Short-baseline neutrino oscillations and neutrinoless double-beta decay   in the framework of three neutrino mixing and a mass hierarchy
  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 << m_2 << m_3 $). In this model, oscillations of the terrestrial neutrinos are characterized by three parameters, $ \Delta m^2 = m_3^2 - m_1^2 $ and the squared moduli of the two mixing matrix elements $U_{e3}$ and $U_{\mu3}$. 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 $|U_{\mu3}|^2$ are allowed: I. $|U_{e3}|^2$ and $|U_{\mu3}|^2$ are both small and II. $|U_{e3}|^2$ is small and $|U_{\mu3}|^2$ is large. If the mixing parameters are in the region I, $ \nu_\mu <-> \nu_e $ oscillations are suppressed. In this case the LSND indication in favor of $ \nu_\mu <-> \nu_e $ oscillations is not compatible with the negative results of all other experiments. If the mixing parameters are in the region II, $ \nu_e <-> \nu_\tau $ oscillations are strongly suppressed. If massive neutrinos are Majorana particles, our analysis shows that neutrinoless double-beta decay could be observed in the experiments of the next generation only if the mixing parameters are in the region I. 
S.M. Bilenky, A. Bottino, C. Giunti and C. W. Kim