Higher Order Corrections in
Perturbative Quantum Field
Theory via Sector Decomposition

Abstract

The calculation of higher order corrections in perturbative quantum field theories is
a particularly important subject. Our current model for particle physics is the stan-
dard model; a quantum field theory which has served to describe a huge amount
of observed data very well. As the Large Hadron Collider is collecting more and
more high energy data with smaller and smaller experimental errors, the accuracy
of theoretical calculations must keep up with experiment in order to discriminate be-
tween physics arising from our current standard model, and beyond standard model
physics.
In chapter 2 we give a brief introduction to the fundamentals of perturbative quan-
tum field theories, with particular emphasis on Quantum ChromoDynamics, where
higher order calculations are particularly important due to the fact that
αs (M_Z) >> α. In chapter 3 we present a review of methods for calculations within
perturbative quantum field theories, both for real and virtual corrections. In chap-
ter 4 we give a detailed explanation of the method of sector decomposition, and
highlight how it can be applied to the calculation of multi-parameter polynomial
integrals, which appear widely in high energy physics, and in particular within the
higher order calculations of perturbative quantum field theories. In chapter 5 we
present SecDec - a publicly available computer code which implements sector de-
composition. We give a range of examples to demonstrate its power in calculating
various integrals appearing in higher order calculations in perturbative quantum
field theories.