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

TL;DR

This paper investigates $S,5S$ to $
S$ $$ transitions using the rescattering model, predicting larger widths than traditional theories and supporting recent BaBar measurements, with detailed analysis of $S$ transitions and $S$ to $
S$ ratios.

Contribution

It introduces a rescattering model analysis for $S,5S$ to $
S,2S$ $$ transitions, predicting larger widths and ratios consistent with new experimental data.

Findings

The width of $S o
S $ exceeds dipion transition width.

The ratio $S o
S $ to dipion transition is 1.8-4.5, much larger than conventional predictions.

$S$ transition widths are highly sensitive to coupling constants, estimated at 10-200 KeV.

Abstract

The $\eta$ transitions of $\Upsilon(4S,5S)$ into $\Upsilon(1S,2S)$ 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 $\Upsilon(4S)$ into $\Upsilon(1S)$ is found to be larger than that of the dipion transition, and the ratio of $\Gamma(\Upsilon(4S)\to\Upsilon(1S)\eta)$ to $\Gamma(\Upsilon(4S)\to\Upsilon(1S)\pi^+\pi^-)$ 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 $\Upsilon(5S)$ are found to be sensitive to the coupling constants $g_{\Upsilon(5S)B^{(*)}B^{(*)}}$ 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 $\Gamma(\Upsilon(5S)\to\Upsilon(1S,2S)\eta)=10{-}200$ KeV can be given. The widths of the $\eta'$ transitions of $\Upsilon(4S,5S)$ are also discussed, and they could be much smaller than that of the corresponding $\eta$ transitions mainly due to the tiny phase space.