相关论文: Calculating four-loop tadpoles with one non-zero m…

Using the parallel/orthogonal space method, we calculate the planar two-loop three-point diagram and two rotated reduced planar two-loop three-point diagrams. Together with the crossed topology, these diagrams are the most complicated ones…

A numerical approach to compute tensor integrals in one-loop calculations is presented. The algorithm is based on a recursion relation which allows to express high rank tensor integrals as a function of lower rank ones. At each level of…

An algorithm is constructed to derive a small momentum expansion for two-loop two-point diagrams in all cases where, due to the presence of physical thresholds, there are singularities at zero external momentum. The coefficients of this…

In this talk we present techniques for calculating one-loop amplitudes for multi-leg processes using Feynman diagrammatic methods in a semi-algebraic context. Our approach combines the advantages of the different methods allowing for a fast…

We present a new Fortran code to calculate the scalar one-loop four-point integral with complex internal masses, based on the method of 't Hooft and Veltman. The code is applicable when the external momenta fulfill a certain physical…

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…

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…

We calculate the two-loop vertex function for the crossed topology, and for arbitrary masses and external momenta. We derive a double integral representation, suitable for a numerical evaluation by a Gaussian quadrature. Real and imaginary…

This article is the first of a series of three presenting an alternative method to compute the one-loop scalar integrals. This novel method enjoys a couple of interesting features as compared with the method closely following 't Hooft and…

An overview is presented on the current status of main mathematical computation methods for the multi-loop corrections to single scale observables in quantum field theory and the associated mathematical number and function spaces and…

We compute the one-loop four-point function in {\cal N}=4 supersymmetric Yang-Mills theory with gauge group U(N). We perform the calculation in {\cal N}=1 superspace using the background field method and obtain the complete off-shell…

We report on the results of an ongoing calculation of massive scalar one-loop one-, two-, three- and four-point functions needed in the NNLO calculation of heavy hadron production.

We present a $(1+\epsilon)$-approximation algorithm running in $O(f(\epsilon)\cdot n \log^4 n)$ time for finding the diameter of an undirected planar graph with non-negative edge lengths.

Reference [1] introduces a method for computing numerically four-dimensional multi-loop integrals without performing an explicit analytic contour deformation around threshold singularities. In this paper, we extend such a technique to…

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 present a method for the direct extraction of rational contributions to one-loop scattering amplitudes, missed by standard four-dimensional unitarity techniques. We use generalised unitarity in $D=4-2\e$ dimensions to write the loop…

A number of exact results for two-loop three-point diagrams with massless internal particles and arbitrary (off-shell) external momenta are presented. Divergent contributions are calculated in the framework of dimensional regularization.

The talk briefly reviews the current state of the art in doing multiloop QCD calculations in a completely analytic way. In particular, we discuss recent analytical calculation of 4-loop O(alpha_s**3) gluino contribution to R(s) and its…

I describe a method to calculate a class of three-loop selfenergy diagrams for arbitrary internal masses and external momentum. This method combines analytical results and numerical integration, and is suitable for implementation in a…

A detailed investigation is presented of a set of algorithms which form the basis for a fast and reliable numerical integration of one-loop multi-leg (up to six) Feynman diagrams, with special attention to the behavior around (possibly)…