Rare weak decays of $η^\prime\to Kπ$

Abstract

Rare weak decays of $η^\prime\to Kπ$ have been investigated in the framework of the $U(3)$ chiral perturbation theory at the leading order. Our study shows that the branching ratio ${\cal B}(η^\prime\to Kπ)$ is of the order of $10^{-11}$, which is far below the present experimental upper bound given by the BESIII Collaboration. By further analysis of $η^\prime\to K^+π^-$ and $η^\prime\to K^0π^0$, the ratio of isospin amplitudes is found that $|A_{1/2}/A_{3/2}|\simeq 35$, which supports that the $ΔI=1/2$ transition enhancement, namely, the $ΔI=1/2$ rule, could be functional in $η^\prime$ weak decays.