${\rm Y}(4S,5S)\to {\rm Y}(1S)\eta$ transitions in the rescattering model and the new BaBar measurement

Abstract

The $\eta$ transitions of ${\rm Y}(4S,5S)$ into ${\rm Y}(1S,2S)$ are studied in the rescattering model by considering the final state interactions above the $B\bar{B}$ threshold. The width of the $\eta$ transition of ${\rm Y}(4S)$ into ${\rm Y}(1S)$ is found to be larger than that of the dipion transition, and the ratio of $\Gamma ({\rm Y}(4S)\to {\rm Y}(1S)\eta )$ to $\Gamma ({\rm Y}(4S)\to {\rm Y}(1S){\pi }^{+}{\pi }^{-})$ is predicted to be $R_4=1.8-4.5$, which is about two orders of magnitude larger than the expectation of the conventional hadronic transition theory, and is supported by the new BaBar measurement. The widths of the $\eta$ transitions of ${\rm Y}(5S)$ are found to be sensitive to the coupling constants $g_{{\rm Y}(5S)B^{(\ast )}{B}^{(\ast )}}$ due to a large cancelation between contributions from the $B\bar{B}$, $B^{\ast }\bar{B}+c.c.$, and $B^{\ast }{\bar{B}}^{\ast }$ channels, and only a rough estimate $\Gamma ({\rm Y}(5S)\to {\rm Y}(1S,2S)\eta )=10-200$ KeV can be given. The widths of the ${\eta }^{\prime }$ transitions of ${\rm Y}(4S,5S)$ are also discussed, and they could be much smaller than that of the corresponding $\eta$ transitions mainly due to the tiny phase space.

Comments: Version published in PRD, 5 pages, 1 figure