The $R_{uds}$ value in the vicinity of $\psi(3770)$ state

TL;DR

This paper models the asymmetric line shape of the $\psi(3770)$ resonance using a Fano-type formula to accurately determine the $R_{uds}$ value, resolving previous discrepancies between experimental data and theoretical predictions.

Contribution

It introduces a Fano-type parameterization to describe the $\psi(3770)$ line shape, enabling precise extraction of the $R_{uds}$ value and improving agreement with theory.

Findings

$R_{uds}$ value determined as 2.156±0.022

Asymmetric line shape modeled successfully with Fano formula

Discrepancy between experiment and theory reduced

Abstract

The anomalous line shape of the $\psi(3770)$ state has resulted in some difficulty in the determination of the $R$ value for the continuum light hadron production in the resonance energy range. We parameterize the asymmetric line shape using a Fano-type formula and extract the $R_{uds}$ value to be $2.156\pm 0.022$ from the data of BESIII Collaboration in the energy region between 3.650 and 3.872 GeV. The small discrepancy between experiment and theory is removed. The cross sections of the $e^+e^- \rightarrow hadrons$ are given by subtracting the part of continuum light hadron production and are compared to the data of the $e^+e^- \rightarrow D\bar{D}$ reaction.