Improved limit on the branching ratio of $K^{+}$→${\pi }^{+}$${\mu }^{+}$$e^{\mathrm{-}}$

A search for the lepton-flavor number-violating decay $K^{+}$→${\pi }^{+}$ ${\mu }^{+}$ $e^{\mathrm{-}}$ has been conducted at the Brookhaven Alternating Gradient Synchrotron. No candidates have been found which would be consistent with this decay mode. An upper limit on the branching ratio is placed at 2.6×${10}^{\mathrm{-}10}$, which can be combined with our previous result to yield an upper limit of 2.1×${10}^{\mathrm{-}10}$ at the 90% confidence level. A limit on the branching ratio for ${\pi }^0$→${\mu }^{+}$ $e^{\mathrm{-}}$ of 1.6×${10}^{\mathrm{-}8}$ (90% C.L.) is also established.