Cross section of e+e- annihilation into hadrons of order αs4n2f in perturbative QCD -: art. no. 012001

We present the first genuine QCD five-loop calculation of the vacuum polarization functions: analytical terms of order alpha(s)(4)n(f)(2) to the absorptive parts of vector and scalar correlators. These corrections form an important gauge-invariant subset of the full O(alpha(s)(4)) correction to e(+)e(-) annihilation into hadrons and the Higgs decay rate into hadrons, respectively. They discriminate between different widely used estimates of the full result.