相关论文: ALGORITHMIC CALCULATION OF TWO-LOOP FEYNMAN DIAGRA…
Recently presented explicit formulae for asymptotic expansions of Feynman diagrams in the Sudakov limit are applied to typical two-loop diagrams. For a diagram with one non-zero mass these formulae provide an algorithm for analytical…
The calculation of the symmetry factor corresponding to a given Feynman diagram is well known to be a tedious problem. We have derived a simple formula for these symmetry factors. Our formula works for any diagram in scalar theory ($\phi^3$…
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…
In this work we report on a new version of FeynCalc, a Mathematica package widely used in the particle physics community for manipulating quantum field theoretical expressions and calculating Feynman diagrams. Highlights of the new version…
We present an algorithm to compute arbitrary multi-loop massive Feynman diagrams in the region where the typical energy scale \sqrt{s} is much larger than the typical mass scale M, i.e. s>>M^2, while various different energy and mass…
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 study the construction of local subtraction schemes through the lenses of tropical geometry. We focus on individual Feynman integrals in parametric presentation, and think of them as particular instances of Euler integrals. We provide a…
This article describes the latest versions of the Mathematica packages FeynArts, FormCalc, and LoopTools for the generation and evaluation of one-loop diagrams.
We present algorithms for the group independent reduction of group theory factors of Feynman diagrams. We also give formulas and values for a large number of group invariants in which the group theory factors are expressed. This includes…
We derive useful reduction formulae which express one-loop Feynman integrals with a large number of external momenta in terms of lower-point integrals carrying easily derivable kinematic coefficients which are symmetric in the external…
We present a Mathematica package AmpRed for the semi-automatic calculations of multi-loop Feynman amplitudes with high efficiency and precision. AmpRed implements the methods of integration by parts and differential equations in the…
The standard procedure for computing scalar multi-loop Feynman integrals consists in reducing them to a basis of so-called master integrals, derive differential equations in the external invariants satisfied by the latter and, finally, try…
FeynRules is a Mathematica-based package which addresses the implementation of particle physics models, which are given in the form of a list of fields, parameters and a Lagrangian, into high-energy physics tools. It calculates the…
A new approach to compute Feynman Integrals is presented. It relies on an integral representation of a given Feynman Integral in terms of simpler ones. Using this approach, we present, for the first time, results for a certain family of…
We introduce a new method to evaluate algebraic integrals over the simplex numerically. This new approach employs techniques from tropical geometry and exceeds the capabilities of existing numerical methods by an order of magnitude. The…
New algebraic approach to analytical calculations of D-dimensional integrals for multi-loop Feynman diagrams is proposed. We show that the known analytical methods of evaluation of multi-loop Feynman integrals, such as integration by parts…
We present a set of Feynman integrals appearing in calculations of different QED processes to the one-loop accuracy. We consider scalar, vector, and tensor integrals with two, three, four and five denominators. The cases of equal and…
Explicit formulae for asymptotic expansions of Feynman diagrams in typical limits of momenta and masses with external legs on the mass shell are presented.
We extend the auxiliary-mass-flow (AMF) method originally developed for Feynman loop integration to calculate integrals involving also phase-space integration. Flow of the auxiliary mass from the boundary ($\infty$) to the physical point…
We use the method of differential equations to analytically evaluate all planar three-loop Feynman integrals relevant for form factor calculations involving massive particles. Our results for ninety master integrals at general $q^2$ are…