Related papers: Numerical Evaluation of One-Loop Diagrams Near Exc…

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)…

Problems occurring in physically important non-trivial examples of loop calculations are discussed. A procedure of deriving expansions of two-loop self-energy diagrams with different masses is constructed. The cases of small and large…

A scheme for systematically achieving accurate numerical evaluation of multi-loop Feynman diagrams is developed. This shows the feasibility of a project aimed to produce a complete calculation for two-loop predictions in the Standard Model.…

We determine the numerical values of scalar multi-loop two-vertex Feynman diagrams, the generalized sunset diagrams, by integrating all but the longitudinal momenta analytically. For the longitudinal momenta we introduce one collective…

We discuss some of the problems that may occur in the calculation of complicated Feynman diagrams. These include the group independent evaluation of color factors, and the summation techniques that are needed for the expansion of diagrams…

In this article, we explore the structure of IR singularity of Feynman diagrams at one loop via power counting in loop momentum. The emphasis is on many known results which follow from this simple analysis.

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…

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 recently proposed scheme for numerical evaluation of Feynman diagrams is extended to cover all two-loop two-point functions with arbitrary internal and external masses. The adopted algorithm is a modification of the one proposed by F. V.…

We discuss the computational complexity of the perturbative evaluation of scattering amplitudes, both by the Caravaglios-Moretti algorithm and by direct evaluation of the individual diagrams. For a self-interacting scalar theory, we…

We initiate a systematic study of one-loop integrals by investigating the connection between their singularity structures and geometric configurations in the projective space associated to their Feynman parametrization. We analyze these…

The paper reports a technique of evaluation of Feynman diagrams in the mixed coordinate-momentum representation. The technique is employed for a recalculation of the two-loop self-energy correction for the ground state of hydrogen-like ions…

We present a perturbation theory by extending a prescription due to Feynman for computing the probability density function for the random flight motion. The method can be applied to a wide variety of otherwise difficult circumstances. The…

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…

The matching problem is a notorious combinatorial optimization problem that has attracted for many years the attention of the statistical physics community. Here we analyze the Euclidean version of the problem, i.e. the optimal matching…

We suggest a possible algorithm to calculate one-loop n-point functions within a variant of light-front perturbation theory. The key ingredients are the covariant Passarino-Veltman scheme and a surprising integration formula that localises…

In this review, we discuss recent developments concerning efficient calculations of multi-loop multi-leg scattering amplitudes. Inspired by the remarkable properties of the Loop-Tree Duality (LTD), we explain how to reconstruct an integrand…

An efficient way to calculate one-loop counterterms within the Feynman diagrammatic approach and dimensional regularization is to expand the propagators in the integrands of the Feynman integrals around vanishing external momentum. In this…

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…

The near threshold expansion of Feynman diagrams is derived from their configuration space representation, by performing all x integrations. The general scalar Feynman diagram is considered, with an arbitrary number of external momenta, an…