Implications of a very light pseudoscalar boson on lepton flavor violation

Abstract

A long-lived very light pseudoscalar boson would favor lepton flavor violating transitions of charged leptons. Its implications on the ${l}_{i}\ensuremath{\rightarrow}{l}_{j}\ensuremath{\gamma}\ensuremath{\gamma}$ and ${l}_{i}\ensuremath{\rightarrow}{l}_{j}{e}^{+}{e}^{\ensuremath{-}}$ transitions are investigated. Assuming that $2{m}_{e}<{m}_{\ensuremath{\phi}}<{m}_{\ensuremath{\mu}}$, it is found that the inequality $B({l}_{i}\ensuremath{\rightarrow}{l}_{j}\ensuremath{\gamma}\ensuremath{\gamma})<B({l}_{i}\ensuremath{\rightarrow}{l}_{j}{e}^{+}{e}^{\ensuremath{-}})$ holds. The experimental constraints on the decays ${l}_{i}\ensuremath{\rightarrow}{l}_{j}\ensuremath{\gamma}$, ${l}_{i}\ensuremath{\rightarrow}{l}_{j}{l}_{k}{l}_{k}$, and ${l}_{i}\ensuremath{\rightarrow}{l}_{j}\ensuremath{\gamma}\ensuremath{\gamma}$ are used to bound the $\ensuremath{\phi}{l}_{i}{l}_{j}$ couplings.