Three-loop QCD corrections from massive quarks to deep-inelastic structure functions and operator matrix elements

Abstract

This thesis discusses higher-order contributions from heavy quarks to inclusive deep-inelastic lepton-nucleon scattering. In this context, massive operator matrix elements play an important role: they enter into the heavy flavour Wilson coefficients through a factorisation relation in the asymptotic limit of large virtualities. Furthermore, they also enter into the definition of the variable flavour number scheme for parton distributions. Here, we present the analytic calculation of of several such massive operator matrix elements at the 3-loop level in perturbative quantum chromodynamics. In particular, we review the necessary mathematical and computational methods for these calculations and give results for the non-singlet and pure-singlet operator matrix elements including their applications in the structure functions, sum rules and and the variable flavour number scheme. Through this calculation we also obtain the pure-singlet and non-singlet anomalous dimensions at 3-loop order. Moreover, we discuss the calculation of certain representative Feynman diagrams with ladder and V-topologies, which serve as a testing ground for the calculational tools. Finally, also all Feynman diagrams of the gluonic operator matrix element are calculated, which is required in a 3-loop description of the variable flavour number scheme.