Study on the radiative decays of ${\rm Y}(nS)\to {\eta }_b+\gamma$

Abstract

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

Comments: 7 pages, 4 figures; Rectification made and a footnote added