Low energy moments of heavy quark current correlators at four loops

We describe several techniques for the calculation of multi-loop integrals and their application to heavy quark current correlators. As new results, we present the fourloop correction to the second and third physical moment in the low-energy expansions of vector, axial-vector and scalar quark current correlators. Using a Ward identity, we obtain the third and fourth moment for the pseudo-scalar correlator. We briefly discuss the impact of these results on the determination of the charm quark mass and the strong coupling constant using lattice simulations for the current correlators and of the charmand bottom-quark mass from experimental data for σ(e+e− → hadrons).