We report about recent progress in computing four-loop massive correlators.
The expansion of these correlators in the external momentum leads to
vacuum integrals. The calculation of these vacuum integrals can be used
to determine Taylor expansion coefficients of the vacuum
polarization function and decoupling functions in perturbative Quantum
chromodynamics. New results at four-loop order for the lowest Taylor
expansion coefficient of the vacuum polarization function and for the
decoupling relation are presented.