Related papers: One-loop three-point Feynman integrals with Appell…
Embedding Feynman integrals in Grassmannians, we can write Feynman integrals as some finite linear combinations of generalized hypergeometric functions. In this paper we present a general method to obtain Gauss relations among those…
A difference equation w.r.t. space-time dimension $d$ for $n$-point one-loop integrals with arbitrary momenta and masses is introduced and a solution presented. The result can in general be written as multiple hypergeometric series with…
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…
Recently in arXiv:2012.05599 Rudenko presented a formula for the volume of hyperbolic orthoschemes in terms of alternating polylogarithms. We use this result to provide an explicit analytic result for the one-loop scalar n-gon Feynman…
We show that the calculation of L-loop Feynman integrals in D dimensions can be reduced to a series of matrix multiplications in D times L dimensions. This gives rise to a new type of expansions for the critical exponents in three…
We give a complete analytical computation of three-point one-loop integrals with one heavy propagator, up to the third tensor rank, for arbitrary values of external momenta and masses.
We present a systematic method for reducing an arbitrary one-loop N-point massless Feynman integral with generic 4-dimensional momenta to a set comprised of eight fundamental scalar integrals: six box integrals in D=6, a triangle integral…
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…
In this article we present the complete massless and massive one-loop triangle diagram results using the negative dimensional integration method (NDIM). We consider the following cases: massless internal fields; one massive, two massive…
A systematic algorithm for obtaining recurrence relations for dimensionally regularized Feynman integrals w.r.t. the space-time dimension $d$ is proposed. The relation between $d$ and $d-2$ dimensional integrals is given in terms of a…
We discuss the systematic evaluation of 3-loop vacuum integrals with arbitrary masses. Using integration by parts, the general integral of this type can be reduced algebraically to a few basis integrals. We define a set of modified finite…
We present an analytical method to calculate the three-loop massive Feynman integral in arbitrary dimensions. The method is based on the Mellin-Barnes representation of the Feynman integral. The Meijer theorem and its corollary are used to…
We propose a general coaction for families of integrals appearing in the evaluation of Feynman diagrams, such as multiple polylogarithms and generalized hypergeometric functions. We further conjecture a link between this coaction and…
We give a complete analytical computation of three and two-point loop integrals occurring in heavy-particle theories, involving a velocity change, for arbitrary real values of the external masses and residual momenta.
This article is the second of a series of three presenting an alternative method to compute the one-loop scalar integrals. It extends the results of the first article to general complex masses. Let us remind the main features enjoyed by…
One-loop two-, three- and four-point scalar functions are analytically integrated directly such that they are expressed in terms of Lauricella's hypergeometric function $F_D$. For two- and three-point functions, exact expressions are…
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 explore the large set of linear transformations of Srivastava's $H_C$ triple hypergeometric function. This function has been recently linked to the massive one-loop conformal scalar 3-point Feynman integral. We focus here on the class of…
We show that all Feynman integrals in two Euclidean dimensions with massless propagators and arbitrary non-integer propagator powers can be expressed in terms of single-valued analogues of Aomoto-Gelfand hypergeometric functions. The latter…
The two point integrals contributing to the self energy of a particle in a three dimensional quantum field theory are calculated to two loop order in perturbation theory as well as the vacuum ones contributing to the effective potential to…