Cross section of e(+)e(-) annihilation into hadrons of order alpha(4)(s)n(2)(f) in perturbative QCD.

We present the first genuine QCD five-loop calculation of the vacuum polarization functions: analytical terms of order alpha(4)(s)n(2)(f) to the absorptive parts of vector and scalar correlators. These corrections form an important gauge-invariant subset of the full omicron(alpha(4)(s)) 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.