O ( α 2 s ) Corrections to Current Correlators ∗

In this contribution three-loop QCD corrections to current correlators are considered. The application of the large momentum procedure, which provides a systematic expansion in (m/q), allows the computation of terms up to n = 6 for the vector and axial-vector correlator and up to n = 4 for the scalar and pseudo-scalar correlator. Some physical applications are discussed. There are plenty of important observables which are essentially given by the transversal part of the current correlators, Π(q), with different tensorial structure. The cross section for the annihilation of ee to hadrons is governed by the vector current correlator. The decay rate of the Z boson as well as the production of top quarks is a combination of the vector and axial-vector correlator. For the decay rate of a scalar of pseudo-scalar Higgs boson the correlators induced by scalar, respectively, pseudo-scalar currents are important. At oneand even at two-loop level results valid for arbitrary external momentum, q, and quark mass, m, are available for quite some time [1]. However, proceeding to three loops the situation is much more difficult. In the high energy region until recently only terms up to O(m/q) were available. Our aim was to use a systematic approach which allows the computation of higher order mass corrections to the current correlators. A well-defined algorithm is provided by the so-called large momentum expansion (LMP) [2]. Whereas at oneand two-loop level it is still possible to apply the LMP “by hand” for the threeloop calculation this is very painful. In the vector case, e.g., from the 18 initial diagrams altogether 240 subgraphs, which have to be expanded in their small quantities, are generated when the LMP is applied. This is barely feasible by hand. Therefore we decided to automate the LMP. Details can be found in [3]. To appear in Proceedings of the International Europhysics Conference on High Energy Physics, Jerusalem, Israel, 19-26 August 1997.