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Related papers: New results for loop integrals: AMBRE, CSectors, h…

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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…

High Energy Physics - Theory · Physics 2024-02-13 Taushif Ahmed , Ekta Chaubey , Mandeep Kaur , Sara Maggio

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…

High Energy Physics - Theory · Physics 2020-08-26 Thiago Fleury , Vasco Goncalves

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…

High Energy Physics - Phenomenology · Physics 2018-09-26 Sophia Borowka , Thomas Gehrmann , Daniel Hulme

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.…

High Energy Physics - Phenomenology · Physics 2014-07-30 Johannes Blümlein , Ievgen Dubovyk , Janusz Gluza , Michał Ochman , Clemens G. Raab , Tord Riemann , Carsten Schneider

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…

High Energy Physics - Theory · Physics 2025-08-25 Giacomo Brunello , Vsevolod Chestnov , Pierpaolo Mastrolia

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…

High Energy Physics - Phenomenology · Physics 2009-11-11 P. Draggiotis , A. van Hameren , R. Kleiss , A. Lazopoulos , C. G. Papadopoulos , M. Worek

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…

High Energy Physics - Phenomenology · Physics 2009-10-22 Dirk Kreimer

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…

Mathematical Physics · Physics 2023-10-23 Michael Borinsky

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…

High Energy Physics - Theory · Physics 2017-12-29 Nima Arkani-Hamed , Ellis Ye Yuan

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 $\gamma$…

High Energy Physics - Theory · Physics 2021-05-28 Markus B. Fröb

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…

High Energy Physics - Phenomenology · Physics 2022-07-26 Ekta Chaubey

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…

High Energy Physics - Phenomenology · Physics 2014-06-13 Adam Alloul , Neil D. Christensen , Celine Degrande , Claude Duhr , Benjamin Fuks

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…

High Energy Physics - Phenomenology · Physics 2008-11-26 R. K. Ellis , W. T. Giele , G. Zanderighi

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…

Computational Physics · Physics 2026-03-24 Reinhard Caspary

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…

funct-an · Mathematics 2008-02-03 Vladimir V. Kisil

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.…

High Energy Physics - Theory · Physics 2026-04-08 Li-Hong Huang , Yan-Qing Ma , Ziwen Wang , Li Lin Yang

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…

Mathematical Software · Computer Science 2018-01-19 Juri Hinz , Jeremy Yee

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…

High Energy Physics - Theory · Physics 2025-11-24 Song He , Xuhang Jiang , Xiang Li , Jiahao Liu

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…

High Energy Physics - Phenomenology · Physics 2023-07-12 O. V. Tarasov