Study ofπ0→μ±e∓decays

We deduce an experimental upper bound $\frac{1}{2}\frac{\left[\Gamma \right({\pi }^0\to {\mu }^{+}{e}^{-}) +\Gamma ({\pi }^0\to {\mu }^{-}{e}^{+}\left)\right]}{ \Gamma ({\pi }^0\to \mathrm{all})}<7\mathrm{}\times {10}^{-8\mathrm{}}$ (90% C.L.) on the branching ratios of ${\pi }^0\to {\mu }^{\pm }{e}^{\mp }$ decays from available data. We consider the existing constraints on the underlying muon-number-violating interaction and find that the present experimental information on ${\mu }^{-}\to e^{-}$ conversion in sulfur implies an upper limit on the ${\pi }^0\to {\mu }^{\pm }{e}^{\mp }$ branching ratios which is not likely to be larger than ${10}^{-15\mathrm{}}$.