Pionium as a source of false events in the $K\to \pi \nu \bar{\nu }$ decays

We suggest that the decay modes of kaons with a pion and a pionium (${\pi }^{+}{\pi }^{-}$ atom) in the final state can constitute a not yet considered background to the very rare decay $K\to \pi \nu \bar{\nu }$. In fact, a part of pioniums may escape the decay region before decaying into two ${\pi }^0$s (or to ${\pi }^0{\pi }^0\gamma$ in the case of excited pionium). To illustrate the importance of this background, we show that it may even explain, under some assumptions, the unexpected $K_L$ decay events that appeared in the KOTO experiment.