Related papers: The SAGEX Review on Scattering Amplitudes, Chapter…
In the context of high-energy particle physics, a reliable theory-experiment confrontation requires precise theoretical predictions. This translates into accessing higher-perturbative orders, and when we pursue this objective, we inevitably…
We provide high-energy approximations for all one-loop scalar 3- and 4-point functions and the corresponding tensor integrals that appear in scattering processes with four external on-shell particles. Our expressions are valid if all…
In this paper, we describe a numerical approach to evaluate Feynman loop integrals. In this approach the key technique is a combination of a numerical integration method and a numerical extrapolation method. Since the computation is carried…
A detailed investigation is presented of a set of algorithms which form the basis for a fast and reliable numerical integration of one-loop multi-leg (up to six) Feynman diagrams, with special attention to the behavior around (possibly)…
We find that all Feynman integrals (FIs), having any number of loops, can be completely determined once linear relations between FIs are provided. Therefore, FIs computation is conceptually changed to a linear algebraic problem. Examples up…
We introduce a new method to evaluate algebraic integrals over the simplex numerically. This new approach employs techniques from tropical geometry and exceeds the capabilities of existing numerical methods by an order of magnitude. The…
The two-loop QCD corrections to vector boson pair production at hadron colliders involve a new class of Feynman integrals: two-loop four-point functions with two off-shell external legs. We describe their reduction to a small set of master…
The precision frontier in collider physics is being pushed at impressive speed, from both the experimental and the theoretical side. The aim of this review is to give an overview of recent developments in precision calculations within the…
Integer relation algorithms can convert numerical results for Feynman integrals to exact evaluations, when one has reason to suspect the existence of reductions to linear combinations of a basis, with rational or algebraic coefficients.…
We reduce all the most complicated Feynman integrals in two-loop five-light-parton scattering amplitudes to basic master integrals, while other integrals can be reduced even easier. Our results are expressed as systems of linear relations…
Canonical Feynman integrals are of great interest in the study of scattering amplitudes at the multi-loop level. We propose to construct $d\log$-form integrals of the hypergeometric type, treat them as a representation of Feynman integrals,…
Precision measurements together with exact theoretical calculations have led to steady progress in fundamental physics. A brief survey is given on recent developments and current achievements in the field of perturbative precision…
Building on the idea of numerically integrating differential equations satisfied by Feynman integrals, we propose a novel strategy for handling branch cuts within a numerical framework. We develop an integrator capable of evaluating a basis…
We compute all planar two-loop six-point Feynman integrals entering scattering observables in massless gauge theories such as QCD. A central result of this paper is the formulation of the differential-equations method under the algebraic…
Over the last year significant progress was made in the understanding of the computation of Feynman integrals using differential equations. These lectures give a review of these developments, while not assuming any prior knowledge of the…
We explore how various topics in modern scattering amplitudes research find application in the description of collider physics processes. After a brief review of experimentally measured quantities and how they are related to amplitudes, we…
An explicit investigation about the equal-mass two-loop sunrise Feynman graph is performed. Such perturbative amplitude is related with many important physical process treated in the standard model context. The background of this…
This PhD thesis explores the potential of quantum computing to address computational challenges in high-energy physics (HEP). As the Standard Model (SM) leaves key questions unanswered and no signs of new physics have emerged since the…
Feynman integrals in quantum field theory evaluate to special functions and numbers that are usefully described by the notion of transcendental weight. In this paper, we propose a way of projecting a given dimensionally-regularised Feynman…
The physics of high-energy collider experiments asks for delicate comparisons between theoretical predictions and experimental data. Signals and potential backgrounds for new physics have to be predicted at sufficient accuracy. The accuracy…