Related papers: Complete reduction of integrals in two-loop five-l…
We present a new and fully general algorithm for the automated construction of the integrands of two-loop scattering amplitudes. This is achieved through a generalisation of the open-loops method to two loops. The core of the algorithm…
We present the powerful module-intersection integration-by-parts (IBP) method, suitable for multi-loop and multi-scale Feynman integral reduction. Utilizing modern computational algebraic geometry techniques, this new method successfully…
We review the current status of high-multiplicity double-virtual QCD corrections to processes relevant for LHC phenomenology. In particular, we discuss the recent full-color calculation of the five-parton process, whose two-loop amplitudes…
In this presentation, we review the general features of integrand-reduction techniques, with a particular focus on their generalization beyond one loop. We start with a brief discussion of the one-loop scenario, a case in which…
We describe three algorithms for computer-aided symbolic multi-loop calculations that facilitated some recent novel results. First, we discuss an algorithm to derive the canonical form of an arbitrary Feynman integral in order to facilitate…
We calculate the two-loop QCD corrections to $gg \to ZZ$ involving a closed top-quark loop. We present a new method to systematically construct linear combinations of Feynman integrals with a convergent parametric representation, where we…
We describe the calculation of the three-loop QCD corrections to quark and gluon form factors. The relevant three-loop Feynman diagrams are evaluated and the resulting three-loop Feynman integrals are reduced to a small set of known master…
Feynman integrals obey linear relations governed by intersection numbers, which act as scalar products between vector spaces. We present a general algorithm for constructing multivariate intersection numbers relevant to Feynman integrals,…
The systematic approach to solving the recurrence relations for multi-loop integrals is described. In particular, the criteria of their reducibility is suggested.
We show how to extract the coefficients of the 4-, 3-, 2- and 1-point one-loop scalar integrals from the full one-loop amplitude of arbitrary scattering processes. In a similar fashion, also the rational terms can be derived. Basically no…
We present the first numerical results for the two-loop helicity amplitudes for the scattering of four partons and a W-boson in QCD. We use a finite field sampling method to reduce directly from Feynman diagrams to the coefficients of a set…
I discuss the recent advances in the computation of two-loop scattering amplitudes for five-particle processes. The latter are fundamental ingredients to obtain predictions at the next-to-next-to-leading order (NNLO) in QCD for many…
The calculation of hard scattering amplitudes up to NLO is automated in numerical tools, such as OpenLoops. The LHC and future experiments, however, demand high-precision predictions at NNLO and beyond for a wide range of particle…
This document is a contribution to the proceedings of the MathemAmplitudes 2019 conference held in December 2019 in Padova, Italy. A key step in modern high energy physics scattering amplitudes computation is to express the latter in terms…
We propose a novel approach for solving the scattering of light onto a two-level atom coupled to a one-dimensional waveguide. We first express the physical quantity of interest in terms of Feynman diagrams and treat the atom as a…
A summary of the calculation of the color-planar and complete light quark contributions to the massive three-loop form factors is presented. Here a novel calculation method for the Feynman integrals is used, solving general uni-variate…
We consider the three-loop scattering amplitudes for the production of a pair of photons in quark-antiquark annihilation in Quantum Chromodynamics (QCD). We use suitably defined projectors to efficiently calculate all helicity amplitudes.…
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.…
Higher orders in perturbation theory require the calculation of Feynman integrals at multiple loops. We report on an approach to systematically solve Feynman integrals by means of symbolic summation and discuss the underlying algorithms.…
We suggest a possible algorithm to calculate one-loop n-point functions within a variant of light-front perturbation theory. The key ingredients are the covariant Passarino-Veltman scheme and a surprising integration formula that localises…