High Precision Test of QCD at Beijing Electron Positron Collider

The generalized Crewther relation relates the cross section ratio $R=\sigma(e^+e^- \to {\rm hadrons})/\sigma(e^+e^- \to {\mu}^+ {\mu}^-)$ in $e^+e^-$ annihilation with the Bjorken sum rule or the Gross-Llewellyn Smith sum rule in deep inelastic scattering and provides a fundamental connection for observables in Quantum Chromodynamics (QCD) without scale or scheme ambiguities. The ratio $R$ can be measured at the upgrated Bejing Electron Positron Collider or the $\tau$-Charm factory with higher precision and thus can be served for a high precision test of QCD in the Standard Model.