A geometric method of sector decomposition

DOI10.1016/j.cpc.2010.04.001zbMath1219.65014arXiv0908.2897OpenAlexW2089281149MaRDI QIDQ547029

Toshiaki Kaneko, Takahiro Ueda

Publication date: 30 June 2011

Published in: Computer Physics Communications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0908.2897

zbMATH Keywords

algorithmsnumerical examplescombinatorial geometryinfrared divergencesconvex geometryelementary particle physicsloop integrationsstatistical experiments

Mathematics Subject Classification ID

Other elementary particle theory in quantum theory (81V25) Applications of statistics to physics (62P35)

Related Items

FIESTA4: optimized Feynman integral calculations with GPU support, Machine learning post-Minkowskian integrals, The on-shell expansion: from Landau equations to the Newton polytope, Tropical Feynman integration in the Minkowski regime, Feynman integrals from positivity constraints, Tropical Monte Carlo quadrature for Feynman integrals, Expansion by regions with pysecdec, Electrostatic potential of a uniformly charged triangle in barycentric coordinates, pySecDec: a toolbox for the numerical evaluation of multi-scale integrals, SecDec: A general program for sector decomposition, Evaluating Feynman integrals by the hypergeometry, Hepp's bound for Feynman graphs and matroids, Flow-oriented perturbation theory, FIESTA5: numerical high-performance Feynman integral evaluation, Massive kite diagrams with elliptics, Collider physics at the precision frontier, SecDec-3.0: numerical evaluation of multi-scale integrals beyond one loop, Systematic approximation of multi-scale Feynman integrals, FIESTA 3: cluster-parallelizable multiloop numerical calculations in physical regions, Non-planar elliptic vertex, Master integrals for the four-loop Sudakov form factor

Uses Software

• FIESTA

Cites Work

• Semi-numerical power expansion of Feynman integrals
• Feynman integral evaluation by a sector decomposition approach (FIESTA)
• Resolution of singularities for multi-loop integrals
• Proof of the Bogoliubov-Parasiuk theorem on renormalization
• Numerical evaluation of phase space integrals by sector decomposition
• Numerical evaluation of multi-loop integrals by sector decomposition
• SECTOR DECOMPOSITION
• Non-planar massless two-loop Feynman diagrams with four on-shell legs
• An automatized algorithm to compute infrared divergent multi-loop integrals.
• Unnamed Item
• Unnamed Item
• Unnamed Item