K$_{Le5}$ decay as a background in search for K$_{L}$ --> $\pi^{0}$ $\mu^{\pm}$e$^{\mp}$

We consider a process K_{L e5} ( K_{L} \rightarrow \pi^{0} \pi^{0} \pi^{\pm} e^{\mp} \nu ) as a standard model background to the experiment K_{L} \rightarrow \pi^{0} \mu^{\pm} e^{\mp}, which seeks for possible violation of lepton family number. Using the lowest order chiral lagrangian, we find that the branching ratio for K_{L} \rightarrow \pi^{0} \pi^{0} \pi^{\pm} e^{\mp} \nu to be 1.1 \times 10^{-9}. A similar decay K_{L} \rightarrow \pi^{\mp} \pi{\mp} \pi^{\pm} e^{\pm} \nu has a rather large branching ratio, 1.5 \times 10^{-8}