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

TL;DR

This paper identifies pionium formation as a potential background in rare kaon decay experiments, which could explain some unexpected events observed in the KOTO experiment.

Contribution

It introduces pionium as a previously overlooked background source in $K o ext{pionium} o ext{neutral pions}$ decay measurements, impacting rare decay searches.

Findings

Pionium can escape decay region before decaying into neutral pions.

This background may account for some anomalous $K_L$ decay events.

Pionium-related background could influence future rare decay experiments.

Abstract

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.