Total hadronic cross section ine+e−annihilation at the four-loop level of perturbative QCD

Abstract

The ratio R(S)=${\mathrm{\sigma }}_{\mathrm{tot}}$(${\mathit{e}}^{+}$ ${\mathit{e}}^{\mathrm{-}}$→hadrons)/σ(${\mathit{e}}^{+}$ ${\mathit{e}}^{\mathrm{-}}$→${\mathrm{\mu }}^{+}$ ${\mathrm{\mu }}^{\mathrm{-}}$) is calculated to the four-loop level in perturbative QCD. The result differs from a previous calculation and is much smaller. In addition, a new result for the four-loop β function in QED is obtained. This result also disagrees with a previous calculation.