Exploring the ${\rm Y}(6S)\to {\chi }_{bJ}\varphi$ and ${\rm Y}(6S)\to {\chi }_{bJ}\omega$ hidden-bottom hadronic transitions

Abstract

In this work, we investigate the hadronic loop contributions to the ${\rm Y}(6S)\to {\chi }_{bJ}\varphi (J=0,1,2)$ along with ${\rm Y}(6S)\to {\chi }_{bJ}\omega (J=0,1,2)$ transitions. We predict that the branching ratios of ${\rm Y}(6S)\to {\chi }_{b0}\varphi$, ${\rm Y}(6S)\to {\chi }_{b1}\varphi$ and ${\rm Y}(6S)\to {\chi }_{b2}\varphi$ are $(0.68\sim 4.62)\times 10^{-6}$, $(0.50\sim 3.43)\times 10^{-6}$ and $(2.22\sim 15.18)\times 10^{-6}$, respectively and those of ${\rm Y}(6S)\to {\chi }_{b0}\omega$, ${\rm Y}(6S)\to {\chi }_{b1}\omega$ and ${\rm Y}(6S)\to {\chi }_{b2}\omega$ are $(0.15\sim 2.81)\times 10^{-3}$, $(0.63\sim 11.68)\times 10^{-3}$ and $(1.08\sim 20.02)\times 10^{-3}$, respectively. Especially, some typical ratios, which reflect the relative magnitudes of the predicted branching ratios, are given, i.e., for ${\rm Y}(6S)\to {\chi }_{bJ}\varphi$ transitions, ${\mathcal{R}}_{10}^{\varphi }=\mathcal{B}[{\rm Y}(6S)\to {\chi }_{b1}\varphi ]/\mathcal{B}[{\rm Y}(6S)\to {\chi }_{b0}\varphi ]\approx 0.74$, ${\mathcal{R}}_{20}^{\varphi }=\mathcal{B}[{\rm Y}(6S)\to {\chi }_{b2}\varphi ]/\mathcal{B}[{\rm Y}(6S)\to {\chi }_{b0}\varphi ]\approx 3.28$, and ${\mathcal{R}}_{21}^{\varphi }=\mathcal{B}[{\rm Y}(6S)\to {\chi }_{b2}\varphi ]/\mathcal{B}[{\rm Y}(6S)\to {\chi }_{b1}\varphi ]\approx 4.43$, and for ${\rm Y}(6S)\to {\chi }_{bJ}\omega$ transitions, ${\mathcal{R}}_{10}^{\omega }=\mathcal{B}[{\rm Y}(6S)\to {\chi }_{b1}\omega ]/\mathcal{B}[{\rm Y}(6S)\to {\chi }_{b0}\omega ]\approx 4.11$, ${\mathcal{R}}_{20}^{\omega }=\mathcal{B}[{\rm Y}(6S)\to {\chi }_{b2}\omega ]/\mathcal{B}[{\rm Y}(6S)\to {\chi }_{b0}\omega ]\approx 7.06$, and ${\mathcal{R}}_{21}^{\omega }=\mathcal{B}[{\rm Y}(6S)\to {\chi }_{b2}\omega ]/\mathcal{B}[{\rm Y}(6S)\to {\chi }_{b1}\omega ]\approx 1.72$. With the running of BelleII in the near future, experimental measurement of these two kinds of transitions will be a potential research issue.

Comments: 10 pages, 10 figures and 1 table. Accepted by Eur. Phys. J. C