Subthreshold poles in electron-positron annihilation. D\bar{D} final states

Abstract

We show that the $\psi(2\mathrm S)$ subthreshold pole influences the cross section of the electron-positron annihilation into the $\mathrm D^+\mathrm D^-$ and $\mathrm D^0\bar\mathrm D^0$ final states. We perform a fit to the merged BES \cite{bes2008} and BESIII \cite{besiii2024} data, providing the cross section for $e^+e^-$ annihilation into those final states. The statistical significance of the $\psi(2\mathrm S)$ as a subthreshold pole is 8.2$\sigma$. A fit assuming it and seven resonances excels with the fit quality characterized by $\chi^2/\mathrm{NDF}=240.4/284$, which means a $p$-value of 97\%.