Uncovering Multiple CP-Nonconserving Mechanisms of $\text{betabeta}$-Decay

We consider the possibility of several different mechanisms contributing to the $\text{betabeta}$-decay amplitude in the general case of CP nonconservation: light Majorana neutrino exchange, heavy left-handed (LH) and heavy right-handed (RH) Majorana neutrino exchanges, lepton charge non-conserving couplings in SUSY theories with R-parity breaking. If the $\text{betabeta}$-decay is induced by, e.g., two “non-interfering” mechanisms, one can determine $\mathrm{\mid }{\eta }_i{\mathrm{\mid }}^2$ and $\mathrm{\mid }{\eta }_j{\mathrm{\mid }}^2$, ${\eta }_i$ and ${\eta }_j$ being the two fundamental parameters characterising these mechanisms, from data on the half-lives of two nuclear isotopes. In the case when two “interfering” mechanisms are responsible for the $\text{betabeta}$-decay, $\mathrm{\mid }{\eta }_i{\mathrm{\mid }}^2$ and $\mathrm{\mid }{\eta }_j{\mathrm{\mid }}^2$ and the interference term can be uniquely determined, in principle, from data on the half-lives of three nuclei. Given the half-life of one isotope, the “positivity conditions” $\mathrm{\mid }{\eta }_i{\mathrm{\mid }}^2\ge 0$ and $\mathrm{\mid }{\eta }_j{\mathrm{\mid }}^2\ge 0$ lead to stringent constraints on the half-lives of the other $\text{betabeta}$-decaying isotopes. These conditions, as well as the conditions for constructive (destructive) interference are derived and their implications are analysed in two specific cases. The method considered by us can be generalised to the case of more than two $\text{betabeta}$-decay mechanisms. It allows to treat the cases of CP conserving and CP nonconserving couplings generating the $\text{betabeta}$-decay in a unique way.