Related papers: Numerical implementation of the Loop-Tree Duality …
We extend useful properties of the $H\to\gamma\gamma$ unintegrated dual amplitudes from one- to two-loop level, using the Loop-Tree Duality formalism. In particular, we show that the universality of the functional form -- regardless of the…
One of the most severe bottlenecks to reach high-precision predictions in QFT is the calculation of multiloop multileg Feynman integrals. Several new strategies have been proposed in the last years, allowing impressive results with deep…
A comprehensive study is performed of two-loop Feynman diagrams with three external legs which, due to the exchange of massless gauge-bosons, give raise to infrared and collinear divergencies. Their relevance in assembling realistic…
We describe the calculation of the one-loop corrections to $H \to \gamma \gamma$ and $g g \to H$ within the four-dimensional unsubtraction/loop-tree duality (FDU/LTD) approach. The fact that these corrections are both IR and UV finite is…
A fully numerical method to calculate loop integrals, a numerical contour-integration method, is proposed. Loop integrals can be interpreted as a contour integral in a complex plane for an integrand with multi-poles in the plane. Stable and…
We present an analytic calculation of three-loop four-point Feynman integrals with two off-shell legs of equal mass. We provide solutions to the canonical differential equations of two integral families in both Euclidean and physical…
A scheme for systematically achieving accurate numerical evaluation of multi-loop Feynman diagrams is developed. This shows the feasibility of a project aimed to produce a complete calculation for two-loop predictions in the Standard Model.…
We describe a constructive procedure to separate overlapping infrared divergences in multi-loop integrals. Working with a parametric representation in D=4-2*epsilon dimensions, adequate subtractions lead to a Laurent series in epsilon,…
We present the integrand reduction via multivariate polynomial division as a natural technique to encode the unitarity conditions of Feynman amplitudes. We derive a recursive formula for the integrand reduction, valid for arbitrary…
The numerical unitarity approach has been important for obtaining reliable QCD predictions for the LHC. Here I discuss the extension of the approach beyond the leading quantum corrections for computing multi-loop amplitudes. The numerical…
We apply the differential equation technique to the calculation of the one-loop massless diagram with five onshell legs. Using the reduction to $\epsilon$-form, we manage to obtain a simple one-fold integral representation exact in…
We present recent developments on the topic of the integrand reduction of scattering amplitudes. Integrand-level methods allow to express an amplitude as a linear combination of Master Integrals, by performing operations on the…
Direct hyperlogarithmic integration offers a strong alternative to differential equation methods for Feynman integration, particularly for multi-particle diagrams. We review a variety of results by the authors in which this method, employed…
Feynman loop integrals are a key ingredient for the calculation of higher order radiation effects, and are responsible for reliable and accurate theoretical prediction. We improve the efficiency of numerical integration in sector…
The computation of multi-loop multi-leg scattering amplitudes plays a key role to improve the precision of theoretical predictions for particle physics at high-energy colliders. In this work, we focus on the mathematical properties of the…
First results towards a general method for asymptotic expansions of Feynman amplitudes in the loop-tree duality (LTD) formalism are presented. The asymptotic expansion takes place at integrand-level in the Euclidean space of the loop…
A proof-of-concept application of a quantum algorithm to multiloop Feynman integrals in the Loop-Tree Duality (LTD) framework is applied to a representative four-loop topology. Bootstrapping causality in the LTD formalism, is a suitable…
At variance with fully inclusive quantities, which have been computed already at the two- or three-loop level, most exclusive observables are still known only at one-loop, as further progress was hampered so far by the greater computational…
We propose multiloop vacuum amplitudes as the optimal building blocks for efficiently assembling theoretical predictions at high-energy colliders. This hypothesis is strongly supported by the manifestly causal properties of the loop-tree…
We discuss the duality theorem, which provides a relation between loop integrals and phase space integrals. We rederive the duality relation for the one-loop case and extend it to two and higher-order loops. We explicitly show its…