相关论文: ALGORITHMIC CALCULATION OF TWO-LOOP FEYNMAN DIAGRA…

We report on some recent developments in algebraic tensor reduction of one-loop Feynman integrals. For 5-point functions, an efficient tensor reduction was worked out recently and is now available as numerical C++ package, PJFry, covering…

We present a new formula for the coaction of a large class of integrals. When applied to one-loop (cut) Feynman integrals, it can be given a diagrammatic representation purely in terms of pinches and cuts of the edges of the graph. The…

We present short review of two methods for obtaining functional equations for Feynman integrals. Application of these methods for finding functional equations for one- and two- loop integrals is described in detail. It is shown that with…

A method for calculating the $1/d$ expansion coefficients for solutions of integration by parts relations for Feynman integrals is presented. The idea is to use linear substitutions to transform these relations to an explicitly recursive…

We show how Feynman diagrams may be evaluated to take advantage of recent developments in the application of Cutkosky rules to the calculation of one-loop amplitudes. A sample calculation of gg->gH, previously calculated by Ellis et al., is…

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…

For the investigation of higher order Feynman integrals, potentially with tensor structure, it is highly desirable to have numerical methods and automated tools for dedicated, but sufficiently 'simple' numerical approaches. We elaborate two…

For certain dimensionally-regulated one-, two- and three-loop diagrams, problems of constructing the epsilon-expansion and the analytic continuation of the results are studied. In some examples, an arbitrary term of the epsilon-expansion…

Details of recent developments of the Feynman diagram analyzer DIANA (DIagram ANAlyser) are presented. Apart from some discussion about QGRAF and new plotting features, we concentrate on a new sophisticated mechanism of momenta mapping.

FeynMaster is a multi-tasking software for particle physics studies. By making use of already existing programs (FeynRules, QGRAF, FeynCalc), FeynMaster automatically generates Feynman rules, generates and draws Feynman diagrams, generates…

We present a method to evaluate numerically Feynman diagrams directly from their Feynman parameters representation. We first disentangle overlapping singularities using sector decomposition. Threshold singularities are treated with an…

A comprehensive study is performed of two-loop Feynman diagrams with three external legs which, due to the exchange of massless gauge-bosons, give raise to infrared and collinear divergencies. Their relevance in assembling realistic…

We discuss the program EXP used to automate the successive application of asymptotic expansions to Feynman diagrams. We focus on the generation of the relevant subgraphs and the determination of the topologies for the remaining integrals.…

An expansion scheme is developed for Feynman diagrams describing the production of one massive and one massless particle near the threshold. As an example application, we compute the correlators of heavy-light quark currents, (\bar b…

In recent years, differential equations have become the method of choice to compute multi-loop Feynman integrals. Whenever they can be cast into canonical form, their solution in terms of special functions is straightforward. Recently,…

The demand for precision predictions in the field of high energy physics has dramatically increased over recent years. Experiments conducted at the LHC, as well as precision measurements at the intensity frontier such as Belle II require…

A new kind of cut diagram is introduced to sum Feynman diagrams with nonabelian vertices. Unlike the Cutkosky diagrams which compute the discontinuity of single Feynman diagrams, the nonabelian cut diagrams represent a resummation of both…

We continue our study of the construction of analytical coefficients of the epsilon-expansion of hypergeometric functions and their connection with Feynman diagrams. In this paper, we apply the approach of obtaining iteratated solutions to…

In this paper we study high order expansions of chart maps for local finite dimensional unstable manifolds of hyperbolic equilibrium solutions of scalar parabolic partial differential equations. Our approach is based on studying an…

New developments concerning the extension of the Feynman diagram analyzer DIANA are presented. We discuss new graphic facilities, application of DIANA to processes with Majorana fermions and different approaches to automation of momenta…