REVIEW 9 cited by
Landau Singularities Revisited: Computational Algebraic Geometry for Feynman Integrals
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Landau Singularities Revisited: Computational Algebraic Geometry for Feynman Integrals
read the original abstract
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 non-planar QCD process with multiple mass scales. The algorithms introduced in this work are implemented in the open-source Julia package PLD.jl available at https://mathrepo.mis.mpg.de/PLD/.
Forward citations
Cited by 9 Pith papers
-
Landau's Leviathans
New algorithm identifies complete Landau singularities of Feynman integrals via Euler characteristic drops over finite fields, applied to non-planar two-loop six-point and massive three-loop graphs.
-
New Tools in the Landau Bootstrap
Certain Feynman-integral discontinuities are 'non-repeating' (a second cut at the same singularity always vanishes), and certain 'Lefschetz-unique' discontinuities are independent of the order of prior cuts.
-
Chebyshev Approximations of Feynman Integrals for Collider Physics
Chebyshev polynomial approximations with adaptive sampling solve canonical differential equations for Feynman integrals, demonstrated to be stable and competitive for two-loop five-point cases in double precision.
-
On Carrollian Loop Amplitudes for Gauge Theory and Gravity
Loop-level Carrollian amplitudes in N=4 SYM and N=8 supergravity are differential operators on tree-level versions, with logarithmic eikonal behavior and IR-safe factorization via natural splitting.
-
Novel cluster-algebraic letters for 5- and 6-point QCD processes
Candidate symbol alphabets for 5- and 6-point QCD processes are derived from the 9-particle N=4 super Yang-Mills cluster algebra, including new nested square-root letters.
-
Disperon QED
Disperon QED is a new technique that feeds experimental data into higher-order QED loop calculations in Monte Carlo generators via dispersion relations and threshold subtraction.
-
SubTropica
SubTropica is a software package that automates symbolic integration of linearly-reducible Euler integrals via tropical subtraction, supported by HyperIntica and an AI-driven Feynman integral database.
-
On Carrollian Loop Amplitudes for Gauge Theory and Gravity
Loop-level Carrollian amplitudes in gauge theory and gravity preserve tree-level structures, show logarithmic dependence in the eikonal regime, and factorize to yield an IR-safe definition.
-
Les Houches 2023 -- Physics at TeV Colliders: Report on the Standard Model Precision Wishlist
The report reviews progress since 2021 in fixed-order computations for LHC applications and identifies processes requiring missing higher-order corrections to match anticipated experimental precision.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.