On the K+ → π0π0π0e+ν Decay

Abstract

The OKA Collaboration has obtained a new upper limit on the K⁺ → π⁰π⁰π⁰e⁺ν decay probability which is 65 times lower than the one currently listed by PDG. However it is still about 10⁴ times worse than the theoretical prediction. It was suggested that production of pionium A_2π in the final state of the semileptonic K⁺ decay with subsequent A_2π → π⁰π⁰ decay will increase the value of theoretical branching ratio due to the absence of five-particle phase space suppression. We demonstrate that despite the gain in the phase space the decay K⁺ → A_2ππ⁰e⁺ν appears to be strongly suppressed because of the smallness of the pionium wave function at zero π mesons separation.