Implications of a very light pseudoscalar boson on lepton flavor violation

A long-lived very light pseudoscalar boson would favor lepton flavor violating transitions of charged leptons. Its implications on the l_i --> l_j \gamma \gamma, and l_i --> l_j e^+ e^- transitions are investigated. Assuming 2 m_e < m_\phi <m_\mu, it is found that the inequality B(l_i --> l_j \gamma \gamma)<B(l_i --> l_j e^+ e^-) is hold. The experimental constraints on the decays l_i --> l_j \gamma, l_i --> l_j l_k l_k, and l_i --> l_j \gamma \gamma are used to bound the \phi l_i l_j couplings.