Two-loop massive corrections for collider phenomenology

In this thesis two-loop massive corrections for two relevant processes at hadron colliders are presented. The first part illustrates the Next-to-next-to-leading order QCD massive corrections to diphoton production at LHC. This process is an important test of the Standard Model and an interesting framework to evaluate the size of massive corrections at NNLO. All the relevant partonic subprocesses are taken into account. In particular, the two-loop amplitude in quark annihilation channel involves elliptic Master Integrals, which have been evaluated through differential equations. A semi-analytical approach to the solution, based on generalised power series expansions, has been adopted. A phenomenological study of the impact of these corrections on the invariant mass distribution is also presented. The second part of the thesis is about the two-loop mixed QCD-Electroweak corrections to qg → Hq and its crossed channels, ¯qg → H¯q and q¯q → Hg, considering the light-quark contribution and the exact dependence on the electroweak boson mass. Also for this process the relevant master integrals have been computed by means of the differential equation method, finding a solution as generalised power series expansions. Compared to the analytical formulae available in literature, our semi-analytical result allows to reduce the evaluation time of the relevant scattering amplitudes of one order of magnitude.