremath{\nu}}_{\ensuremath{\mu}}\ensuremath{\leftrightarrows}{\ensuremath{\nu}}_{e}$ oscillations is not compatible with the negative results of all other experiments. If the mixing parameters are in region II, ${\ensuremath{\nu}}_{e}\ensuremath{\leftrightarrows}{\ensuremath{\nu}}_{\ensuremath{\tau}}$ oscillations are strongly suppressed. If massive neutrinos are Majorana particles, our analysis shows that neutrinoless double-$\ensuremath{\beta}$ decay could be observed in the experiments of the next generation only if the mixing parameters are in region I.