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

TL;DR

This paper searches for the missing $ ext{psi}(4S)$ resonance in electron-positron collision data, estimating its properties and branching ratios, and suggests further experimental verification to confirm its existence.

Contribution

The study provides the first detailed estimation of the $ ext{psi}(4S)$ resonance parameters using recent experimental data and proposes measurable ratios to confirm its existence.

Findings

Estimated $ ext{psi}(4S)$ mass as 4243 MeV.

Upper limit of $ ext{psi}(4S)$ decay to $ ext{psi}(2S) o ext{pi}^+ ext{pi}^-$ is below $3 imes 10^{-3}$.

Resonance parameters consistent with previous predictions.

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 $\psi(4S)$.