QCD precision calculations for high-energy colliders: the way to precision determinations of the fundamental parameters of the Standard Model

The precision determination of the fundamental parameters, such as the different couplings and fermion and boson masses of the Standard Model of elementary particles is one central goal of experimental high luminosity experimental physics, paired with high precision calculations in Quantum Field Theories. We report on recent progress in the determination of the strong coupling constant and the heavy quark masses, requiring QCD 3-and 4-loop calculations for massless an massive processes. The analysis of the data from HERA, the LHC, and in the near and more distant future at the EIC and the FCC, need these theoretical accuracies. Analytic and numeric calculations of this kind are long term processes and do regularly require to develop new mathematical and computer- algebraic technologies. We describe the development during the last 20 years in an understandable way, report on the results obtained, and give some outlook into the future. Finally, all these efforts sharpen our knowledge of the Standard Model and one may hope to decipher even more fundamental theories behind it.

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