Related papers: Advances towards the systematization of calculatio…
Various first order approaches have been proposed in the literature to solve Linear Programming (LP) problems, recently leading to practically efficient solvers for large-scale LPs. From a theoretical perspective, linear convergence rates…
The MadGraph5 aMC@NLO framework aims to automate all types of leading- and next-to-leading-order-accurate simulations for any user-defined model that stems from a renormalisable Lagrangian. In this paper, we present all of the key…
New approach to computing the amplitudes of multi-particle processes in renormalizable quantum field theories is presented. Its major feature is a separation of the renormalization from the computation. Within the suggested approach new…
We invent an automated method for computing the divergent part of Feynman integrals in dimensional regularization. Our method exploits simplifications from four-dimensional integration-by-parts identities. Leveraging algorithms from the…
Integration-by-parts (IBP) identities and differential equations are the primary modern tools for the evaluation of high-order Feynman integrals. They are commonly derived and implemented in the momentum-space representation. We provide a…
We review some of the recent advances in the computation of one-loop scattering amplitudes which led to the construction of efficient and automated computational tools for NLO predictions. Particular attention is devoted to unitarity-based…
Complete Feynman diagram automatic computation systems are now coming of age after many years of development. They are made available to the high energy physics community through user-friendly interfaces. Theorists and experimentalists can…
We construct a diagrammatic coaction acting on one-loop Feynman graphs and their cuts. The graphs are naturally identified with the corresponding (cut) Feynman integrals in dimensional regularization, whose coefficients of the Laurent…
In this talk we present recent next-to-leading order results relevant for LHC phenomenology obtained with the GOLEM method. After reviewing the status of this Feynman diagrammatic approach for multi-leg one-loop calculations we discuss…
We device a new method to calculate a large number of Mellin moments of single scale quantities using the systems of differential and/or difference equations obtained by integration-by-parts identities between the corresponding Feynman…
We present an algorithm for the numerical calculation of one-loop QCD amplitudes. The algorithm consists of subtraction terms, approximating the soft, collinear and ultraviolet divergences of one-loop amplitudes and a method to deform the…
Using the Feynman parameter method, we have calculated in an elegant manner a set of one$-$loop box scalar integrals with massless internal lines, but containing 0, 1, 2, or 3 external massive lines. To treat IR divergences (both soft and…
We present a new regularization procedure called autoregularization. The new procedure regularizes the divergences, encountered previously in a scattering process, using the intrinsic scale of the process. We use autoregularization to…
The linearization of the meteorological equations around a specified reference state, usually applied in NWP to define the linear system of constant-coefficients semi-implicit schemes, is outlined as an unnecessarily restrictive approach…
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…
Scattering amplitudes are expected to admit a factorised structure in special kinematic limits, such as the Regge, soft and collinear limits. However, less is known about the precise mechanisms through which factorisation of $n$-particle…
We study the problem of computing the value function from a discretely-observed trajectory of a continuous-time diffusion process. We develop a new class of algorithms based on easily implementable numerical schemes that are compatible with…
Calculation of amplitudes in perturbative quantum field theory involve large loop integrals. The complexity of those integrals, in combination with the large number of Feynman diagrams, make the calculations very difficult. Reduction…
A method is developed whereby spinor helicity techniques can be used to simplify the calculation of loop amplitudes. This is achieved by using the Feynman-parameter representation where the offending off-shell loop momenta do not appear.…
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…