$K_{L e5}$ decay as a background in search for $K_{L} \to π^{0} μ^{\pm} e^{\mp}$

We consider a process $K_{L e5} ( K_{L} \rightarrow π^{0} π^{0} π^{\pm} e^{\mp} ν)$ as a standard model background to the experiment $K_{L} \rightarrow π^{0} μ^{\pm} e^{\mp}$, which seeks for possible violation of lepton family number. Using the lowest order chiral lagrangian, we find that the branching ratio for $K_{L} \rightarrow π^{0} π^{0} π^{\pm} e^{\mp} ν$ to be $6.2 \times 10^{-12}$. A similar decay $K_{L} \rightarrow π^{\mp} π^{\mp} π^{\pm} e^{\pm} ν$ has a branching ratio, $1.7 \times 10^{-11}$.

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