Abstract: Newer lattice results indicate that, in the Landau gauge at low spacelike momenta, the gluon propagator and the ghost dressing function are finite non-zero. This leads to a definition of the QCD running coupling, in a specific scheme, that goes to zero at low spacelike momenta. We construct a running coupling which fulfills these conditions, and at the same time reproduces to a high precision the perturbative behavior at high momenta. The coupling is constructed in such a way that it reflects qualitatively correctly the holomorphic (analytic) behavior of spacelike observables in the complex plane of the squared momenta, as dictated by the general principles of quantum field theories. Further, we require the coupling to reproduce correctly the nonstrange semihadronic decay rate of tau lepton which is the best measured low-momentum QCD observable with small higher-twist effects. Subsequent application of the Borel sum rules to the V + A spectral functions of tau lepton decays, as measured by OPAL Collaboration, determines the values of the gluon condensate and of the V + A six-dimensional condensate, and reproduces the data to a significantly higher precision than the usual (MS) over bar running coupling.

Abstract: 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.

Abstract: The numerical evaluation of multi-loop scattering amplitudes in the Feynman representation usually requires to deal with both physical (causal) and unphysical (non-causal) singularities. The loop-tree duality (LTD) offers a powerful framework to easily characterise and distinguish these two types of singularities, and then simplify analytically the underling expressions. In this paper, we work explicitly on the dual representation of multi-loop Feynman integrals generated from three parent topologies, which we refer to as Maximal, Next-to-Maximal and Next-to-Next-to-Maximal loop topologies. In particular, we aim at expressing these dual contributions, independently of the number of loops and internal configurations, in terms of causal propagators only. Thus, providing very compact and causal integrand representations to all orders. In order to do so, we reconstruct their analytic expressions from numerical evaluation over finite fields. This procedure implicitly cancels out all unphysical singularities. We also interpret the result in terms of entangled causal thresholds. In view of the simple structure of the dual expressions, we integrate them numerically up to four loops in integer space-time dimensions, taking advantage of their smooth behaviour at integrand level.