相关论文: Critical Points and Syzygies for Feynman Integrals

The Symmetries of Feynman Integrals method (SFI) associates a natural Lie group with any diagram, depending only on its topology. The group acts on parameter space and the method determines the integral's dependence within group orbits.…

Intersection numbers are rational scalar products among functions that admit suitable integral representations, such as Feynman integrals. Using these scalar products, the decomposition of Feynman integrals into a basis of linearly…

We use the loop-by-loop Baikov representation to investigate the geometries in Feynman integrals contributing to the classical dynamics of a black-hole two-body system in the post-Minkowskian expansion of general relativity. These…

Standard integration-by-parts (IBP) reduction methods typically yield Feynman integral bases where the reduction of some integrals gives rise to coefficients singular as the dimensional regulator $\epsilon\rightarrow 0$. These singular…

Let $F \in \R[X_1,\ldots,X_n]$ and the zero set $V=\zero(\mathcal{P},\R^n)$, where $\mathcal{P}:=\{P_1,\ldots,P_s\} \subset \R[X_1,\ldots,X_n]$ is a finite set of polynomials. We investigate existence of critical points of $F$ on an…

Numerical evaluations of Feynman integrals often proceed via a deformation of the integration contour into the complex plane. While valid contours are easy to construct, the numerical precision for a multi-loop integral can depend…

Higher-point functions in N = 4 super Yang-Mills theory can be constructed using integrability by triangulating the surfaces on which Feynman graphs would be drawn. It remains hard to analytically compute the necessary re-gluing of the…

In this work, we study the computation of reduction coefficients for multi loop Feynman integrals using generating functions constructed within the Baikov representation. Compared with traditional Feynman rules, the Baikov formalism offers…

We show how a large class of Feynman integrals can be efficiently reduced to master integrals by suitable covariant differentiation on the vector space dual to the one spanned by the master integrals. The connections needed in the covariant…

The method of Symmetries of Feynman Integrals defines for any Feynman diagram a set of partial differential equations. On some locus in parameter space the equations imply that the diagram can be reduced to a linear combination of simpler…

Finite-part integration is a recent method of evaluating a convergent integral in terms of the finite-parts of divergent integrals deliberately induced from the convergent integral itself [E. A. Galapon, Proc. R. Soc., A 473, 20160567…

We present a novel approach to optimizing the reduction of Feynman integrals using integration-by-parts identities. By developing a priority function through the FunSearch algorithm, which combines large language models and genetic…

We evaluate analytically all previously unknown nonplanar master integrals for massless five-particle scattering at two loops, using the differential equations method. A canonical form of the differential equations is obtained by…

We compute a complete set of the two-loop Feynman integrals that are required for the next-to-next-to-leading order QCD corrections to on-shell top-pair production in association with a $W$ boson at hadron colliders in the leading colour…

We compute three families of two-loop six-point massless Feynman integrals in dimensional regularization, namely the double-box, the pentagon-triangle, and the hegaxon-bubble family. This constitutes the first analytic computation of…

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…

In this paper we discuss the geometric integrand expansion of the five-point Wilson loop with one Lagrangian insertion in maximally supersymmetric Yang-Mills theory. We construct the integrand corresponding to an all-loop class of…

Over the last year significant progress was made in the understanding of the computation of Feynman integrals using differential equations. These lectures give a review of these developments, while not assuming any prior knowledge of the…

In even space-time dimensions the multi-loop Feynman integrals are integrals of rational function in projective space. By using an algorithm that extends the Griffiths--Dwork reduction for the case of projective hypersurfaces with…

We consider four-point integrals arising in the planar limit of the conformal "fishnet" theory in four dimensions. They define a two-parameter family of higher-loop Feynman integrals, which extend the series of ladder integrals and were…