Infrared Divergences from Soft and Collinear Gauge Bosons

To compare with experiment it is vital that theoretical predictions are finite. Beyond leading order in perturbation theory many processes contain infrared divergences. It is often argued that these singularities are eliminated at the level of the inclusive cross-section [1,2]. During this talk I will show that the infrared divergences are still poorly understood. I also expose some questionable assumptions which must be made to render the theoretical cross-section finite. There are two types of infrared singularities – soft and collinear. Soft divergences are associated with low energy photons. Collinear divergences occur in high-energy or theories with massless charges. It is common practice to use the Bloch-Nordsieck trick [1] for the soft divergences. By adding the bremsstrahlung process to the crosssection with a virtual loop the overall cross-section is soft finite. Soft divergences can be regulated by dimensional regularisation where the number of dimensions, D = 4 + 2εIR. Focusing on the infrared pole, the Bloch-Nordsieck trick is summarised diagrammatically at next-to-leading order by: