An analytical form of the $e^{+}{e}^{-}$ annihilation cross section including initial-state radiation near the $Z$ is presented. Its accuracy is 0.1% within ($M-3\mathrm{}{\Gamma }_Z$, $M+2\mathrm{}{\Gamma }_Z$) and 0.4% within ($M-4\mathrm{}{\Gamma }_Z$, $M+4\mathrm{}{\Gamma }_Z$) for the lepton as well as hadron channels. The formulas could be used to extract the physical parameters of the $Z$ boson from the data of $e^{+}{e}^{-}$ colliding experiments.

• Received 19 June 1990

DOI:https://doi.org/10.1103/PhysRevD.43.1459