| THE PHYSICS OF ELEMENTARY PARTICLES AND FIELDS |
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Molecular Nature of $X(3872)$ in $B^0 \to K^0 X(3872)$ and $B^+ \to K^+ X(3872)$ Decays |
| Hao-Nan Wang1,2, Li-Sheng Geng3,4,5, Qian Wang1,6,7, and Ju-Jun Xie2,8* |
1Guangdong Provincial Key Laboratory of Nuclear Science, Institute of Quantum Matter, South China Normal University, Guangzhou 510006, China
2Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China
3Peng Huanwu Collaborative Center for Research and Education, Beihang University, Beijing 100191, China
4School of Physics, Beihang University, Beijing 102206, China
5Beijing Key Laboratory of Advanced Nuclear Materials and Physics, Beihang University, Beijing 102206, China
6Guangdong-Hong Kong Joint Laboratory of Quantum Matter, Southern Nuclear Science Computing Center, South China Normal University, Guangzhou 510006, China
7Theoretical Physics Center for Science Facilities, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China
8School of Nuclear Sciences and Technology, University of Chinese Academy of Sciences, Beijing 101408, China
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| Cite this article: |
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Hao-Nan Wang, Li-Sheng Geng, Qian Wang et al 2023 Chin. Phys. Lett. 40 021301 |
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Abstract We investigate the decays of $B^0 \to K^0 X(3872)$ and $B^+ \to K^+ X(3872)$ based on the picture where the $X(3872)$ resonance is strongly coupled to the $D\bar{D}^* + c.c.$ channel. In addition to the decay mechanism where the $X(3872)$ resonance is formed from the $c\bar{c}$ pair hadronization with the short-distance interaction, we have also considered the $D\bar{D}^*$ rescattering diagrams in the long-distance scale, where $D$ and $\bar{D}^*$ are formed from $c$ and $\bar{c}$ separately. Because of the difference of the mass thresholds of charged and neutral $D\bar{D}^*$ channels, and the rather narrow width of the $X(3872)$ resonance, at the $X(3872)$ mass, the loop functions of $D^0\bar{D}^{*0}$ and $D^+\bar{D}^{*-}$ are much different. Taking this difference into account, the ratio of $\mathcal{B}[B^0\to K^0X(3872)]/\mathcal{B}[B^+ \to K^+ X(3872)] \simeq 0.5$ can be naturally obtained. Based on this result, we also evaluate the decay widths of $B_s^0 \to \eta(\eta') X(3872)$. It is expected that future experimental measurements of these decays can be used to elucidate the nature of the $X(3872)$ resonance.
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Received: 05 December 2022
Published: 17 January 2023
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