Production of single charm pentaquark based on molecular configuration
Authors: Xing Ye , Li Na , Yang Ling-Bin , Hu Xiao-Hui ,   School of Materials Science and Physics, China University of Mining and Technology, Xuzhou 221116, China
Published: May 2024

<sec>In this work, the authors use the effective Lagrangian method to investigate the production of singly charm pentaquark state with spin parity <inline-formula><tex-math id="M14">\begin{document}$J ^ P={1/2}^{-} $\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20240447_M14.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20240447_M14.png"/></alternatives></inline-formula>. Based on the possible molecular state images of hadrons, the author discusses the production of singly charm pentaquark state <inline-formula><tex-math id="M15">\begin{document}${c\bar suud}$\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20240447_M15.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20240447_M15.png"/></alternatives></inline-formula> and decuplet baryon <inline-formula><tex-math id="M16">\begin{document}$\bar \varDelta$\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20240447_M16.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20240447_M16.png"/></alternatives></inline-formula> by <inline-formula><tex-math id="M17">\begin{document}$B_{\mathrm{s}}$\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20240447_M17.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20240447_M17.png"/></alternatives></inline-formula> meson with different molecular state configurations of <inline-formula><tex-math id="M18">\begin{document}$ND_{\mathrm{s}} $\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20240447_M18.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20240447_M18.png"/></alternatives></inline-formula> or <inline-formula><tex-math id="M19">\begin{document}$ND ^ * _{\mathrm{s}} $\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20240447_M19.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20240447_M19.png"/></alternatives></inline-formula>. To determine the coupling between pentaquark and their constituents in the molecular scheme, the authors follow the Weinberg compositeness condition to estimate the self-energy diagram of the singly charmed pentaquark. Further study on the production of pentaquark from <inline-formula><tex-math id="M20">\begin{document}$B_{\mathrm{s}}$\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20240447_M20.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20240447_M20.png"/></alternatives></inline-formula> meson can be propeled by computing the transition matrix elements, or the triangle diagrams, which can be careful divided into two part subprocess, one associated with weak transition can be represented into form factor and decay constant, another one related to strong coupling of hadrons can be described by effective Lagrangian. Selecting the scale parameter <i>α</i> (10–200 MeV) and binding energy <i>ε</i> (5, 20, 50 MeV), the authors can find the branching ratio of the production <inline-formula><tex-math id="M23">\begin{document}$\bar B_{\mathrm{s}} \to P_ {{\mathrm{c}}\bar {{\mathrm{s}}}}\bar \varDelta $\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20240447_M23.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20240447_M23.png"/></alternatives></inline-formula>. Under the configuration of <inline-formula><tex-math id="M24">\begin{document}$ND_{\mathrm{s}}$\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20240447_M24.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20240447_M24.png"/></alternatives></inline-formula> molecule, the branching ratio of the Cabibbo allowed process <inline-formula><tex-math id="M25">\begin{document}$\bar B_{\mathrm{s}} \rightarrow P_{{{\mathrm{c}} \bar{{\mathrm{s}}}}} \bar \varDelta$\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20240447_M25.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20240447_M25.png"/></alternatives></inline-formula> can reach to order of <inline-formula><tex-math id="M26">\begin{document}$10^{-5}$\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20240447_M26.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20240447_M26.png"/></alternatives></inline-formula>. Moreover, the production branching ratio of <inline-formula><tex-math id="M27">\begin{document}$ND^*_{\mathrm{s}}$\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20240447_M27.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20240447_M27.png"/></alternatives></inline-formula> molecule is only at the order of <inline-formula><tex-math id="M28">\begin{document}$10^{-8}$\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20240447_M28.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20240447_M28.png"/></alternatives></inline-formula>. </sec><sec>A increasing scale parameter <i>α</i> can significantly improve the production branching ratio of the singly charm pentaquark. In addition, the binding energy and the coupling constants will also affect the magnitude of production. Therefore, considering the above factors, the production branching ratio of singly charm pentaquark in <inline-formula><tex-math id="M29">\begin{document}$B_{\mathrm{s}}$\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20240447_M29.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20240447_M29.png"/></alternatives></inline-formula> decays have considerable results, which is worth experimental and theoretical research in the future. The findings of our work can provide a reference for the experimental search and study of singly charm pentaquark, and it is hoped that they will be verified in future experimental detections at <i>B</i> factories such as LHCb, Belle, and BaBar.</sec>