Related papers: One-loop Feynman Integral Reduction by Differentia…

By introducing an auxiliary parameter, we find a new representation for Feynman integrals, which defines a Feynman integral by analytical continuation of a series containing only vacuum integrals. The new representation therefore…

We present a new approach to the reduction of one-loop amplitudes obtained by reconstructing the tensorial expression of the scattering amplitudes. The reconstruction is performed at the integrand level by means of a sampling in the…

We study operator-splitting schemes for approximating Koopman generators of linear semigroups induced by nonlinear flows, a framework originating with Dorroh and Neuberger. Building on ideas of Lie, Kowalewski, and Gr\"{o}bner, we analyze…

Dimensional regularization of Euclidean momentum space integrals is a highly successful technique in renormalization of quantum field theories. While it yields a straightforward algorithmic method, with which to evaluate diagrams beyond…

By taking the Weyl equation with external electro-magnetic potentials as the simplest representative for a system of PDOs, we give a new method of treating non-commutativity of coefficients matrices. More precisely, we construct a Fourier…

We present a novel approach for loop integral reduction in the Feynman parametrization using intersection theory and relative cohomology. In this framework, Feynman integrals correspond to boundary-supported differential forms in the…

A method is introduced to calculate the UV-divergent parts at one-loop level in dimensional regularization. The method is based on the recursion, and the basic integrals are just the scaleless integrals after the recursive reduction, which…

We present a novel approach to optimizing the reduction of Feynman integrals using integration-by-parts identities. By developing a priority function through the FunSearch algorithm, which combines large language models and genetic…

We describe in detail the constrained procedure of differential renormalization and develop the techniques required for one-loop calculations. As an illustration we renormalize Scalar QED and show that the two-, three- and four-point Ward…

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 recently presented a new method for the evaluation of one-loop amplitude of arbitrary scattering processes, in which the reduction to scalar integrals is performed at the integrand level. In this talk, we review the main features of the…

We consider one-loop scalar and tensor integrals with an arbitrary number of external legs relevant for multi-parton processes in massless theories. We present a procedure to reduce N-point scalar functions with generic 4-dimensional…

In this paper we describe a method of calculation of master integrals based on the solution of systems of difference equations in one variable. Various explicit examples are given, as well as the generalization to arbitrary diagrams.

Building on the open-loop algorithm we introduce a new method for the automated construction of one-loop amplitudes and their reduction to scalar integrals. The key idea is that the factorisation of one-loop integrands in a product of loop…

Light-front gauge is the most popular one to work with fundamental interactions, due to its characteristic maximum kinematical Poincare operators that it allows. However, it is also known to be one of the trickiest gauges one can work with…

This article is the second of a series of three presenting an alternative method to compute the one-loop scalar integrals. It extends the results of the first article to general complex masses. Let us remind the main features enjoyed by…

The tensor Feynman amplitudes are reduced to scalar integrals by a procedure of Passarino and Veltman. We provide an alternative approach based on the causal formalism.

This work investigates in detail the performance and advantages of a new quantum Monte Carlo integrator, dubbed Quantum Fourier Iterative Amplitude Estimation (QFIAE), to numerically evaluate for the first time loop Feynman integrals in a…

The Koopman Operator (KO) offers a promising alternative methodology to solve ordinary differential equations analytically. The solution of the dynamical system is analyzed in terms of observables, which are expressed as a linear…

We present the computation of a full set of planar five-point two-loop master integrals with one external mass. These integrals are an important ingredient for two-loop scattering amplitudes for two-jet-associated W-boson production at…