Machine learning discovers a tube-seeding strategy for IBP reduction of Feynman integrals that scales linearly with numerator power, demonstrated on rank-20 2-loop 5-point integrals.
Canonical reference
Integration-by-parts reductions from unitarity cuts and algebraic geometry
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abstract
We show that the integration-by-parts reductions of various two-loop integral topologies can be efficiently obtained by applying unitarity cuts to a specific set of subgraphs and solving associated polynomial (syzygy) equations.
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representative citing papers
Four-loop non-singlet splitting functions in QCD are computed analytically for the first time, with numerical representations provided.
Syzygy solutions for IBP reduction are systematically constructed as maximal minors of certificate matrices derived from the leading Landau singularities of Feynman diagrams.
Magic relations in Feynman integral families coincide with higher-dimensional critical varieties, enabling a practical test to detect and handle them.
Gravitational Compton amplitude computed to third post-Minkowskian order via worldline EFT with infrared and forward divergences regulated to connect to black hole perturbation theory.
Two-loop all-plus helicity amplitudes for self-dual Higgs plus gluons are obtained via four-dimensional unitarity cuts into one-loop and tree amplitudes plus finite-field tensor reduction.
Leading-colour two-loop virtual amplitudes for ttbar+jet are extracted analytically via finite-field evaluations and differential equations, then packaged in a C++ library with new numerical integration techniques.
Kira 2.0 implements finite-field coefficient reconstruction for IBP reductions and improved user-equation handling, yielding lower memory use and faster performance on state-of-the-art problems.
First numerical evaluation of planar two-loop helicity amplitudes for W-boson plus four partons using finite-field reduction and sector decomposition on a subset of master integrals.
A closed formula computes static post-Newtonian corrections at arbitrary odd orders in gravity, yielding the explicit seventh post-Newtonian potential that matches an independent diagrammatic method.
AMFlow 2.0 cuts symbolic and numerical cost of multi-loop Feynman integral evaluation via an FT recursion mode, a C++ DE solver, and modern IBP reducers, demonstrated on a three-loop five-point family.
Contour equivalence in Feynman parameterization yields universal reduction formulas for one-loop integrals without integration-by-parts.
citing papers explorer
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Efficient AI-Inspired Reduction of Feynman Integrals via Tube Seeding
Machine learning discovers a tube-seeding strategy for IBP reduction of Feynman integrals that scales linearly with numerator power, demonstrated on rank-20 2-loop 5-point integrals.
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The four-loop non-singlet splitting functions in QCD
Four-loop non-singlet splitting functions in QCD are computed analytically for the first time, with numerical representations provided.
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Compact Syzygies for Feynman Integrals from Landau Singularities
Syzygy solutions for IBP reduction are systematically constructed as maximal minors of certificate matrices derived from the leading Landau singularities of Feynman diagrams.
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Magic Relations and Critical Varieties of Feynman Integrals
Magic relations in Feynman integral families coincide with higher-dimensional critical varieties, enabling a practical test to detect and handle them.
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The gravitational Compton amplitude at third post-Minkowskian order
Gravitational Compton amplitude computed to third post-Minkowskian order via worldline EFT with infrared and forward divergences regulated to connect to black hole perturbation theory.
-
Two-loop all-plus helicity amplitudes for self-dual Higgs boson with gluons via unitarity cut constraints
Two-loop all-plus helicity amplitudes for self-dual Higgs plus gluons are obtained via four-dimensional unitarity cuts into one-loop and tree amplitudes plus finite-field tensor reduction.
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Double virtual QCD corrections to $t\bar{t}+$jet production at the LHC
Leading-colour two-loop virtual amplitudes for ttbar+jet are extracted analytically via finite-field evaluations and differential equations, then packaged in a C++ library with new numerical integration techniques.
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Integral Reduction with Kira 2.0 and Finite Field Methods
Kira 2.0 implements finite-field coefficient reconstruction for IBP reductions and improved user-equation handling, yielding lower memory use and faster performance on state-of-the-art problems.
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A numerical evaluation of planar two-loop helicity amplitudes for a W-boson plus four partons
First numerical evaluation of planar two-loop helicity amplitudes for W-boson plus four partons using finite-field reduction and sector decomposition on a subset of master integrals.
-
All-order structure of static gravitational interactions and the seventh post-Newtonian potential
A closed formula computes static post-Newtonian corrections at arbitrary odd orders in gravity, yielding the explicit seventh post-Newtonian potential that matches an independent diagrammatic method.
-
AMFlow 2.0: significant algorithmic and software improvements for Feynman integral evaluation
AMFlow 2.0 cuts symbolic and numerical cost of multi-loop Feynman integral evaluation via an FT recursion mode, a C++ DE solver, and modern IBP reducers, demonstrated on a three-loop five-point family.
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Feynman Integral Reduction without Integration-By-Parts
Contour equivalence in Feynman parameterization yields universal reduction formulas for one-loop integrals without integration-by-parts.