$Υ(4S,5S)\toΥ(1S)η$ transitions in the rescattering model and the new BaBar measurement

Abstract

The $η$ transitions of $Υ(4S,5S)$ into $Υ(1S,2S)$ are studied in the rescattering model by considering the final state interactions above the $B\bar B$ threshold. The width of the $η$ transition of $Υ(4S)$ into $Υ(1S)$ is found to be larger than that of the dipion transition, and the ratio of $Γ(Υ(4S)\toΥ(1S)η)$ to $Γ(Υ(4S)\toΥ(1S)π^+π^-)$ 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 $η$ transitions of $Υ(5S)$ are found to be sensitive to the coupling constants $g_{Υ(5S)B^{(*)}B^{(*)}}$ due to a large cancelation between contributions from the $B\bar{B}$, $B^*\bar{B}+c.c.$, and $B^*\bar{B}^*$ channels, and only a rough estimate $Γ(Υ(5S)\toΥ(1S,2S)η)=10{-}200$ KeV can be given. The widths of the $η'$ transitions of $Υ(4S,5S)$ are also discussed, and they could be much smaller than that of the corresponding $η$ transitions mainly due to the tiny phase space.

Version published in PRD, 5 pages, 1 figure