Study on the radiative decays of $Υ(nS)\to η_b+γ$

In this work, we investigate the characteristics of the spin-singlet state $η_b$ of the bottomonia family via the radiative decays of $Υ(nS)\to η_b+γ$. The theoretical estimation of the decay widths is carried out in terms of the light-front quark model (LFQM). Recently CLEO and BaBar collaborations have measured $\mathcal{B}(Υ(3S)\toγη_b)$ and the mass of ${η_b}$. In terms of the data we fix the concerned input parameters in our calculations of $Υ(nS)\to η_b+γ$. A special attention is paid on the transition of $Υ(5S)\to η_b+γ$. The BELLE data showed that the width of $Υ(5S)\to Υ(2S,1S)+ππ$ is two orders larger than that of $Υ(4S)\to Υ(2S,1S)+ππ$, thus some theoretical explanations have been proposed. Among them, it is suggested the inelastic final state interaction (IFSI) $Υ(5S)\to B\bar B\to Υ(1S)+ππ$ may be a natural one. If so, a similar mechanism also applies to $Υ(5S)\to B^{(*)}\bar B^{(*)}\to η_b+γ$, the precise measurement would serve as a good test whether $Υ(5S)$ possess exotic components. Our calculation in the LFQM indicates that the rate of the direct process $Υ(5S)\toη_b+γ$ is not anomalous compared to $Υ(mS)\toη_b+γ(m=1,2,3,4)$, thus if the IFSI does apply, the rate of $Υ(5S)\toη_b+γ$ should be larger than the others by orders.

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