Related papers: Reduction of multi-leg loop integrals
Bilevel optimisation is used in inverse imaging problems for hyperparameter learning/identification and experimental design, for instance, to find optimal regularisation parameters and forward operators. However, computationally, 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 ideas behind the concept of algebraic ("integration-by-parts") algorithms for multiloop calculations are reviewed. For any topology and mass pattern, a finite iterative algebraic procedure is proved to exist which transforms the…
I present an algorithm for the reconstruction of multivariate rational functions from black-box probes. The arguably most important application in high-energy physics is the calculation of multi-loop and multi-leg amplitudes, where rational…
This paper presents a novel feedback method on the motion planning for unicycle robots in environments with static obstacles, along with an extension to the distributed planning and coordination in multi-robot systems. The method employs a…
Direct hyperlogarithmic integration offers a strong alternative to differential equation methods for Feynman integration, particularly for multi-particle diagrams. We review a variety of results by the authors in which this method, employed…
We provide a sufficient condition for avoiding squared propagators in the intermediate stages of setting up differential equations for loop integrals. This condition is satisfied in a large class of two- and three-loop diagrams. For these…
In this paper, we generalize the unitarity method to two-loop diagrams and use it to discuss the integral bases of reduction. To test out method, we focus on the four-point double-box diagram as well as its related daughter diagrams, i.e.,…
One remaining problem of unitarity cut method for one-loop integral reduction is that tadpole coefficients can not be straightforward obtained through this way. In this paper, we reconsider the problem by applying differential operators…
A comprehensive study is performed of general massive, tensor, two-loop Feynman diagrams with two and three external legs. Reduction to generalized scalar functions is discussed. Integral representations, supporting the same class of…
This paper addresses the problem of efficiently computing higher-order variational integrators in simulation and trajectory optimization of mechanical systems as those often found in robotic applications. We develop $O(n)$ algorithms to…
We examine maximal unitarity in the nonplanar case and derive remarkably compact analytic expressions for coefficients of master integrals with two-loop crossed box topology in massless four-point amplitudes in any gauge theory, thereby…
Recently there is an alternative reduction method proposed by Chen in [1,2]. In this paper, using the one-loop scalar integrals with propagators having higher power, we show the power of the improved version of Chen's new method in which we…
We review several multi-loop techniques for analytical massless Feynman diagram calculations in relativistic quantum field theories: integration by parts, the method of uniqueness, functional equations and the Gegenbauer polynomial…
We illustrate a duality relation between one-loop integrals and single-cut phase-space integrals. The duality relation is realised by a modification of the customary +i0 prescription of the Feynman propagators. The new prescription…
The differential-reduction algorithm, which allows one to express generalized hypergeometric functions with parameters of arbitrary values in terms of such functions with parameters whose values differ from the original ones by integers, is…
We review an approach for the computation of Feynman integrals by use of multiple polylogarithms, with an emphasis on the related criterion of linear reducibility of the graph. We show that the set of graphs which satisfies the linear…
A Mathematica implementation of the program LERG-I is presented that performs the reduction of tensor integrals, encountered in one-loop Feynman diagram calculations, to scalar integrals. The program was originally coded in REDUCE and in…
Magnetic quadrupoles are essential components of particle accelerators like the Large Hadron Collider. In order to study numerically the stability of the particle beam crossing a quadrupole, a large number of particle revolutions in the…
We present an efficient method to shorten the analytic integration-by-parts (IBP) reduction coefficients of multi-loop Feynman integrals. For our approach, we develop an improved version of Leinartas' multivariate partial fraction…