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Related papers: Numerical evaluation of multi-loop integrals

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We present a formalism for the calculation of multi-particle one-loop amplitudes, valid for an arbitrary number N of external legs, and for massive as well as massless particles. A new method for the tensor reduction is suggested which…

High Energy Physics - Phenomenology · Physics 2013-12-16 T. Binoth , J. Ph. Guillet , G. Heinrich , E. Pilon , C. Schubert

The FormCalc package automates the computation of FeynArts amplitudes up to one loop including the generation of a Fortran code for the numerical evaluation of the squared matrix element. Major new or enhanced features in Version 5 are:…

High Energy Physics - Phenomenology · Physics 2009-11-11 T. Hahn , M. Rauch

Quantum simulators, in which well controlled quantum systems are used to reproduce the dynamics of less understood ones, have the potential to explore physics that is inaccessible to modeling with classical computers. However, checking the…

Quantum Physics · Physics 2015-06-18 C. Senko , J. Smith , P. Richerme , A. Lee , W. C. Campbell , C. Monroe

The possibility of treating colour in one-loop amplitude calculations alike the other quantum numbers is briefly discussed for semi-numerical algorithms based on generalized unitarity and parametric integration techniques. Numerical results…

High Energy Physics - Phenomenology · Physics 2015-03-17 Jan Winter

I present a Mathematica package designed for manipulations and evaluations of triple-K integrals and conformal correlation functions in momentum space. Additionally, the program provides tools for evaluation of a large class of 2- and…

High Energy Physics - Theory · Physics 2020-08-26 Adam Bzowski

We study the application of a tailored quasi-Monte Carlo (QMC) method to a class of optimal control problems subject to parabolic partial differential equation (PDE) constraints under uncertainty: the state in our setting is the solution of…

Numerical Analysis · Mathematics 2024-03-28 Philipp A. Guth , Vesa Kaarnioja , Frances Y. Kuo , Claudia Schillings , Ian H. Sloan

Dimensional regularization of Euclidean momentum space integrals is a highly successful technique in renormalization of quantum field theories. While it yields a straightforward algorithmic method, with which to evaluate diagrams beyond…

Mathematical Physics · Physics 2020-09-03 Juuso Österman

We discuss a practical approach to compute master integrals entering physical quantities which depend on one parameter. As an example we consider four-loop QCD corrections to the relation between a heavy quark mass defined in the…

High Energy Physics - Phenomenology · Physics 2021-10-11 Matteo Fael , Fabian Lange , Kay Schönwald , Matthias Steinhauser

We describe our 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 a contour…

High Energy Physics - Phenomenology · Physics 2026-03-06 Stephen P. Jones , Anton Olsson , Thomas Stone

Mathematical models are essential for understanding and making predictions about systems arising in nature and engineering. Yet, mathematical models are a simplification of true phenomena, thus making predictions subject to uncertainty.…

Numerical Analysis · Mathematics 2023-03-03 Mark Hobbs , Hussein Rappel , Tim Dodwell

Multilevel Monte Carlo is a key tool for approximating integrals involving expensive scientific models. The idea is to use approximations of the integrand to construct an estimator with improved accuracy over classical Monte Carlo. We…

Methodology · Statistics 2023-03-15 Kaiyu Li , Daniel Giles , Toni Karvonen , Serge Guillas , François-Xavier Briol

The state of art of electromagnetic integral equations has seen significant growth over the past few decades, overcoming some of the fundamental bottlenecks: computational complexity, low frequency and dense discretization breakdown,…

Numerical Analysis · Mathematics 2022-09-21 A. M. A. Alsnayyan , B. Shanker

An improved method is presented for the numerical evaluation of multi-loop integrals in dimensional regularization. The technique is based on Mellin-Barnes representations, which have been used earlier to develop algorithms for the…

High Energy Physics - Phenomenology · Physics 2014-11-20 Ayres Freitas , Yi-Cheng Huang

A real-time path integral Monte Carlo approach is developed to study the dynamics in a many-body quantum system until reaching a nonequilibrium stationary state. The approach is based on augmenting an exact reduced equation for the…

Mesoscale and Nanoscale Physics · Physics 2009-11-13 Lothar Mühlbacher , Eran Rabani

We describe a practical approach for accessing the logical failure rates of quantum error-correcting (QEC) circuits under low physical (component) failure rate regimes. Standard Monte Carlo is often the de facto approach for studying the…

Quantum Physics · Physics 2025-09-23 Carolyn Mayer , Anand Ganti , Uzoma Onunkwo , Tzvetan Metodi , Benjamin Anker , Jacek Skryzalin

A new approach is presented to evaluate multi-loop integrals, which appear in the calculation of cross-sections in high-energy physics. It relies on a fully numerical method and is applicable to a wide class of integrals with various mass…

High Energy Physics - Phenomenology · Physics 2015-06-03 F. Yuasa , E. de Doncker , N. Hamaguchi , T. Ishikawa , K. Kato , Y. Kurihara , J. Fujimoto , Y. Shimizu

We consider the problem of estimating expectations with respect to a target distribution with an unknown normalizing constant, and where even the unnormalized target needs to be approximated at finite resolution. This setting is ubiquitous…

Numerical Analysis · Mathematics 2023-03-23 Kody J. H. Law , Neil Walton , Shangda Yang , Ajay Jasra

The quantum transverse Ising model and its extensions play a critical role in various fields, such as statistical physics, quantum magnetism, quantum simulations, and mathematical physics. Although it does not suffer from the sign problem…

Strongly Correlated Electrons · Physics 2025-12-23 Wei Xu , Xue-Feng Zhang

Metallic quantum critical phenomena are believed to play a key role in many strongly correlated materials, including high temperature superconductors. Theoretically, the problem of quantum criticality in the presence of a Fermi surface has…

Strongly Correlated Electrons · Physics 2019-05-03 Erez Berg , Samuel Lederer , Yoni Schattner , Simon Trebst

The fast computation of large kernel sums is a challenging task, which arises as a subproblem in any kernel method. We approach the problem by slicing, which relies on random projections to one-dimensional subspaces and fast Fourier…

Numerical Analysis · Mathematics 2025-02-25 Johannes Hertrich , Tim Jahn , Michael Quellmalz