High precision test of QCD at Beijing electron positron collider

The generalized Crewther relation relates the cross section ratio R=sigma(e(+)e(-) -->hadrons) / sigma(e (+)e (-)-->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 Beijing 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.