Related papers: Fuchsia and master integrals for splitting functio…
Dimensionally or analytically regulated Feynman integrals lead to relative twisted period integrals. We present a recent extension of the Griffiths-Dwork pole reduction algorithm for deriving the D-module of differential operators acting on…
We introduce SOFIA, a Mathematica package that automatizes the computation of singularities of Feynman integrals, based on new theoretical understanding of their analytic structure. Given a Feynman diagram, SOFIA generates a list of…
We report on a new method for the numerical evaluation of loop integrals, based on the Feynman Tree Theorem. The loop integrals are replaced by phase-space integration over fictitious extra on-shell particles. This integration can be…
A numerical program is presented which facilitates the computation of the full set of one-gluon loop diagrams (including ghost loop contributions), with M attached external gluon lines in all possible ways. The feasibility of such a task…
This work explores an unexpected application of Implicit Computational Complexity (ICC) to parallelize loops in imperative programs. Thanks to a lightweight dependency analysis, our algorithm allows splitting a loop into multiple loops that…
We propose a modification of the Hybrid-Monte-Carlo algorithm that allows for a larger step-size of the integration scheme at constant acceptance rate. The key ingredient is the splitting of the pseudo-fermion action into two parts. We test…
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…
We discuss a progress in calculation of Feynman integrals which has been done with help of the differential equation method and demonstrate the results for a class of two-point two-loop diagrams.
The derivation of the Feynman rules for lattice perturbation theory from actions and operators is complicated, especially for highly improved actions such as HISQ. This task is, however, both important and particularly suitable for…
We have studied possible applications of a particular pseudo-differential algebra in singular analysis for the construction of fundamental solutions and Green's functions of a certain class of elliptic partial differential operators. The…
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…
We present a symbolic-numeric Las Vegas algorithm for factoring Fuchsian ordinary differential operators with rational function coefficients. The new algorithm combines ideas of van Hoeij's "local-to-global" method and of the ''analytic''…
We present a detailed description of the recent idea for a direct decomposition of Feynman integrals onto a basis of master integrals by projections, as well as a direct derivation of the differential equations satisfied by the master…
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…
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 describe how a dlog representation of Feynman integrals leads to simple differential equations. We derive these differential equations directly in loop momentum or embedding space making use of a localization trick and generalized…
In this talk we discuss the construction of a basis of master integrals for the family of the $l$-loop equal-mass banana integrals, such that the differential equation is in an $\varepsilon$-factorised form. As the $l$-loop banana integral…
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…
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,…
Operator-splitting methods are widespread in the numerical solution of differential equations, especially the initial-value problems in ordinary differential equations that arise from a method-of-lines discretization of partial differential…