Landau Singularities Revisited: Computational Algebraic Geometry for Feynman Integrals

Fevola, Claudia; Mizera, Sebastian; Telen, Simon

doi:10.1103/PhysRevLett.132.101601

Title: Landau Singularities Revisited: Computational Algebraic Geometry for Feynman Integrals

Journal Article · 03 March 2024 · Physical Review Letters

DOI: https://doi.org/10.1103/PhysRevLett.132.101601 · OSTI ID:2318566

;

We reformulate the analysis of singularities of Feynman integrals in a way that can be practically applied to perturbative computations in the standard model in dimensional regularization. After highlighting issues in the textbook treatment of Landau singularities, we develop an algorithm for classifying and computing them using techniques from computational algebraic geometry. We introduce an algebraic variety called the principal Landau determinant, which captures the singularities even in the presence of massless particles or UV/IR divergences. We illustrate this for 114 example diagrams, including a cutting-edge 2-loop 5-point nonplanar QCD process with multiple mass scales. Published by the American Physical Society 2024

View Journal Article

Cite

Export

Save

Sponsoring Organization:: USDOE

Grant/Contract Number:: SC0009988

OSTI ID:: 2318566

Journal Information:: Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 10 Vol. 132; ISSN 0031-9007; ISSN PRLTAO

Publisher:: American Physical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

References (27)

Tropical Feynman integration in the Minkowski regime Borinsky, Michael; Munch, Henrik J.; Tellander, Felix Computer Physics Communications, Vol. 292 https://doi.org/10.1016/j.cpc.2023.108874	journal	November 2023
Four lectures on Euler integrals Matsubara-Heo, Saiei-Jaeyeong; Mizera, Sebastian; Telen, Simon SciPost Physics Lecture Notes https://doi.org/10.21468/SciPostPhysLectNotes.75	journal	October 2023
Ordinary and Anomalous Thresholds in Perturbation Theory Nakanishi, Noboru Progress of Theoretical Physics, Vol. 22, Issue 1 https://doi.org/10.1143/PTP.22.128	journal	July 1959
Singularities of the Second Type Fairlie, D. B.; Landshoff, P. V.; Nuttall, J. Journal of Mathematical Physics, Vol. 3, Issue 4 https://doi.org/10.1063/1.1724262	journal	July 1962
On Analytic Properties of Vertex Parts in Quantum Field Theory Collected Papers of L.D. Landau https://doi.org/10.1016/B978-0-08-010586-4.50103-6	book	January 1965
The on-shell expansion: from Landau equations to the Newton polytope Gardi, Einan; Herzog, Franz; Jones, Stephen Journal of High Energy Physics, Vol. 2023, Issue 7 https://doi.org/10.1007/JHEP07(2023)197	journal	July 2023
An Introduction to Quantum Field Theory Sterman, George https://doi.org/10.1017/CBO9780511622618	book	January 1993
Three-Point Energy Correlator in N=4 Supersymmetric Yang-Mills Theory Yan, Kai; Zhang, Xiaoyuan Physical Review Letters, Vol. 129, Issue 2 https://doi.org/10.1103/PhysRevLett.129.021602	journal	July 2022
Symbol alphabets from the Landau singular locus Dlapa, Christoph; Helmer, Martin; Papathanasiou, Georgios Journal of High Energy Physics, Vol. 2023, Issue 10 https://doi.org/10.1007/JHEP10(2023)161	journal	October 2023
Scattering Amplitudes in Quantum Field Theory Badger, Simon; Henn, Johannes; Plefka, Jan Christoph Lecture Notes in Physics https://doi.org/10.1007/978-3-031-46987-9	book	January 2024
Two-loop hexa-box integrals for non-planar five-point one-mass processes Abreu, Samuel; Ita, Harald; Page, Ben Journal of High Energy Physics, Vol. 2022, Issue 3 https://doi.org/10.1007/JHEP03(2022)182	journal	March 2022
Foundation and generalization of the expansion by regions Jantzen, Bernd Journal of High Energy Physics, Vol. 2011, Issue 12 https://doi.org/10.1007/JHEP12(2011)076	journal	December 2011
Generalized Euler integrals and A-hypergeometric functions Gelfand, I. M.; Kapranov, M. M.; Zelevinsky, A. V. Advances in Mathematics, Vol. 84, Issue 2 https://doi.org/10.1016/0001-8708(90)90048-R	journal	December 1990
Critical points and number of master integrals Lee, Roman N.; Pomeransky, Andrei A. Journal of High Energy Physics, Vol. 2013, Issue 11 https://doi.org/10.1007/JHEP11(2013)165	journal	November 2013
Tropical Monte Carlo quadrature for Feynman integrals Borinsky, Michael Annales de l’Institut Henri Poincaré D https://doi.org/10.4171/AIHPD/158	journal	January 2023
The hierarchical principle in perturbation theory Landshoff, P. V.; Olive, D. I.; Polkinghorne, J. C. Il Nuovo Cimento A Series 10, Vol. 43, Issue 2 https://doi.org/10.1007/BF02752870	journal	May 1966
Expansion by regions with pySecDec Heinrich, G.; Jahn, S.; Jones, S. P. Computer Physics Communications, Vol. 273 https://doi.org/10.1016/j.cpc.2021.108267	journal	April 2022
Singularities of integrals Pham, Frédéric Universitext https://doi.org/10.1007/978-0-85729-603-0	book	January 2011
What is the iε for the S-matrix? Hannesdottir, Holmfridur Sigridar; Mizera, Sebastian SpringerBriefs in Physics https://doi.org/10.1007/978-3-031-18258-7	book	January 2022
Kinematic singularities of Feynman integrals and principal A-determinants Klausen, René Pascal Journal of High Energy Physics, Vol. 2022, Issue 2 https://doi.org/10.1007/JHEP02(2022)004	journal	February 2022
Feynman polytopes and the tropical geometry of UV and IR divergences Arkani-Hamed, Nima; Hillman, Aaron; Mizera, Sebastian Physical Review D, Vol. 105, Issue 12 https://doi.org/10.1103/PhysRevD.105.125013	journal	June 2022
Looking for a bulk point Maldacena, Juan; Simmons-Duffin, David; Zhiboedov, Alexander Journal of High Energy Physics, Vol. 2017, Issue 1 https://doi.org/10.1007/JHEP01(2017)013	journal	January 2017
Landau discriminants Mizera, Sebastian; Telen, Simon Journal of High Energy Physics, Vol. 2022, Issue 8 https://doi.org/10.1007/JHEP08(2022)200	journal	August 2022
Expansion by regions: revealing potential and Glauber regions automatically Jantzen, Bernd; Smirnov, Alexander V.; Smirnov, Vladimir A. The European Physical Journal C, Vol. 72, Issue 9 https://doi.org/10.1140/epjc/s10052-012-2139-2	journal	September 2012
Implications of the Landau equations for iterated integrals Hannesdottir, Holmfridur S.; McLeod, Andrew J.; Schwartz, Matthew D. Physical Review D, Vol. 105, Issue 6 https://doi.org/10.1103/PhysRevD.105.L061701	journal	March 2022
Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals Panzer, Erik Computer Physics Communications, Vol. 188 https://doi.org/10.1016/j.cpc.2014.10.019	journal	March 2015
Classical Polylogarithms for Amplitudes and Wilson Loops Goncharov, A. B.; Spradlin, M.; Vergu, C. Physical Review Letters, Vol. 105, Issue 15 https://doi.org/10.1103/PhysRevLett.105.151605	journal	October 2010