Majorana neutrino masses, neutrinoless double beta decay, and nuclear matrix elements

The effective Majorana neutrino mass $m_{\beta \beta }$ is evaluated by using the latest results of neutrino oscillation experiments. The problems of the neutrino mixing pattern, the absolute mass scale of neutrinos, and the effect of CP phases are addressed. A connection to the next generation of neutrinoless double beta decay $(0\mathrm{}\nu \beta \beta$ decay) experiments is discussed. The calculations are performed for ${}^{76}\mathrm{Ge},$ ${}^{100}\mathrm{Mo},$ ${}^{136}\mathrm{Xe},$ and ${}^{130}\mathrm{Te}$ by using the advantage of recently evaluated nuclear matrix elements with significantly reduced theoretical uncertainty. The importance of observation of the $0\nu \beta \beta$ decay of several nuclei is stressed.