On the $K^+ \to π^0π^0π^0 e^+ ν$ decay
The OKA Collaboration has obtained a new upper limit on the $K^+ \to π^0π^0π^0 e^+ ν$ 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 $A_{2π}$ in the final state of the semileptonic $K^+$ decay with subsequent $A_{2π} \to π^0 π^0$ 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 $K^+ \to A_{2π}π^0 e^+ ν$ appeares to be strongly suppressed because of the smallness of the pionium wave function at zero $π$ mesons separation.
hep-ph↗