Related papers: Multi-Loop Calculations in the Standard Model: Tec…
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.
In this paper we present a method of discrete modeling and analysis of multi-level dynamics of complex large-scale hierarchical dynamic systems subject to external dynamic control mechanism. In a model each state describes parallel dynamics…
For two-loop two-point diagrams with arbitrary masses, an algorithm to derive the asymptotic expansion at large external momentum squared is constructed. By using a general theorem on asymptotic expansions of Feynman diagrams, the…
We extend existing dispersive approach in subloop insertion to the case of crossed two-loop box type topologies. Based on the ideas of the Feynman trick, mass shift approach and dispersive representation of two-point Passarino-Veltman…
Scattering amplitudes at loop level can be expressed in terms of Feynman integrals. The latter satisfy partial differential equations in the kinematical variables. We argue that a good choice of basis for (multi-)loop integrals can lead to…
A simple systematic method for calculating derivative expansions of the one-loop effective action is presented. This method is based on using symbols of operators and well known deformation quantization theory. To demonstrate its advantages…
Two-loop vertex Feynman diagrams with infrared and collinear divergences are investigated by two independent methods. On the one hand, a method of calculating Feynman diagrams from their small momentum expansion extended to diagrams with…
We introduce a new method for computing massless Feynman integrals analytically in parametric form. An analysis of the method yields a criterion for a primitive Feynman graph $G$ to evaluate to multiple zeta values. The criterion depends…
A formalism for the numerical integration of one- and two-loop integrals is presented. It is based on subtraction terms which remove the soft, collinear and some of the ultraviolet divergences from the integrand. The numerical integral is…
We review the main steps of the differential equation approach to the analytic evaluation of Feynman graphs, showing at the same time its application to the 3-loop sunrise graph in a particular kinematical configuration.
A method of Feynman diagrams summation, based on using Schwinger-Dyson equations and Ward identities, is verified by calculating some four-loop diagrams in N=1 supersymmetric electrodynamics, regularized by higher derivatives. In…
We review the method of the calculation of multiloop integrals suggested in Ref.\cite{Lee2010}.
We present a new methodology, suitable for implementation on computer, to perform the $\epsilon$-expansion of hypergeometric functions with linear $\epsilon$ dependent Pochhammer parameters in any number of variables. Our approach allows…
The role of differential equations in the process of calculating Feynman integrals is reviewed. An example of a diagram is given for which the method of differential equations was introduced, the properties of the inverse-mass-expansion…
An important aspect of improving perturbative predictions in high energy physics is efficiently reducing dimensionally regularised Feynman integrals through integration by parts (IBP) relations. The well-known triangle rule has been used to…
In this paper, we study systematically scalar one-loop two-, three-, and four-point Feynman integrals with complex internal masses. Our analytic results presented in this report are valid for both real and complex internal masses. The…
We discuss a progress in calculations of Feynman integrals based on the Gegenbauer Polynomial Technique and the Differential Equation Method. We demonstrate the results for a class of two-point two-loop diagrams and the evaluation of most…
In this talk, we discuss recent progress in the application of generalizations of polylogarithms in the symbolic computation of multi-loop integrals. We briefly review the Maple program MPL which supports a certain approach for the…
Motivated by the results of the electroweak precision experiments, studies of two-loop self-energy Feynman diagrams are performed. An algebraic method for the reduction of all two-loop self-energies to a set of standard scalar integrals is…
We present a program that implements the OPP reduction method to extract the coefficients of the one-loop scalar integrals from a user defined (sub)-amplitude or Feynman Diagram, as well as the rational terms coming from the 4-dimensional…