Massive and Massless Four-Loop Integrals

The physical motivations have been discussed extensively in the reports of the recent years. Thus, we only would like to mention that the problems treated within this project aim for the evaluation of so-called Feynman diagrams which in turn lead to quantum corrections within a given quantum field theory like Quantum Electrodynamics or Quantum Chromodynamics but also supersymmetric theories. Among the various physical applications are predictions for high-energy reactions to be measured in experiments like the Large Hadron Collider (LHC) at CERN in Geneva but also precise determinations of fundamental parameters like quark masses and coupling constants. Quantum corrections can be classified by closed loops appearing in the Feynman diagrams. In general the mathematical input for a Feynman diagram is rather compact. However, in the process of evaluating the corresponding integrals at the higher loop level one often obtains intermediate expressions which can easily reach up to several tera bytes. Several manipulations have to be applied before finally the final expression, which is again relatively compact, emerges. The typical CPU time reaches from several hours to several months depending on the concrete problem under consideration. In order to be able to manipulate huge expressions a special tool is necessary. Our workhorse for such calculations is the computer algebra program FORM [1] and its parallel versions ParFORM [2] and TFORM [3]. The parallelization concept for FORM is quite simple: The original expression is divided into several pieces which are then distributed to the individual processors or cores (workers). Once the workers have finished their job the resulting expressions have to be collected by one processor which combines