Search for missing $\psi (4S)$ in the $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}\psi (2S)$ process

Abstract

A detailed analysis to find a missing $\psi (4S)$ is made by utilizing the recent precise mesurements of the cross section for the process $e^{+}{e}^{-}\to \psi (2S){\pi }^{+}{\pi }^{-}$ by Belle. Assuming three resonances $Y(4360)$, $Y(4660)$, and $\psi (4S)$ to fit the data, we obtain the resonance parameters for $\psi (4S)$ as $m=4243$ MeV and $\Gamma =16\pm 31$ MeV showing a narrow state as predicted before. A combined fit to the data $e^{+}{e}^{-}\to \psi (2S){\pi }^{+}{\pi }^{-},h_c{\pi }^{+}{\pi }^{-}$, and ${\chi }_{c0}\omega$ is also performed to obtain the similar resonance parameters of $\psi (4S)$. The upper limit of the branching ratio is fitted to be $\mathcal{B}(\psi (4S)\to \psi (2S){\pi }^{+}{\pi }^{-})<3\times 10^{-3}$, which can be understood by hadronic loop contributions in reasonable parameters range. In addition, the ratios of the branching ratios of the $\psi (4S)$ dipion transition to the one of $\psi (4S)\to {\chi }_{c0}\omega$ are fitted, which can be further measured by BESIII and forthcoming BelleII to confirm the existence of $\psi (4S)$.

Comments: 9 pages, 10 figures