Majorana neutrinos, neutrino mass spectrum, CP violation, and neutrinoless double β decay. II. Mixing of four neutrinos

Assuming four-neutrino mixing and massive Majorana neutrinos, we study the implications of neutrino oscillation solutions of the solar and atmospheric neutrino problems, of the results of the Liquid Scintillation Neutrino Detector (LSND) experiment and of the constraints on neutrino oscillations, obtained in reactor and accelerator experiments, for the predictions of the effective Majorana mass in neutrinoless double beta $\left(\right(\beta \beta {)}_{0\nu }-)$ decay, |〈m〉|. All four-neutrino mass spectra compatible with the existing neutrino mass and oscillation data are considered: $2+2A,B$ and $3+1A,B,C.$ The general case of CP nonconservation is investigated. The predicted values of |〈m〉| depend strongly on the value of the lightest neutrino mass $m_1,$ on the type of the neutrino mass spectrum, on the LSND neutrino mass-squared difference $\Delta m_{\mathrm{SBL}}^2,$ on the solution of the solar neutrino problem, as well as on the values of the three Majorana CP-violating phases, present in the lepton mixing matrix. If CP invariance holds, |〈m〉| is very sensitive to the values of the relative CP parities of the massive Majorana neutrinos. We also analyze in detail the question of whether a measurement of $|〈m〉|\gtrsim 0.01\mathrm{eV}$ in the next generation of $(\beta \beta {)}_{0\nu }$-decay experiments (NEMO3, CUORE, EXO, and GENIUS), combined with the data from the solar, atmospheric, reactor and accelerator neutrino oscillation experiments and from the future neutrino mass ${}^3\mathrm{H}$ β-decay experiment KATRIN would allow us, and under what conditions, (i) to determine the absolute values of the neutrino masses and thus the neutrino mass spectrum, and (ii) to establish the existence of CP violation in the lepton sector. We have pointed out, in particular, that the $2+2A$ and $3+1A$ spectra can be critically tested by the KATRIN experiment. The latter, in particular, can provide information on the value of the lightest neutrino mass $m_1$ in the cases of the spectra $2+2A,$ $3+1A,$ $3+1B,$ and $3+1C.$ For these neutrino mass spectra there exists a direct relation between |〈m〉| or $m_1$ and the neutrino mass measured in ${}^3\mathrm{H}$ β decay, $m_{{\nu }_e},$ and the measurement of $|〈m〉|\gtrsim 0.01\mathrm{eV}$ and of $m_{{\nu }_e}\gtrsim 0.4\mathrm{eV}$ will provide the unique possibility to determine the absolute values of all four neutrino masses and to obtain information on CP violation in the lepton sector.