Lepton flavour violating pion decay pi^+ --> mu^- nu_μ e^+ e^+ and the SU(3)_C X SU(3)_L X U(1) model

In the framework of the minimal ${SU}(3)_C\otimes {SU}(3)_L \otimes {U}(1)_N$ model, the lepton-flavour-violating decay $\pi^+ \ra \mu^- \nu_\mu e^+ e^+ $ is calculated without directly invoking lepton mixing. The branching ratio for this rare pion decay mode is found to be much smaller than the current experimental upper limit. Dropping out anomalous interactions, this result coincides with the previous calculation .