On the CP violation associated with Majorana neutrinos and neutrinoless double-beta decay

Assuming 3-ν mixing and massive Majorana neutrinos, we analyze the possibility of establishing the existence of CP violation associated with Majorana neutrinos in the lepton sector by (i) measuring of the effective Majorana mass |〈m〉| in neutrinoless double beta decay with a sufficient precision and (ii) by measuring of, or obtaining a stringent upper limit on, the lightest neutrino mass m1. Information on m1 can be obtained in the 3H β-decay experiment KATRIN and from astrophysical and cosmological observations. Proving that the indicated CP violation takes place requires, in particular, a relative experimental error on the measured value of |〈m〉| not bigger than 20%, a “theoretical uncertainty” in the value of |〈m〉| due to an imprecise knowledge of the corresponding nuclear matrix elements smaller than a factor of 2, a value of tan2θ⊙≳0.55, and values of the relevant Majorana CP-violating phases typically within the intervals of ∼(π2–3π4) and ∼(5π4–3π2). In the case of, e.g., quasi-degenerate neutrino mass spectrum it requires also that the neutrino masses have values not smaller than ∼0.7 eV.