$B^{(\ast )}{\bar{B}}^{(\ast )}$ intermediate state contribution to ${\rm Y}(4S,5S)\to {\eta }_b+\gamma$ radiative decay

Abstract

In this work, we investigate the re-scattering effects in the radiative decay ${\rm Y}(5S)\to {\eta }_b+\gamma$, which were suggested to be crucially important for understanding the anomalous largeness of the branching ratios $B({\rm Y}(5S)\to {\rm Y}(1S)+\pi \pi )$ and $B({\rm Y}(5S)\to {\rm Y}(1S)+\eta )$. Our calculations show that the re-scattering effects may enhance $\Gamma ({\rm Y}(10860)\to {\eta }_b+\gamma )$ by four orders, but the tetraquark structure does not. Recently the BaBar and CLEO collaborations have measured the mass of ${\eta }_b$ and the branching ratios $\mathcal{B}({\rm Y}(2S)\to {\eta }_b+\gamma )$, $\mathcal{B}({\rm Y}(3S)\to {\eta }_b+\gamma )$. We hope that very soon, ${\rm Y}(10860)\to {\eta }_b+\gamma$ will be measured and it would be an ideal opportunity for testing whether the re-scattering or the tetraquark structure is responsible for the anomaly of $\mathcal{B}({\rm Y}(5S)\to {\rm Y}(nS){\pi }^{+}{\pi }^{-}(n=1,2,3))$, $i.e.$, the future measurements on the radiative decays of ${\rm Y}(5S)$ might be a touchstone of the two mechanisms.

Comments: 7 pages, 2 figures. Typos corrected and more discussions added. accepted for publication in Physical Review D