New results for two-loop scattering in quantum chromodynamics

Decreasing statistical and systematic uncertainties for particle collisions experiments at the Large Hadron Collider (LHC) put increasing demands on precision in theoretical predictions. At the LHC protons are collided at high energy in order to study fundamental interactions. The scattering processes are dominated by strong interactions which are modelled by Quantum Chromodynamics (QCD). In this energy regime theoretical predictions can be calculated using perturbation theory in the coupling constant and hence higher precision is achieved by including higher orders. The higher orders include both processes of additional unresolved external states (higher multiplicity) or internal states (more loops). Currently, calculations at next-to-next-to-leading order (NNLO) precision are in demand for current and future analyses. These calculations require the development of new techniques to handle the growth in complexity. The topic of this thesis is loop calculations in QCD using modern on-shell techniques. We present new results for planar 2 → 3 gluon scattering at two loops. The amplitudes are obtained by employing generalised unitarity and finite field reconstruction methods. The universality of the pole structure is used for verification of the results, but also allows us to reconstruct only a finite remainder. Strategies to obtain compact analytic expressions both at the level of the integrand and after integration are discussed. Integrals are dealt with using a variety of approaches including sector decomposition, integration-by-parts identities, and dimensional shifting and recurrence relations. We also describe a new unitarity compatible method for dealing with massive fermions at one loop. This method involves an explicit construction of six-dimensional spinors and a discussion of the renormalisation of effective field theories