A coherent study of <i>e</i>⁺<i>e</i>⁻→<i>ωπ</i>⁰, <i>ωπ</i>⁺<i>π</i>⁻, and <i>ωη</i>

Abstract

In this work, a combined analysis is performed on the processes of <inline-formula><tex-math id="M7">\begin{document}$e^+e^-\to\omega\pi^0\pi^0$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0086_M7.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0086_M7.png"/></alternatives></inline-formula>, <inline-formula><tex-math id="M8">\begin{document}$e^+e^-\to\omega\pi^+\pi^-$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0086_M8.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0086_M8.png"/></alternatives></inline-formula>, and <inline-formula><tex-math id="M9">\begin{document}$e^+e^-\to\omega\eta$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0086_M9.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0086_M9.png"/></alternatives></inline-formula> to study possible <inline-formula><tex-math id="M10">\begin{document}$\omega$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0086_M10.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0086_M10.png"/></alternatives></inline-formula> excited states at approximately 2.2 GeV. The resonance parameters are extracted by simultaneous fits of the Born cross section line shapes of these processes. In the fit with one resonance, the mass and width are fitted to be <inline-formula><tex-math id="M11">\begin{document}$(2207\pm14)$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0086_M11.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0086_M11.png"/></alternatives></inline-formula> MeV<inline-formula><tex-math id="M12">\begin{document}$/c^2$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0086_M12.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0086_M12.png"/></alternatives></inline-formula> and <inline-formula><tex-math id="M13">\begin{document}$(104\pm16)$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0086_M13.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0086_M13.png"/></alternatives></inline-formula> MeV, respectively. The result is consistent with previous measurements. In the fit with two resonances, the mass and width for the first resonance are fitted to be <inline-formula><tex-math id="M14">\begin{document}$(2160\pm36)$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0086_M14.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0086_M14.png"/></alternatives></inline-formula> MeV<inline-formula><tex-math id="M15">\begin{document}$/c^2$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0086_M15.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0086_M15.png"/></alternatives></inline-formula> (solution I), <inline-formula><tex-math id="M16">\begin{document}$(2154\pm12)$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0086_M16.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0086_M16.png"/></alternatives></inline-formula> MeV<inline-formula><tex-math id="M17">\begin{document}$/c^2$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0086_M17.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0086_M17.png"/></alternatives></inline-formula> (solution II) and <inline-formula><tex-math id="M18">\begin{document}$(141\pm74)$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0086_M18.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0086_M18.png"/></alternatives></inline-formula> MeV (solution I), <inline-formula><tex-math id="M19">\begin{document}$(152\pm77)$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0086_M19.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0086_M19.png"/></alternatives></inline-formula> MeV (solution II), respectively. The mass and width for the second resonance are fitted to be <inline-formula><tex-math id="M20">\begin{document}$(2298\pm19)$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0086_M20.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0086_M20.png"/></alternatives></inline-formula> MeV<inline-formula><tex-math id="M21">\begin{document}$/c^2$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0086_M21.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0086_M21.png"/></alternatives></inline-formula> (solution I), <inline-formula><tex-math id="M22">\begin{document}$(2309\pm6)$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0086_M22.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0086_M22.png"/></alternatives></inline-formula> MeV<inline-formula><tex-math id="M23">\begin{document}$/c^2$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0086_M23.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0086_M23.png"/></alternatives></inline-formula> (solution II) and <inline-formula><tex-math id="M24">\begin{document}$(106\pm77)$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0086_M24.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0086_M24.png"/></alternatives></inline-formula> MeV (solution I), <inline-formula><tex-math id="M25">\begin{document}$(99\pm23)$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0086_M25.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0086_M25.png"/></alternatives></inline-formula> MeV (solution II), respectively. The result is consistent with the theoretical prediction of <inline-formula><tex-math id="M26">\begin{document}$\omega(4S)$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0086_M26.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0086_M26.png"/></alternatives></inline-formula> and <inline-formula><tex-math id="M27">\begin{document}$\omega(3D)$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0086_M27.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0086_M27.png"/></alternatives></inline-formula>. The intermediate subprocesses in <inline-formula><tex-math id="M28">\begin{document}$e^+e^-\to\omega\pi^+\pi^-$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0086_M28.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0086_M28.png"/></alternatives></inline-formula> are analyzed using the resonance parameters of the previous fits in this work. In the fit with one resonance, the fitting result of <inline-formula><tex-math id="M29">\begin{document}$\varGamma^{e^+e^-}_{{\rm{R}}}B_{{\rm{R}}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0086_M29.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0086_M29.png"/></alternatives></inline-formula> is partially consistent with the previous result. In the fit with two resonances, the fitting result of <inline-formula><tex-math id="M30">\begin{document}$\varGamma^{e^+e^-}_{{\rm{R}}}B_{{\rm{R}}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0086_M30.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="JUSTC-2023-0086_M30.png"/></alternatives></inline-formula> is of the same order of magnitude as the theoretical prediction. This work may provide useful information for studying the light flavor vector meson family.