Double beta decays and Majorana neutrinos - Majorana neutrino masses and neutrino-less double beta decays

Neutrino-less double beta decays (0 nu beta beta) are sensitive and realistic probes for studying the Majorana nature of neutrinos (nu), the nu-mass spectrum, the absolute.-mass scale, the Majorana CP phases and other fundamental properties of neutrinos and weak interactions. Current 0 nu beta beta experiments, which use detectors with the mass sensitivity of the order of 300 meV, study the nu-mass in that mass region. Future experiments with higher sensitivities of the orders of 100meV and 30 meV, using different nuclei and methods (calorimetric, spectroscopic), are indispensable for establishing 0 nu beta beta in the quasi degenerate and the inverted hierarchy mass regions. R&D for ultra-high sensitivity detectors are encouraged for studying the normal hierarchy mass region. Theoretical and experimental studies for evaluating nuclear matrix elements are important for extracting the sensible.-mass from the 0 nu beta beta rate. Charge exchange reactions by means of nuclear, electromagnetic and. probes provide valuable data which are used to evaluate the nuclear matrix elenments. International collaborations for 0 nu beta beta experiments and for the matrix elements are crucial for next generation 0 nu beta beta studies.