Infrared finite amplitudes

Abstract

Soft and collinear singularities, known collectively as infrared singularities here, plague the calculation of scattering amplitudes in gauge theories with massless particles such as QCD. The aim of this thesis is to describe methods of deriving amplitudes that are infrared finite and therefore do not suffer from this problem. We begin with an overview of scattering theory which includes a detailed discussion of the source of infrared singularities and outlines approaches that can be used to avoid them. Taking one of these approaches, namely that of dressed states, we give a detailed description of how such states can be constructed. We then proceed to give an explicit example calculation of the total cross section of the process e+e(^-) →2 jets at NLO. In this example we construct dressed amplitudes and demonstrate their lack of infrared singularities and then go on to show that the total cross section is the same as that calculated using standard field theory techniques. We then move on and attempt to improve the efficiency of calculations using dressed states amplitudes. We describe some of the problems of the method, specifically the large numbers of diagrams produced and the multiple different delta functions present in each amplitude. In attempting to fix these issues we demonstrate the difficulties of producing covariant amplitudes from this formalism. Finally we propose the use of the asymptotic interaction representation as a solution to these difficulties and outline a method of producing covariant infrared finite scattering amplitudes using this.