Search for a feebly interacting particle $X$ in the decay $K^{+}\rightarrow\pi^{+}X$

A search for the $K^{+}\rightarrow\pi^{+}X$ decay, where $X$ is a long-lived feebly interacting particle, is performed through an interpretation of the $K^{+}\rightarrow\pi^{+}\nu\bar{\nu}$ analysis of data collected in 2017 by the NA62 experiment at CERN. Two ranges of $X$ masses, $0$-$110\,\text{MeV}/c^{2}$ and $154$-$260\,\text{MeV}/c^{2}$, and lifetimes above $100\,\text{ps}$ are considered. The limits set on the branching ratio, $\text{BR}(K^{+}\rightarrow\pi^{+}X)$, are competitive with previously reported searches in the first mass range, and improve on current limits in the second mass range by more than an order of magnitude.