相关论文: 3-loop Feynman Integral Extrapolations for the Bas…
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…
General prescriptions for evaluation of coefficients at arbitrary powers and logarithms in the asymptotic expansion of Feynman diagrams in the Sudakov limit are discussed and illustrated by two-loop examples. Peculiarities connected with…
We explore inequality constraints as a new tool for numerically evaluating Feynman integrals. A convergent Feynman integral is non-negative if the integrand is non-negative in either loop momentum space or Feynman parameter space. Applying…
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…
We develop a geometric framework in Feynman-parameter space to determine constraints on the sequential discontinuities of Feynman integrals. Our method is based on tracking the deformation of the integration contour as external kinematics…
We present a new method for numerically computing generic multi-loop Feynman integrals. The method relies on an iterative application of Feynman's trick for combining two propagators. Each application of Feynman's trick introduces a…
We review in a pedagogical way the method of differential equations for the evaluation of D-dimensionally regulated Feynman integrals. After dealing with the general features of the technique, we discuss its application in the context of…
We introduce a new approach for the computation of the class of Feynman integrals whose integrands vanish in strictly four-dimensions, so-called ''pseudo-evanescent'' integrals. We argue that, up to $\mathcal{O}(\epsilon)$ corrections,…
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)…
A new powerful method to calculate Feynman diagrams is proposed. It consists in setting up a Taylor series expansion in the external momenta squared (in general multivariable). The Taylor coefficients are obtained from the original diagram…
We propose a strategy to study the analytic structure of Feynman parameter integrals where singularities of the integrand consist of rational irreducible components. At the core of this strategy is the identification of a selected stratum…
We evaluate the three-loop five-point pentagon-box-box massless integral family in the dimensional regularization scheme, via canonical differential equation. We use tools from computational algebraic geometry to enable the necessary…
We present an approach to analyze the scalar integrals of any Feynman diagrams in detail here. This method not only completely recovers some well-known results in the literature, but also produces some brand new results on the $C_{_0}$…
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 method for the evaluation of the epsilon expansion of multi-loop massless Feynman integrals is introduced. This method is based on the Gegenbauer polynomial technique and the expansion of the Gamma function in terms of harmonic sums.…
In this talk, we discuss how ideas from geometry help to improve Feynman integral reduction and the construction of $\varepsilon$-factorised differential equations. In particular, we outline a systematic procedure to obtain an…
We study a 3-loop 5-propagator Feynman Integral, which we call the vacuum seagull, with arbitrary masses and spacetime dimension using the Symmetries of Feynman Integrals method. It is our first example with potential numerators. We…
The $\varepsilon$-form of a system of differential equations for Feynman integrals has led to tremendeous progress in our abilities to compute Feynman integrals, as long as they fall into the class of multiple polylogarithms. It is…
New analytic formulas for one-loop three-point Feynman integrals in general space-time dimension ($d$) are presented in this paper. The calculations are performed at general configurations for internal masses and external momenta. The…
Using contour deformations and integrations over modular forms, we compute certain Bessel moments arising from diagrammatic expansions in two-dimensional quantum field theory. We evaluate these Feynman integrals as either explicit constants…