New methods for Scattering Amplitudes in Gauge Theories

In the thesis, we present the application of on-shell and unitarity-based techniques and of the differential equation methods via Magnus expansion to the evaluation of the one-loop scattering amplitudes contributing to gg>>gH at NLO. Their analytic expressions were obtained with standard techniques, and our results are in full agreement with them. The recently proposed Four dimensional formulation (FDF) of the d-dimensional regularization scheme allows for a purely four-dimensional regularization of the amplitudes. The implementation of d-dimensional generalized unitarity within exactly four space-time dimensions can be realized, avoiding any higher-dimensional extension of either the Dirac or the spinor algebra. The method of differential equations is one of the most effective techniques for computing dimensionally regulated multi-loop integrals. Proper choices of MI's can simplify the form of the systems of differential equations, considering a form where the dependance on the dimensional parameter is factorized from the kinematic. The integration of a system in canonical form trivializes and can be addressed by using Magnus series expansion.