Exploring the and hidden-bottom hadronic transitions

Qi Huang; Bo Wang; Xiang Liu; Dian-Yong Chen; Takayuki Matsuki

doi:10.1140/epjc/s10052-017-4726-8

2024 Impact factor 4.8

Particles and Fields

Open Access

Eur. Phys. J. C (2017) 77: 165
https://doi.org/10.1140/epjc/s10052-017-4726-8

Regular Article - Theoretical Physics

Exploring the $\Upsilon (6S)\rightarrow \chi _{bJ}\phi$ and $\Upsilon (6S)\rightarrow \chi _{bJ}\omega$ hidden-bottom hadronic transitions

Qi Huang¹^,2, Bo Wang¹^,2, Xiang Liu¹^,2^*, Dian-Yong Chen³ and Takayuki Matsuki⁴^,5

¹ School of Physical Science and Technology, Lanzhou University, Lanzhou, 730000, China
² Research Center for Hadron and CSR Physics, Lanzhou University and Institute of Modern Physics of CAS, Lanzhou, 730000, China
³ Department of Physics, Southeast University, Nanjing, 210094, China
⁴ Tokyo Kasei University, 1-18-1 Kaga, Itabashi, Tokyo, 173-8602, Japan
⁵ Theoretical Research Division, Nishina Center, RIKEN, Wako, Saitama, 351-0198, Japan

^* e-mail: xiangliu@lzu.edu.cn

Received: 5 January 2017
Accepted: 27 February 2017
Published online: 17 March 2017

Abstract

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