Massive 2- and 3-loop corrections to hard scattering processes in QCD

TL;DR

This paper presents high-precision calculations of two-mass contributions to QCD processes at three-loop order, improving theoretical predictions for collider experiments involving heavy quarks.

Contribution

It provides the first calculation of two-mass three-loop corrections to polarized operator matrix elements in QCD, with a new Fortran library for their evaluation.

Findings

Calculated two-mass contributions to operator matrix elements at order α_s^3.

Discussed the mathematical structure and phenomenological relevance of these corrections.

Developed a computational tool for evaluating heavy quark effects in QCD analyses.

Abstract

With the increasing experimental precision available at colliders, higher-order perturbative calculations are required to reduce the theory uncertainty in order to extract crucial QCD parameters, such as the strong coupling constant, to the required precision, often the order of one percent. For this reason, the contributions of the massive charm and bottom quarks need to be taken into account in hadronic processes such as deep-inelastic scattering. In this thesis, we calculate to order $\alpha_s^3$ the two-mass contributions to the twist-two polarized operator matrix elements $A_{gg,Q}^{(3)}$ and $A_{Qq}^{(3),PS}$ as functions of the heavy quark mass ratio. We discuss the mathematical structure of these objects and discuss their phenomenological importance for the variable flavour number scheme and mathematical and computer-algebraic aspects of their calculation. We further address the impact of the heavy quarks to the scheme-invariant evolution of structure functions and introduce a Fortran library for their evaluation. We also discuss a computer algebra implementation of a solver for partial linear difference equations.