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$B^{(*)}\bar B^{(*)}$ intermediate state contribution to $Υ(4S,5S)\to η_b+γ$ radiative decay

In this work, we investigate the re-scattering effects in the radiative decay $Υ(5S)\toη_b+γ$, which were suggested to be crucially important for understanding the anomalous largeness of the branching ratios $B(Υ(5S)\to Υ(1S)+ππ)$ and $B(Υ(5S)\to Υ(1S)+η)$. Our calculations show that the re-scattering effects may enhance $Γ(Υ(10860)\to η_b+γ)$ by four orders, but the tetraquark structure does not. Recently the BaBar and CLEO collaborations have measured the mass of ${η_b}$ and the branching ratios $\mathcal{B}(Υ(2S)\rightarrowη_b+γ)$, $\mathcal{B}(Υ(3S)\rightarrowη_b+γ)$. We hope that very soon, $Υ(10860)\to η_b+γ$ 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 $\mathcal{B}\big(Υ(5S)\rightarrowΥ(nS)π^+π^- (n=1,2,3)\big)$, $i.e.$, the future measurements on the radiative decays of $Υ(5S)$ might be a touchstone of the two mechanisms.