Related papers: Fun with higher-loop Feynman diagrams
We review the recent developments of the Loop-Tree Duality method, focussing our discussion on the first numerical implementation and its use in the direct numerical computation of multi-leg Feynman integrals. Non-trivial examples are…
Dimensionally-regulated Feynman integrals are a cornerstone of all perturbative computations in quantum field theory. They are known to exhibit a rich mathematical structure, which has led to the development of powerful new techniques for…
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…
Based on the method developed in [K.~H.~Phan and T.~Riemann, Phys.\ Lett.\ B {\bf 791} (2019) 257], detailed analytic results for scalar one-loop two-, three-, four-point integrals in general $d$-dimension are presented in this paper. The…
General algorithms for tensor reduction of two-loop massive vacuum diagrams are discussed. Some explicit useful formulae are presented.
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 $C_{_0}$…
We present an analytic calculation of three-loop four-point Feynman integrals with two off-shell legs of equal mass. We provide solutions to the canonical differential equations of two integral families in both Euclidean and physical…
We reduce all the most complicated Feynman integrals in two-loop five-light-parton scattering amplitudes to basic master integrals, while other integrals can be reduced even easier. Our results are expressed as systems of linear relations…
In the context of planar holography, integrability plays an important role for solving certain massless quantum field theories such as N=4 SYM theory. In this letter we show that integrability also features in the building blocks of massive…
In the present review we provide an extensive analysis of the intertwinement between Feynman integrals and cohomology theories in the light of the recent developments. Feynman integrals enter in several perturbative methods for solving non…
A complete analytical reduction of general one-loop Feynman integrals with five legs for tensors up to rank R=3 and six legs for tensors up to rank 4 is reviewed. An elegant formalism with extensive use of signed minors was developed for…
We develop a new representation for the integrals associated with Feynman diagrams. This leads directly to a novel method for the numerical evaluation of these integrals, which avoids the use of Monte Carlo techniques. Our approach is based…
The evaluation of higher-loop Feynman integrals is at the core of the quest to reduce the uncertainty of theoretical predictions and match experimental data from the LHC and future colliders. pySecDec is a program to evaluate such integrals…
In this paper, we study the singularities of Feynman integrals using homological techniques. We analyse the Feynman integrals by compactifying the integration domain as well as the ambient space by embedding them in higher-dimensional…
Complete Feynman diagram automatic computation systems are now coming of age after many years of development. They are made available to the high energy physics community through user-friendly interfaces. Theorists and experimentalists can…
The approach to the constructing explicit solutions of the recurrence relations for multi-loop integrals are suggested. The resulting formulas demonstrate a high efficiency, at least for 3-loop vacuum integrals case. They also produce a new…
We calculate the two-loop QCD corrections to $gg \to ZZ$ involving a closed top-quark loop. We present a new method to systematically construct linear combinations of Feynman integrals with a convergent parametric representation, where we…
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…
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…
The 4-th order Runge-Kutta method in the complex plane is proposed for numerically advancing the solutions of a system of first order differential equations in one external invariant satisfied by the master integrals related to a Feynman…