Search for $K^+$ decays into the $\pi^+e^+e^-e^+e^-$ final state

The first search for ultra-rare $K^+$ decays into the $\pi^+e^+e^-e^+e^-$ final state is reported, using a dataset collected by the NA62 experiment at CERN in 2017-2018. An upper limit of $1.4\times 10^{-8}$ at 90% CL is obtained for the branching ratio of the $K^+\to\pi^+e^+e^-e^+e^-$ decay, predicted in the Standard Model to be $(7.2 \pm0 .7)\times 10^{-11}$. Upper limits at 90% CL are obtained at the level of $10^{-9}$ for the branching ratios of two prompt decay chains involving pair-production of hidden-sector mediators: $K^+\to\pi^+ a a$, $a \to e^+e^-$ and $K^+\to\pi^+ S$, $S\to A^\prime A^\prime$, $A^\prime \to e^+ e^-$.