Finite scattering amplitudes in field theory

Abstract

In this thesis we explore the infrared problem perturbatively in massless field theory. We review the current conventional methods and theorems that are applied in the calculation of QCD jet observables and then discuss the formulation of an alternative approach called the Asymptotic Interaction Picture (AIP). The AIP is based on a unitary transformation such that long-ranged interactions are present in the asymptotic Lagrangian and thus the states associated with this picture are no longer free Fock states but are asymptotic states containing soft and collinear interactions. Under the guidance of the AIP we are led to modifying conventional perturbation theory, cutting up amplitudes in a manner that allows for the construction of infrared finite amplitudes that are in correspondence with the asymptotic states of the AIP. We apply this formalism to several NLO corrections to QCD observables and construct dressed states who's amplitudes are finite in all regions of phase space. Using these amplitudes we compute several observables and show agreement with the conventional calculations in infrared safe regions. Higher-order calculations are then investigated in ϕ (^3)theory and the infrared pole structure is shown to behave as expected such that NNLO corrections to dressed states are obtained. Finally we present part of the NNLO correction to the dressed two-parton amplitude in QCD and show that, with several provisos, this approach may potentially be applied to the precision calculations of observables at the International Linear Collider (ILC). We therefore give a possible alternative to current subtraction methods at NNLO when no initial state radiation is present.