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*
1 Guangdong Provincial Key Laboratory of Nuclear Science, Institute of Quantum Matter, South China Normal University, Guangzhou 510006, China2 Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China3 Peng Huanwu Collaborative Center for Research and Education, Beihang University, Beijing 100191, China4 School of Physics, Beihang University, Beijing 102206, China5 Beijing Key Laboratory of Advanced Nuclear Materials and Physics, Beihang University, Beijing 102206, China6 Guangdong-Hong Kong Joint Laboratory of Quantum Matter, Southern Nuclear Science Computing Center, South China Normal University, Guangzhou 510006, China7 Theoretical Physics Center for Science Facilities, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China8 School of Nuclear Sciences and Technology, University of Chinese Academy of Sciences, Beijing 101408, China
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.
收稿日期: 2022-12-05
出版日期: 2023-01-17
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