Few active mechanisms of the0νββdecay and effective mass of Majorana neutrinos

It is well known that there exist many mechanisms that may contribute to neutrinoless double beta decay. By exploiting the fact that the associated nuclear matrix elements are target dependent we show that, given definite experimental results on a sufficient number of targets, one can determine or sufficiently constrain all lepton violating parameters including the mass term. As a specific example we show that, assuming the observation of the $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ decay in three different nuclei, e.g., $\mathrm{G}^{76}\mathrm{e}$, $^{100}\mathrm{Mo}$, and $^{130}\mathrm{Te}$, and just three lepton number violating mechanisms (light- and heavy-neutrino mass mechanisms as well as the $R$-parity breaking supersymmetry mechanism) being active, there are only four different solutions for the lepton violating parameters, provided that they are relatively real. In particular, our analysis shows that the effective neutrino Majorana mass $|{m}_{\ensuremath{\beta}\ensuremath{\beta}}|$ can be almost uniquely extracted by utilizing other existing constraints (cosmological observations and tritium $\ensuremath{\beta}$-decay experiments). We also point out the possibility that the nonobservation of the $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ decay for some isotopes could be in agreement with a value of $|{m}_{\ensuremath{\beta}\ensuremath{\beta}}|$ in the sub-eV region. We thus suggest that it is important to have at least two different $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$-decay experiments for a given nucleus. We note that obtained results are sensitive to the accuracy of measured half-lives and to uncertainties in calculated nuclear matrix elements.