Constraints of Mixing Angles from Lepton Number Violating Processes

Abstract

We discuss the constraints of lepton mixing angles from lepton number violating processes such as neutrinoless double beta decay, (\mu^-)-(e^+) conversion and K decay, $K^- \to \pi^+\mu^-\mu^-$ which are allowed only if neutrinos are Majorana particles. The rates of these processes are proportional to the averaged neutrino mass defined by $<m_{\nu} >_{a b}\equiv |\sum_{j=1}^{3}U_{a j} U_{b j}m_j|$ in the absence of right-handed weak coupling. Here $a, b (j)$ are flavour(mass) eigen states and $U_{a j}$ is the left-handed lepton mixing matrix. We obtain the consistency conditions which are satisfied irrelevant to the concrete values of CP violation phases (three phases in Majorana neutrinos). These conditions constrain the lepton mixing angles, neutrino masses $m_i$ and (< m_{\nu} >_{a b}). By using these constraints we obtain the limits on the averaged neutrino masses for (\mu^-)-(e^+) conversion and K decay, $K^- \to \pi^+\mu^-\mu^-$.