相关论文: New results for loop integrals: AMBRE, CSectors, h…

We study a set of two-loop non-planar master integrals needed for the NNLO QCD corrections to diphoton and dijet production at hadron colliders. The top-sector topology contains an internal massive fermion loop and is known to contain…

We have computed the simplest five point function in $\mathcal{N} = 4$ SYM at two loops using the hexagonalization approach to correlation functions. Along the way we have determined all two-particle mirror contributions at two loops and we…

We report on the current status of the Golem project which aims at the construction of a general one-loop evaluator for matrix elements. We construct the one-loop matrix elements from Feynman diagrams in a highly automated way and provide a…

An algorithm for the systematic analytical approximation of multi-scale Feynman integrals is presented. The algorithm produces algebraic expressions as functions of the kinematical parameters and mass scales appearing in the Feynman…

The construction of Mellin-Barnes (MB) representations for non-planar Feynman diagrams and the summation of multiple series derived from general MB representations are discussed. A basic version of a new package AMBREv.3.0 is supplemented.…

Twisted period integrals are ubiquitous in theoretical physics and mathematics, where they inhabit a finite-dimensional vector space governed by an inner product known as the intersection number. In this work, we uncover the associated…

The usefulness of recursive equations to compute scattering matrix elements for arbitrary processes is discussed. Explicit results at tree and one-loop order, obtained by the HELAC/PHEGAS package that is based on the Dyson-Schwinger…

We give a new method for the reduction of tensor integrals to finite integral representations and UV divergent analytic expressions. This includes a new method for the handling of the gamma-algebra. TYPO IN EQUATION (5) CORRECTED, MACROS…

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…

We initiate a systematic study of one-loop integrals by investigating the connection between their singularity structures and geometric configurations in the projective space associated to their Feynman parametrization. We analyze these…

I present the tensor computer algebra package FieldsX, which extends the xAct suite of tensor algebra packages to perform computations in field theory with fermions and gauge fields. This includes the standard tools of curved-space $\gamma$…

We highlight the latest developments in computing higher-order scattering amplitudes with massive internal propagators. The contributing Feynman integrals often lead to special classes of functions, for example, functions associated with…

The program FeynRules is a Mathematica package developed to facilitate the implementation of new physics theories into high-energy physics tools. Starting from a minimal set of information such as the model gauge symmetries, its particle…

We present a semi-numerical algorithm to calculate one-loop virtual corrections to scattering amplitudes. The divergences of the loop amplitudes are regulated using dimensional regularization. We treat in detail the case of amplitudes with…

Matrix elements of spherical tensor operators are fundamental to the analysis of lanthanide spectra in both amorphous and crystalline host materials. In the intermediate coupling scheme, the eigenvectors of the Hamiltonian define the…

We describe some connections between three different fields: combinatorics (umbral calculus), functional analysis (linear functionals and operators) and harmonic analysis (convolutions on group-like structures). Systematic usage of…

Feynman integral reduction based on intersection theory provides an alternative to the traditional integration-by-parts method, yet its practical application has been constrained by the large number of variables required in the computation.…

This short paper gives an introduction to the \emph{rcss} package. The R package \emph{rcss} provides users with a tool to approximate the value functions in the Bellman recursion using convex piecewise linear functions formed using…

We revisit the symbol bootstrap program for the seven-particle MHV and NMHV amplitudes in planar $\mathcal{N}=4$ super-Yang-Mills (SYM) based on the alphabet associated with the $E_6$ cluster algebra. After imposing integrability, cluster…

The method for functional reduction of Feynman integrals, proposed by the author, is used to calculate one-loop integrals corresponding to diagrams with four external lines. The integrals that emerge from amplitudes for the scattering of…