On the $K^+ \to \pi^0\pi^0\pi^0 e^+ \nu$ decay

TL;DR

This paper reports a new experimental upper limit on the rare decay $K^+ o ext{pi}^0 ext{pi}^0 ext{pi}^0 e^+ u$, discusses potential enhancements from pionium production, and analyzes the suppression factors affecting this decay.

Contribution

The paper provides the most stringent experimental upper limit to date on the decay probability and offers theoretical estimates on the suppression of pionium-mediated decay channels.

Findings

New upper limit on decay probability is 65 times lower than previous PDG value.

Pionium production in the decay is theoretically suppressed due to small wave function at zero separation.

Despite phase space advantages, the decay via pionium is strongly suppressed.

Abstract

The OKA Collaboration has obtained a new upper limit on the $K^+ \to \pi^0\pi^0\pi^0 e^+ \nu$ decay probability which is 65 times lower than the one currently listed by PDG. However it is still about $10^{4}$ times worse than the theoretical prediction. It was suggested that production of pionium $A_{2\pi}$ in the final state of the semileptonic $K^+$ decay with subsequent $A_{2\pi} \to \pi^0 \pi^0$ decay will increase the value of theoretical branching ratio due to the absence of five-particle phase space suppression. The estimates done in our paper show that despite the gain in the phase space the decay $K^+ \to A_{2\pi}\pi^0 e^+ \nu$ appeares to be strongly suppressed because of the smallness of the pionium wave function at zero $\pi$ mesons separation.