In this work, we investigate the rescattering 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 rescattering 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 rescattering 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.

• Received 21 July 2010

DOI:https://doi.org/10.1103/PhysRevD.82.054030