Precision Physics in High Energy Colliders: new techniques of calculating radiative corrections

Abstract

In this thesis we make two investigations in the context of precision physics, firstly in the multi-leg and secondly in the multi-loop frontier. In the first part, we approach the problem of making automated NLO phenomenological studies of gluon fusion driven Higgs production. Here we calculate the R2 vertices necessary to use the effective theory of Higgs/gluon interactions at one loop in MadGraph5 aMC@NLO for both a scalar and pseudoscalar coupling. This has allowed for a study of the CP properties of the Higgs/top-quark coupling where it is found that correlations between the di-jet azimuthal angles in Higgs + 2 jets provide valuable CP information. In the second part we work in the framework of the Four Dimensional Regularization (FDR) approach, where we develop two-loop translation rules between FDR and dimensional regularization in massless QCD in the form of a coupling constant shift. To achieve this we set up a framework for comparison between the two strategies and develop an algorithm for the automation of the FDR defining expansion at two loops. During the investigation we find that a naive global prescription in the scheme breaks locality and universality in correlation functions with external fermions and so we introduce a “sub-prescription” to deal with this. In this way we solve a problem analogous to the breakdown of unitarity at two loops in the four dimensional helicity method and provide explicit evidence of the consistency of FDR at two loops. Furthermore we gain insight into the relation between the FDR approach and a canonical counterterm picture, witnessing a direct cancellation between FDR sub-vacua and counterterms.