Update of hadronic decays of $J/\psi$ and $\psi(2S)$ though virtual photons

Abstract

The hadronic decay branching ratios of $J/\psi$ and $\psi(2S)$ through virtual photons, $B(J/\psi, \psi(2S) \rightarrow \gamma^*\rightarrow \text{hadrons})$, are updated by using the latest published measurements of the $R$ value and the branching ratios of $J/\psi, \psi(2S) \rightarrow l^+l^-$. Their respective precision increases by about 4 and 3 times.