First search for $K^+\to\pi^0\pi\mu e$ decays

The first search for the lepton number violating decay $K^+\to\pi^0\pi^-\mu^+e^+$ and lepton flavour violating decays $K^+\to\pi^0\pi^+\mu^-e^+$, $K^+\to\pi^0\pi^+\mu^+e^-$ has been performed using a dataset collected by the NA62 experiment at CERN in 2016-2018. Upper limits of $2.9\times 10^{-10}$, $3.1\times 10^{-10}$ and $5.0\times 10^{-10}$, respectively, are obtained at 90% CL for the branching ratios of the three decays on the assumption of uniform phase-space distributions.