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

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.

Comments: 4 pages, 5 figures