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Register a new userTentative sensitivity of future $0 u betabeta$-decay experiments to neutrino masses and Majorana CP phases
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In the near future, the neutrinoless double-beta ($0 ubetabeta$) decay experiments will hopefully reach the sensitivity of a few ${rm meV}$ to the effective neutrino mass $|m^{}_{betabeta}|$. In this paper, we tentatively examine the sensitivity of future $0 ubetabeta$-decay experiments to neutrino masses and Majorana CP phases by following the Bayesian statistical approach. Provided experimental setups corresponding to the sensitivity of $|m^{}_{betabeta}| simeq 1~{rm meV}$, the null observation of $0 ubetabeta$ decays in the case of normal neutrino mass ordering leads to a very competitive bound on the lightest neutrino mass $m^{}_1$. Namely, the $95%$ credible interval turns out to be $1.6~{rm meV} lesssim m^{}_1 lesssim 7.3~{rm meV}$ or $0.3~{rm meV} lesssim m^{}_1 lesssim 5.6~{rm meV}$ when the uniform prior on $m^{}_1/{rm eV}$ or on $log^{}_{10}(m^{}_1/{rm eV})$ is adopted. Moreover, one of two Majorana CP phases is strictly constrained, i.e., $140^circ lesssim rho lesssim 220^circ$ for both priors of $m^{}_1$. In contrast, if a relatively worse sensitivity of $|m^{}_{betabeta}| simeq 10~{rm meV}$ is assumed, the constraint becomes accordingly $0.6~{rm meV} lesssim m^{}_1 lesssim 26~{rm meV}$ or $0 lesssim m^{}_1 lesssim 6.1~{rm meV}$, while two Majorana CP phases will be essentially unconstrained. In the same statistical framework, the prospects for the determination of neutrino mass ordering and the discrimination between Majorana and Dirac nature of massive neutrinos in the $0 ubetabeta$-decay experiments are also discussed. Given the experimental sensitivity of $|m^{}_{betabeta}| simeq 10~{rm meV}$ (or $1~{rm meV}$), the strength of evidence to exclude the Majorana nature under the null observation of $0 ubetabeta$ decays is found to be inconclusive (or strong), no matter which of two priors on $m^{}_1$ is taken.
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We consider the possibility of several different mechanisms contributing to the $betabeta$-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 $betabeta$-decay is induced by, e.g., two non-interfering mechanisms, one can determine $|eta_i|^2$ and $|eta_j|^2$, $eta_i$ 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 $betabeta$-decay, $|eta_i|^2$ and $|eta_j|^2$ 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 $|eta_i|^2geq 0$ and $|eta_j|^2geq 0$ lead to stringent constraints on the half-lives of the other $betabeta$-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 $betabeta$-decay mechanisms. It allows to treat the cases of CP conserving and CP nonconserving couplings generating the $betabeta$-decay in a unique way.
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