New calculation techniques and precision physics in high energy colliders

Abstract

In this thesis we have studied, tested, and developed the four dimensional regularization/renormalization (FDR) scheme, a novel approach to the calculation of radiative corrections in perturbative quantum field theory (pQFT), a task that is primarily hindered by the presence of unphysical infinities emerging from loop and phase space integration. Unlike the methods traditionally used to cope with this problem, in FDR the subtraction of the ultraviolet (UV) divergences is built in the definition of a new loop integral, made finite at the integrand level, and without ever modifying the Lagrangian. The method is fully four-dimensional, and it automatically preserves gauge invariance, as we have verified by calculating the one-loop amplitude for H ! !! in arbitrary gauge. By studying the gluonic corrections to the top-loop induced H ! !! process, we have also shown that FDR is particularly convenient when applied to two-loop calculations, as it avoids a great deal of the work that in dimensional regularization (DR) is induced by "/" terms. Infrared (IR) singularities in virtual and final state real radiation can also be cured in the same framework; the matching and cancellation of this type of divergence in inclusive observables was also studied, by reviewing the analytic calculation of the next-to-leading-order (NLO) decay rate for H ! gg, and by applying to this same process some FDR-based numerical Monte Carlo (MC) methods.