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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NeatIBP 1.0, a package generating small- size integration-by-parts relations for Feynman inte- grals
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representative citing papers
A self-supervised transformer learns to unscramble Feynman integrals for online IBP reduction, delivering bounded memory use on complex two-loop topologies while matching Kira's speed on the hardest cases tested.
NNLO QCD predictions for ttW production with two-loop amplitudes evaluated explicitly in the generalised leading-colour limit.
Derives gravitational Compton amplitude at O(G^4) and N-matrix element for scattering phase shift, verified by agreement with black-hole perturbation theory.
NNLO QCD predictions for ttW production at hadron colliders using direct two-loop amplitude computation in the generalised leading-colour limit.
Magic relations in Feynman integral families coincide with higher-dimensional critical varieties, enabling a practical test to detect and handle them.
SIRENA automates IBP reduction of sum-integrals in finite-temperature QFT, reproduces known results to 3 loops, supplies new 3-loop fermionic reductions, and derives an analytic factorization formula for arbitrary 2-loop fermionic sum-integrals.
OPE-based recursive renormalization for mixed composite operators gives five-loop anomalous dimensions in phi^4 and two-loop in phi^3 models.
Branch representation reduces the variable count for intersection-theory-based Feynman integral reduction to at most 3L-3 for L-loop integrals regardless of leg number.
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.
Inconsistency in spanning cuts for IBP reductions arises because cuts can make hidden terms in IBP relations finite via pinch singularities that cancel vanishing parameters, linked to hidden linear relations between propagators, for which an algorithm is provided.
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.
A geometric order relation in IBP reduction yields a master-integral basis with Laurent-polynomial differential equations on the maximal cut that are then ε-factorized.
Outlines a Schwinger-Keldysh path-integral framework that derives worldline equations of motion and computes weak-field gravitational waveforms independently for unspecified relativistic orbits.
Explicit three-loop computation of negative geometries for F(g,z) with all-loop resummation of one-cycle diagrams and extraction of the cusp anomalous dimension via z-integration.
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.
Contour equivalence in Feynman parameterization yields universal reduction formulas for one-loop integrals without integration-by-parts.
Analytic expressions for one-loop helicity amplitudes in ttj and ttγ production are derived to O(ε²) as linear combinations of pentagon functions with rational coefficients in momentum-twistor variables, obtained via differential equations solved numerically by generalized power series expansion.
Feynman integrals with mixed geometries (K3 surfaces, curves, points) can be computed more efficiently by extracting and using their algebraic geometric properties.
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.
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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Learning to Unscramble Feynman Loop Integrals with SAILIR
A self-supervised transformer learns to unscramble Feynman integrals for online IBP reduction, delivering bounded memory use on complex two-loop topologies while matching Kira's speed on the hardest cases tested.
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NNLO QCD predictions for $t\bar{t}W$ production at the LHC
NNLO QCD predictions for ttW production with two-loop amplitudes evaluated explicitly in the generalised leading-colour limit.
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Gravitational Compton scattering at the fourth post-Minkowskian order
Derives gravitational Compton amplitude at O(G^4) and N-matrix element for scattering phase shift, verified by agreement with black-hole perturbation theory.
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NNLO QCD predictions for $t\bar t W$ production at hadron colliders
NNLO QCD predictions for ttW production at hadron colliders using direct two-loop amplitude computation in the generalised leading-colour limit.
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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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SIRENA -- Sum-Integral REductioN Algorithm
SIRENA automates IBP reduction of sum-integrals in finite-temperature QFT, reproduces known results to 3 loops, supplies new 3-loop fermionic reductions, and derives an analytic factorization formula for arbitrary 2-loop fermionic sum-integrals.
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The OPE Approach to Renormalization: Operator Mixing
OPE-based recursive renormalization for mixed composite operators gives five-loop anomalous dimensions in phi^4 and two-loop in phi^3 models.
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Feynman integral reduction with intersection theory made simple
Branch representation reduces the variable count for intersection-theory-based Feynman integral reduction to at most 3L-3 for L-loop integrals regardless of leg number.
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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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On the spanning cuts consistency problem in the IBP reductions of Feynman integrals
Inconsistency in spanning cuts for IBP reductions arises because cuts can make hidden terms in IBP relations finite via pinch singularities that cancel vanishing parameters, linked to hidden linear relations between propagators, for which an algorithm is provided.
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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.
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New algorithms for Feynman integral reduction and $\varepsilon$-factorised differential equations
A geometric order relation in IBP reduction yields a master-integral basis with Laurent-polynomial differential equations on the maximal cut that are then ε-factorized.
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Weak-field waveforms for generic relativistic orbits
Outlines a Schwinger-Keldysh path-integral framework that derives worldline equations of motion and computes weak-field gravitational waveforms independently for unspecified relativistic orbits.
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Multi-Loop Negative Geometries
Explicit three-loop computation of negative geometries for F(g,z) with all-loop resummation of one-cycle diagrams and extraction of the cusp anomalous dimension via z-integration.
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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.
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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.
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One-loop amplitudes for $t\bar{t}j$ and $t\bar{t}\gamma$ productions at the LHC through $\mathcal{O}(\epsilon^2)$
Analytic expressions for one-loop helicity amplitudes in ttj and ttγ production are derived to O(ε²) as linear combinations of pentagon functions with rational coefficients in momentum-twistor variables, obtained via differential equations solved numerically by generalized power series expansion.
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From geometry to phenomenology
Feynman integrals with mixed geometries (K3 surfaces, curves, points) can be computed more efficiently by extracting and using their algebraic geometric properties.
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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.
- Four-loop Anomalous Dimensions of Scalar-QED Theory from Operator Product Expansion