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A fully numerical method to calculate loop integrals, a numerical contour-integration method, is proposed. Loop integrals can be interpreted as a contour integral in a complex plane for an integrand with multi-poles in the plane. Stable and…

High Energy Physics - Phenomenology · Physics 2009-11-11 Y. Kurihara , T. Kaneko

Three-loop vacuum integrals are an important building block for the calculation of a wide range of three-loop corrections. Until now, only results for integrals with one and two independent mass scales are known, but in the electroweak…

High Energy Physics - Phenomenology · Physics 2021-04-08 Ayres Freitas

We invent an automated method for computing the divergent part of Feynman integrals in dimensional regularization. Our method exploits simplifications from four-dimensional integration-by-parts identities. Leveraging algorithms from the…

High Energy Physics - Theory · Physics 2023-09-19 Johannes Henn , Rourou Ma , Kai Yan , Yang Zhang

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

AMFlow is a Mathematica package to numerically compute dimensionally regularized Feynman integrals via the recently proposed auxiliary mass flow method. In this framework, integrals are treated as functions of an auxiliary mass parameter…

High Energy Physics - Phenomenology · Physics 2022-10-28 Xiao Liu , Yan-Qing Ma

We construct a basis set of infra-red and/or collinearly divergent scalar one-loop integrals and give analytic formulas, for tadpole, bubble, triangle and box integrals, regulating the divergences (ultra-violet, infra-red or collinear) by…

High Energy Physics - Phenomenology · Physics 2011-06-30 R. Keith Ellis , Giulia Zanderighi

We present SubTropica, a Mathematica package that performs symbolic integration of multi-polylogarithmic integrals using recent advances in tropical geometry. It focuses on the class of linearly-reducible Euler integrals, such as Feynman…

High Energy Physics - Theory · Physics 2026-04-24 Mathieu Giroux , Sebastian Mizera , Giulio Salvatori

We review in a pedagogical way the method of differential equations for the evaluation of D-dimensionally regulated Feynman integrals. After dealing with the general features of the technique, we discuss its application in the context of…

High Energy Physics - Phenomenology · Physics 2008-11-26 Mario Argeri , Pierpaolo Mastrolia

This paper describes a new MATLAB software package of iterative regularization methods and test problems for large-scale linear inverse problems. The software package, called IR Tools, serves two related purposes: we provide implementations…

Numerical Analysis · Mathematics 2018-07-03 Silvia Gazzola , Per Christian Hansen , James G. Nagy

We present a semi-numerical method to compute one-loop corrections to processes involving many particles. We treat in detail cases with up to five external legs and massless internal propagators, although the method is more general.

High Energy Physics - Phenomenology · Physics 2008-11-26 G. Zanderighi

We present a new approach for obtaining very precise integration results for infrared vertex and box diagrams, where the integration is carried out directly without performing any analytic integration of Feynman parameters. Using an…

High Energy Physics - Phenomenology · Physics 2008-12-18 F. Yuasa , E. de Doncker , J. Fujimoto , N. Hamaguchi , T. Ishikawa , Y. Shimizu

We have developed a Python package ZMCintegral for multi-dimensional Monte Carlo integration on multiple Graphics Processing Units(GPUs). The package employs a stratified sampling and heuristic tree search algorithm. We have built three…

Computational Physics · Physics 2022-09-19 Hong-Zhong Wu , Jun-Jie Zhang , Long-Gang Pang , Qun Wang

This article is the third and last of a series presenting an alternative method to compute the one-loop scalar integrals. It extends the results of first two articles to the infrared divergent case. This novel method enjoys a couple of…

High Energy Physics - Phenomenology · Physics 2020-02-26 J. Ph. Guillet , E. Pilon , Y. Shimizu , M. S. Zidi

We introduce the fortran-library COLLIER for the numerical evaluation of one-loop scalar and tensor integrals in perturbative relativistic quantum field theories. Important features are the implementation of dedicated methods to achieve…

High Energy Physics - Phenomenology · Physics 2014-07-02 Ansgar Denner , Stefan Dittmaier , Lars Hofer

In this paper, we propose and study a fast multilevel dimension iteration (MDI) algorithm for computing arbitrary $d$-dimensional integrals based on tensor product approximations. It reduces the computational complexity (in terms of the CPU…

Numerical Analysis · Mathematics 2022-10-26 Xiaobing Feng , Huicong Zhong

SPARKX is an open-source Python package developed to analyze simulation data from heavy-ion collision experiments. By offering a comprehensive suite of tools, SPARKX simplifies data analysis workflows, supports multiple formats such as…

Data Analysis, Statistics and Probability · Physics 2026-02-02 Nils Sass , Hendrik Roch , Niklas Götz , Renata Krupczak , Carl B. Rosenkvist

The various non-linear transformations incurred by the rays in an optical system can be modelled by matrix products up to any desired order of approximation. Mathematica software has been used to find the appropriate matrix coefficients for…

Optics · Physics 2009-11-10 Jose B. Almeida

We present the Mathematica package DREAM for arbitrarily high precision computation of multiloop integrals within the DRA (Dimensional Recurrence & Analyticity) method as solutions of dimensional recurrence relations. Starting from these…

High Energy Physics - Phenomenology · Physics 2018-01-10 Roman N. Lee , Kirill T. Mingulov

We present the Mathematica package SpinorHelicity4D, a dedicated suite for analytic and numeric calculations involving four-dimensional massless and massive spinor-helicity formalism. Analytic features of the package include for example:…

High Energy Physics - Theory · Physics 2023-04-05 Manuel Accettulli Huber

We present a computer code that analytically evaluates the matrix elements of the microscopic nuclear Hamiltonian and unity operator between Slater determinants of displaced gaussian single particle orbits. Such matrix elements appear in…

Nuclear Theory · Physics 2009-10-22 K. Varga