Constraints of Mixing Angles from Lepton Number Violating Processes

We discuss the constraints of lepton mixing angles from lepton number violating processes such as neutrinoless double beta decay, μ--e+ conversion and K decay, K-→π+μ-μ- which are allowed only if neutrinos are Majorana particles. The rates of these processes are proportional to the averaged neutrino mass defined by in the absence of right-handed weak coupling. Here a, b(j) are flavor(mass) eigenstates and Uaj is the left-handed lepton mixing matrix. We give general conditions imposed on ab in terms of mi, lepton mixing angles and CP violating phases (three phases in Majorana neutrinos). These conditions are reduced to the constraints among mi, lepton mixing angles and ab which are irrelevant to the concrete values of CP phases. Given a ab experimentally, these conditions constrain mi and the lepton mixing angles. Though these constraints are still loose except for neutrinoless double beta decay, they will become helpful through rapid improvements of experiments. By using these constraints we also derive the limits on averaged neutrino masses for μ--e+ conversion and K decay, K-→π+μ-μ-, respectively. We also present the bounds for CP phases in terms of mi, mixing angles and ab.