Electronic width of the $\psi(3770)$ resonance interfering with the background

TL;DR

This paper discusses methods to extract the electronic decay width of the $\psi(3770)$ resonance from $e^+e^- o Dar D$ data, emphasizing the importance of interference effects and proposing a model that allows a unique determination of this width.

Contribution

It introduces a model for the $D$ meson form factor that accounts for interference and resonance mixing, enabling a unique extraction of the $\psi(3770)$ electronic width.

Findings

The proposed model satisfies Watson's theorem.

It allows unique determination of $\Gamma_{\psi(3770)e^+e^-}$ from experimental data.

The extracted widths are compared with potential model estimates.

Abstract

Methods for extracting the $\psi(3770)\to e^+e^-$ decay width from the data on the reaction cross section $e^+e^-\to D\bar D$ are discussed. Attention is drawn to the absence of the generally accepted method for determining $\Gamma_{\psi(3770)e^+e^-}$ in the presence of interference between the contributions of the $\psi(3770)$ resonance and background. It is shown that the model for the experimentally measured $D$ meson form factor, which satisfies the requirement of the Watson theorem and takes into account the contribution of the complex of the mixed $\psi(3770)$ and $\psi(2S)$ resonances, allows uniquely determine the value of $\Gamma_{\psi(3770)e^+e^-}$ by fitting. The $\Gamma_{\psi(3770)e^+ e^-}$ values found from the data processing are compared with the estimates in the potential models.