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The analysis of experimental results with Python often requires writing many code scripts which all need access to the same set of functions. In a common field of research, this set will be nearly the same for many users. The qspec Python…

Computational Physics · Physics 2025-03-18 Patrick Müller , Wilfried Nörtershäuser

A method of Feynman diagrams summation, based on using Schwinger-Dyson equations and Ward identities, is verified by calculating some four-loop diagrams in N=1 supersymmetric electrodynamics, regularized by higher derivatives. In…

High Energy Physics - Theory · Physics 2009-11-11 A. B. Pimenov , K. V. Stepanyantz

In these lectures I discuss Feynman graphs and the associated Feynman integrals. Of particular interest are the classes functions, which appear in the evaluation of Feynman integrals. The most prominent class of functions is given by…

High Energy Physics - Phenomenology · Physics 2013-01-30 Stefan Weinzierl

We review the method of the differential equations for the evaluation of multi-loop Feynman integrals. In particular, we focus on the series expansion approach for solving the system of differential equation and we discuss how to perform…

High Energy Physics - Phenomenology · Physics 2025-11-21 Tommaso Armadillo

Over the last year significant progress was made in the understanding of the computation of Feynman integrals using differential equations. These lectures give a review of these developments, while not assuming any prior knowledge of the…

High Energy Physics - Phenomenology · Physics 2015-06-23 Johannes M. Henn

FeynGame is an open-source software tool to draw Feynman diagrams, but also to get acquainted with their structure. This article reports on a number of new features which have been added to FeynGame since its first release. These include…

High Energy Physics - Phenomenology · Physics 2024-01-24 Robert Harlander , Sven Yannick Klein , Magnus Schaaf

We present a new algorithm for the reduction of one-loop tensor Feynman integrals within the framework of the XLOOPS project, covering both mathematical and programming aspects. The new algorithm supplies a clean way to reduce the one-loop…

High Energy Physics - Phenomenology · Physics 2009-11-07 C. Bauer , H. S. Do

In this paper, we study systematically scalar one-loop two-, three-, and four-point Feynman integrals with complex internal masses. Our analytic results presented in this report are valid for both real and complex internal masses. The…

High Energy Physics - Phenomenology · Physics 2018-09-19 K. H. Phan , T. N. H. Pham

We introduce a machine-learning framework based on symbolic regression to extract the full symbol alphabet of multi-loop Feynman integrals. By targeting the analytic structure rather than reduction, the method is broadly applicable and…

High Energy Physics - Phenomenology · Physics 2025-10-28 Yuanche Liu , Yingxuan Xu , Yang Zhang

We present a method for rewriting dimensionally regulated Feynman parameter integrals in the Minkowski regime as a sum of real, positive integrands multiplied by complex prefactors. This representation eliminates the need for contour…

High Energy Physics - Phenomenology · Physics 2025-07-01 Stephen Jones , Anton Olsson , Thomas Stone

We describe the main building blocks of a generic automated package for the calculation of Feynman diagrams. These blocks include the generation and creation of a model file, the graph generation, the symbolic calculation at an intermediate…

High Energy Physics - Phenomenology · Physics 2008-11-26 G. Belanger , F. Boudjema , J. Fujimoto , T. Ishikawa , T. Kaneko , K. Kato , Y. Shimizu

We report on the calculation of multi-loop Feynman integrals for single-scale problems by means of difference equations in Mellin space. The solution to these difference equations in terms of harmonic sums can be constructed algorithmically…

Mathematical Physics · Physics 2008-12-18 S. Moch , C. Schneider

We present the integrand reduction via multivariate polynomial division as a natural technique to encode the unitarity conditions of Feynman amplitudes. We derive a recursive formula for the integrand reduction, valid for arbitrary…

High Energy Physics - Phenomenology · Physics 2015-06-16 P. Mastrolia , E. Mirabella , G. Ossola , T. Peraro

Using integration by parts relations, Feynman integrals can be represented in terms of coupled systems of differential equations. In the following we suppose that the unknown Feynman integrals can be given in power series representations,…

Symbolic Computation · Computer Science 2016-08-19 Jakob Ablinger , Arnd Behring , Johannes Bluemlein , Abilio de Freitas , Carsten Schneider

We report on a new method for the numerical evaluation of loop integrals, based on the Feynman Tree Theorem. The loop integrals are replaced by phase-space integration over fictitious extra on-shell particles. This integration can be…

High Energy Physics - Phenomenology · Physics 2010-02-08 Wolfgang Kilian , Tobias Kleinschmidt

Integration-by-parts (IBP) identities and differential equations are the primary modern tools for the evaluation of high-order Feynman integrals. They are commonly derived and implemented in the momentum-space representation. We provide a…

High Energy Physics - Phenomenology · Physics 2023-10-09 Daniele Artico , Lorenzo Magnea

Methods for computing the integral of the Planck blackbody function over a finite spectral range, the so-called incomplete Planck integral, are necessary to perform multigroup radiative transfer calculations. We present a comparison, in…

Computational Physics · Physics 2025-03-13 Whit Lewis , Ryan G. McClarren

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

Modern advances in particle physics depend strongly on the usage of reliable computer programs. In this context two issues become important: The usage of powerful algorithms to handle the amount of evaluated data properly, and a software…

High Energy Physics - Phenomenology · Physics 2023-03-01 Marvin Gerlach

SecDec is a program which can be used for the factorization of dimensionally regulated poles from parametric integrals, in particular multi-loop integrals, and the subsequent numerical evaluation of the finite coefficients. Here we present…

High Energy Physics - Phenomenology · Physics 2015-09-22 S. Borowka , G. Heinrich , S. P. Jones , M. Kerner , J. Schlenk , T. Zirke