Studio di una regolarizzazione finita di massa delle divergenze infrarosse

The main goal of today’s collider experiments is to improve our understanding of the Standard Model in order to grasp hints of the high-energy physics beyond what we currently know. This leads in particular to the search for better tools to study the theory of strong interactions. And it is precisely in this direction, towards this goal that the work of this thesis aims to make a contribution. Since the Large Hadron Collider (LHC) is a very precise machine, the need to develop algorithms for calculating observables, derives from the search for better precision to approach the experimental results. Among these observables, there are partonic cross sections beyond the first-orden approximation in the strong couplig constant. However this implies facing the presence of infra-red (IR) divergences when the emission of massless particles are taken into account. Although the cancellation of these Soft and Collinear singularities is guaranteed by the Kinoshita-Lee-Naunberg (KLN) Theorem, the construction of an algorithm that is able to deal with these divergences is far more complex. Actually at the next-to-leading order (NLO) there exist well established methods to do this, however what is sought is a simpler method that allows a more effective extension to NNLO (and beyond). The aim of this thesis is to study the possibility of addressing IR divergences by introducing a regularization scheme that assigns a finite (small) mass to the gluon. The advantage of this method would be to overcome the need for subtraction procedures (currently used to treat the problem), hopefully allowing for the calculation of quantum corrections with greater efficiency. The work in this thesis is performed in QED, taken as a simplification of QCD.