We present the first full analytic evaluation of the scattering amplitude for the process qq → $$ Q\overline{Q} $$ up-to two loops in Quantum Chromodynamics, for a massless (q) and a massive (Q) quark flavour. The interference terms of the one- and two-loop amplitudes with the Born amplitude, decomposed in terms of gauge invariant form factors depending on the colour and flavour structure, are analytically calculated by keeping complete dependence on the squared center-of-mass energy, the squared momentum transfer, and the heavy-quark mass. The results are expressed as Laurent series around four space-time dimensions, with coefficients given in terms of generalised polylogarithms and transcendental constants up-to weight four. Our results validate the known, purely numerical calculations of the squared amplitude, and extend the analytic knowledge, previously limited to a subset of form factors, to their whole set, coming from both planar and non-planar diagrams, up-to the second order corrections in the strong coupling constant.

This contribution aims at elucidating the method we employed in the calculation of double-virtual interferences of di-muon production via electron-positron annihilation at Next-to-Next-to-Leading Order (NNLO) in Quantum Electrodynamics (QED), and heavy-quark pair production via light-quark annihilation at NNLO Quantum Chromodynamics (QCD).

Higgs-pair production is one of the targets of the high-luminosity LHC and of future hadron colliders, as it allows for a direct probe of the trilinear Higgs coupling and hence of the mechanism behind electroweak symmetry breaking. This contribution focuses on the impact of the full next-to-leading order QCD corrections to Higgs-pair production via gluon fusion, the main production mechanism at hadron colliders, in the Standard Model and in Two-Higgs-Doublet models. The uncertainties due to the top-mass scale-and-scheme choice will be discussed.

In this contribution the next-to-leading (NLO) QCDcorrections toHiggs boson pair production are discussed. A brief sketch of the calculation is given. The differential cross section as a function of the invariant Higgs pair mass and the total hadronic cross section are presented. Furthermore, the uncertainties not only from the renormalisation and factorisation scales but also the uncertainties due to the scheme-and-scale choice of the top mass are shown. In addition, the effects of varying the Higgs self-coupling strength on the cross section are investigated.

We present the current status of the Next-to-Next-to-Leading Order QED contribution to the mu e-scattering. Particular focus is given to the techniques involved to tackle the virtual amplitude and their automatic implementation. Renormalization of the amplitude will be also discuss in details.

We present the current status of the Next-to-Next-to-Leading Order QED contribution to the µescattering. Particular focus is given to the techniques involved to tackle the virtual amplitude and their automatic implementation. Renormalization of the amplitude will be also discuss in details.

Higgs-pair production via gluon fusion is the dominant production mechanism of Higgs-boson pairs at hadron colliders. In this work, we present details of our numerical determination of the full next-to-leading-order (NLO) QCD corrections to the leading top-quark loops. Since gluon fusion is a loop-induced process at leading order, the NLO calculation requires the calculation of massive two-loop diagrams with up to four different mass/energy scales involved. With the current methods, this can only be done numerically, if no approximations are used. We discuss the setup and details of our numerical integration. This will be followed by a phenomenological analysis of the NLO corrections and their impact on the total cross section and the invariant Higgs-pair mass distribution. The last part of our work will be devoted to the determination of the residual theoretical uncertainties with special emphasis on the uncertainties originating from the scheme and scale dependence of the (virtual) top mass. The impact of the trilinear Higgs-coupling variation on the total cross section will be discussed.

In this thesis, we present a novel idea to address the evaluation of multi-loop Feynman integrals, inspired by unitarity of S-matrix. In the first part of this work, we present the Feynman integral formalism. Within the dimensional regularization scheme, Feynman integrals are known to obey integration-by-parts identities (IBPs), yielding the identification of an independent integral basis, dubbed master integrals. We describe the currently adopted strategy for the amplitudes decomposition, known as reduction algorithm, which is based on IBPs for integrands with denominators that depend quadratically on the loop momenta (quadratic denominators). In the second part of this thesis, we present a novel strategy to decompose Feynman integrals based on the use of partial fractions decomposition of its integrand. Within this approach any multi-loop integrand is first decomposed into a combination of integrands that contain just a minimal, irreducible number of quadratic denominators and several other denominators that carry a linear dependence of the loop momenta (linear denominators). After partial fractioning, IBPs are applied to integrals with linear denominators, in order to identify an alternative set of master integrals. Finally, the obtained relations are combined back to restore the IBPs for the original integrals containing quadratic denominators only. We examine the underlying algebraic structure of dimensionally regulated integrals with linear denominators, classifying all spurious, vanishing classes of integrals that may emerge after partial fractioning. In the last part of the thesis, we present the implementation of the novel algorithm within a Mathematica code called Parsival (Partial fractions-baSed method for feynman Integral eVALuation), which has been interfaced to the public package Reduze, for the IBPs decomposition. Preliminary results for the application of Parsival+Reduze framework to 1-loop integrals for 2 -- n (n = 1; 2; 3) scattering processes, and to 2-loop integrals, corresponding to planar and non-planar diagrams for 2 -- n (n = 1; 2) scattering amplitudes are given in the final chapter. The proposed algorithm is suitable for parallelization, and the preliminary results show that its effectiveness can be improved by exploiting the symmetries of the integrand under redefinition of loop-momenta, not accounted for in the present version of the code. The proposed strategy is very general and it can be applied to any scattering reduction.