Rare weak decays of ${\eta }^{\prime }\to K\pi$

Abstract

Rare weak decays of ${\eta }^{\prime }\to K\pi$ have been investigated in the framework of the $U(3)$ chiral perturbation theory at the leading order. Our study shows that the branching ratio $\mathcal{B}({\eta }^{\prime }\to K\pi )$ 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 ${\eta }^{\prime }\to K^{+}{\pi }^{-}$ and ${\eta }^{\prime }\to K^0{\pi }^0$, the ratio of isospin amplitudes is found that $|A_{1/2}/A_{3/2}|\simeq 35$, which supports that the $\Delta I=1/2$ transition enhancement, namely, the $\Delta I=1/2$ rule, could be functional in ${\eta }^{\prime }$ weak decays.

Comments: LaTex, 6 pages, minor changes and references added. To appear in Phys. Rev. D