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.
hub Mixed citations
Reduze 2 - Distributed Feynman Integral Reduction
Mixed citation behavior. Most common role is background (50%).
22
Pith papers citing it
Background
50% of classified citations
abstract
Reduze is a computer program for reducing Feynman integrals to master integrals employing a variant of Laporta's reduction algorithm. This article describes version 2 of the program. New features include the distributed reduction of single topologies on multiple processor cores. The parallel reduction of different topologies is supported via a modular, load balancing job system. Fast graph and matroid based algorithms allow for the identification of equivalent topologies and integrals.
hub tools
citation-role summary
background 5
method 3
baseline 1
other 1
citation-polarity summary
representative citing papers
Four-loop non-singlet splitting functions in QCD are computed analytically for the first time, with numerical representations provided.
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.
Mixed QCD-EW corrections to qqbar -> HH computed analytically via differential equations, matched to large-mass limit, implemented in POWHEG-BOX, showing up to +10% effect on invariant mass distribution near threshold.
An algorithm reconstructs symbolic IBP reduction coefficients via intermediate bases, demonstrated on massive box-triangle and pentagon-triangle integrals using 3289 and 13013 samplings versus over a million unknowns.
Calculates O(α α_s) scheme-conversion coefficients for semileptonic weak operators in MOM/SMOM schemes using projectors that eliminate pure-QCD artifacts and yield reduced scale dependence.
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 new generating-function framework turns IBP relations into differential equations in a non-commutative algebra, yielding an iterative algorithm that derives symbolic reduction rules and checks completeness for topologies such as the sunset and double-box diagrams.
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.
Covariant differentiation on the dual vector space spanned by master integrals reduces a large class of Feynman integrals to masters, with connections reusable across mass configurations.
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.
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.
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.
Algorithms that factor denominators in IBP coefficients inside the FUEL interface reduce reconstruction cost and improve robustness of large-scale Feynman integral reductions.
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.
Two-loop QCD corrections to H → b b-bar g amplitude computed at higher orders in ε via Lorentz projection.
Contour equivalence in Feynman parameterization yields universal reduction formulas for one-loop integrals without integration-by-parts.
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.
A general numerical framework is described for high-precision evaluation and analytic continuation of multivariate hypergeometric functions via Pfaffian systems and the Frobenius method.
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.
A primer by six leading developers maps the full Monte Carlo chain (matrix elements, parton showers, hadronisation, detector simulation, tuning, analysis) and the computing and reproducibility issues that come with it.
citing papers explorer
-
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.
-
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.
-
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.
-
Electroweak corrections to Higgs boson pair production: The quark channel
Mixed QCD-EW corrections to qqbar -> HH computed analytically via differential equations, matched to large-mass limit, implemented in POWHEG-BOX, showing up to +10% effect on invariant mass distribution near threshold.
-
Taming Symbolic IBP Reduction with Intermediate Bases
An algorithm reconstructs symbolic IBP reduction coefficients via intermediate bases, demonstrated on massive box-triangle and pentagon-triangle integrals using 3289 and 13013 samplings versus over a million unknowns.
-
Semileptonic weak Hamiltonian to $\mathcal{O}(\alpha \alpha_s(\mu_{\mathrm{Lattice}}))$ in momentum-space subtraction schemes
Calculates O(α α_s) scheme-conversion coefficients for semileptonic weak operators in MOM/SMOM schemes using projectors that eliminate pure-QCD artifacts and yield reduced scale dependence.
-
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.
-
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.
-
An Algorithm for the Symbolic Reduction of Multi-loop Feynman Integrals via Generating Functions
A new generating-function framework turns IBP relations into differential equations in a non-commutative algebra, yielding an iterative algorithm that derives symbolic reduction rules and checks completeness for topologies such as the sunset and double-box diagrams.
-
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.
-
Feynman integral reduction by covariant differentiation
Covariant differentiation on the dual vector space spanned by master integrals reduces a large class of Feynman integrals to masters, with connections reusable across mass configurations.
-
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.
-
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 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.
-
Factorization of denominators as a `fuel' for Feynman integral reduction
Algorithms that factor denominators in IBP coefficients inside the FUEL interface reduce reconstruction cost and improve robustness of large-scale Feynman integral reductions.
-
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.
-
Two-loop QCD corrections to $ H \rightarrow b + \bar{b} + g $ at higher powers in the dimensional regulator
Two-loop QCD corrections to H → b b-bar g amplitude computed at higher orders in ε via Lorentz projection.
-
Feynman Integral Reduction without Integration-By-Parts
Contour equivalence in Feynman parameterization yields universal reduction formulas for one-loop integrals without integration-by-parts.
-
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.
-
Numerical analytical continuation of multivariate hypergeometric functions
A general numerical framework is described for high-precision evaluation and analytic continuation of multivariate hypergeometric functions via Pfaffian systems and the Frobenius method.
-
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.
-
The Monte Carlo Ecosystem in High-Energy Physics: A Primer
A primer by six leading developers maps the full Monte Carlo chain (matrix elements, parton showers, hadronisation, detector simulation, tuning, analysis) and the computing and reproducibility issues that come with it.