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

The anomalous line shape of the $ψ(3770)$ 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.

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