Related papers: Evaluating massive planar two-loop tensor vertex i…
This article presents results for the last unknown two-loop contributions to the $Z$-boson partial widths and $Z$-peak cross-section. These are the so-called bosonic electroweak two-loop corrections, where "bosonic" refers to diagrams…
We introduce a tensor renormalization group scheme for coarse-graining a two-dimensional tensor network that can be successfully applied to both classical and quantum systems on and off criticality. The key innovation in our scheme is to…
The three-loop master integrals for ladder-box diagrams with one massive leg are computed from an eighty-five by eighty-five system of differential equations, solved by means of Magnus exponential. The results of the considered box-type…
The aim of XLOOPS is to calculate one-particle irreducible Feynman diagrams with one or two closed loops for arbitrary processes in the Standard model of particles and related theories. Up to now this aim is realized for all one-loop…
The prediction of the effective electroweak mixing angle $\sin^2\theta_{\rm eff}^{\rm b}$ in the Standard Model at two-loop accuracy has now been completed by the first calculation of the bosonic two-loop corrections to the $Z{\bar b}b$…
During the last several years remarkable progress has been made in numerical calculations of dimensionally regulated multi-loop Feynman diagrams using Mellin-Barnes (MB) representations. The bottlenecks were non-planar diagrams and…
We describe three algorithms for computer-aided symbolic multi-loop calculations that facilitated some recent novel results. First, we discuss an algorithm to derive the canonical form of an arbitrary Feynman integral in order to facilitate…
We determine the numerical values of scalar multi-loop two-vertex Feynman diagrams, the generalized sunset diagrams, by integrating all but the longitudinal momenta analytically. For the longitudinal momenta we introduce one collective…
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…
In this work, we systematically analyse Feynman integrals in the `t Hooft-Veltman scheme. We write an explicit reduction resulting from partial fractioning the high-multiplicity integrands to a finite basis of topologies at any given loop…
We revisit the idea of numerically integrating the differential form of Feynman integrals. With a novel approach for the treatment of branch cuts, we develop an integrator capable of evaluating a basis of master integrals in double and…
We present a simplified variant of the integrand reduction algorithm for multiloop scattering amplitudes in $d = 4 - 2\epsilon$ dimensions, which exploits the decomposition of the integration momenta in parallel and orthogonal subspaces,…
We compute the two-loop master integrals for non-leptonic heavy-to-heavy decays analytically in a recently-proposed canonical basis. For this genuine two-loop, two-scale problem we first derive a basis for the master integrals that…
We systematically analyze the $d=5$ Weinberg operator at 2-loop order. Using a diagrammatic approach, we identify two different interesting categories of neutrino mass models: (i) Genuine 2-loop models for which both, tree-level and 1-loop…
We consider the case of a two-loop five-point pentagon-box integral configuration with one internal massive propagator that contributes to top-quark pair production in association with a jet at hadron colliders. We construct the system of…
We report on a program for the numerical evaluation of divergent multi-loop integrals. The program is based on iterated sector decomposition. We improve the original algorithm of Binoth and Heinrich such that the program is guaranteed to…
We evaluate the master integrals for the two-loop, planar box-diagrams contributing to the elastic scattering of muons and electrons at next-to-next-to leading-order in QED. We adopt the method of differential equations and the Magnus…
We present results on the two-loop leading and angular-dependent next-to-leading logarithmic virtual corrections to arbitrary processes at energies above the electroweak scale. In the `t Hooft-Feynman gauge the relevant Feynman diagrams…
For the calculation of multi-loop Feynman integrals, a novel numerical method, the Direct Computation Method (DCM) is developed. It is a combination of a numerical integration and a series extrapolation. In principle, DCM can handle…
We study the applicability of the Z-Sum approach to multi-loop calculations with massive particles in perturbative quantum field theory. We systematically analyze the case of one-loop scalar integrals, which represent the building blocks of…