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.
hub Tool reference
Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals
Tool reference. 83% of classified Pith citations use this work as a method, library, or software dependency, not as a substantive claim.
14
Pith papers citing it
Method reference
83% of classified citations
abstract
We provide algorithms for symbolic integration of hyperlogarithms multiplied by rational functions, which also include multiple polylogarithms when their arguments are rational functions. These algorithms are implemented in Maple and we discuss various applications. In particular, many Feynman integrals can be computed by this method.
hub tools
citation-role summary
method 5
background 1
citation-polarity summary
representative citing papers
Conformal moments of the two-loop DVCS coefficient functions have been computed with a new technique.
Fixes the leading AdS curvature corrections to the type IIA Virasoro-Shapiro amplitude in AdS4 x CP3 by matching resonances in the ABJM stress-tensor correlator to a single-valued polylog worldsheet ansatz.
The all-loop bare perturbative part of the four-quark Bethe-Salpeter kernel is computed analytically in the large-Nf limit of massless QCD.
Local subtraction reduces pseudo-evanescent Feynman integrals to products of one-loop integrals or one-fold integrals, with the finite part of the two-loop all-plus five-point amplitude arising solely from ultraviolet regions after infrared cancellations.
LinApart3 performs multivariate partial fraction decomposition for linear-denominator rational functions using linear algebra and residue extraction on hyperplane arrangements, with guarantees on term structure, no spurious singularities, ordering independence, and spectator-variable insensitivity.
Three-loop five-point dual conformal master integrals on the Coulomb branch of N=4 SYM are computed via DCI-preserving regularization, cross-ratio factorization, and HyperInt for residual regions.
Quasi-finite Feynman integrals produce sparse Fano and reflexive polytopes that encode degenerate Calabi-Yau varieties and link to del Pezzo surfaces, K3 surfaces, and Calabi-Yau threefolds.
Analytic expressions for the planar master integrals in two-loop NLO EW light-fermion contributions to gg → ZH are derived via canonical differential equations and expressed using Goncharov polylogarithms or one-fold integrals over them.
Characterizes numerators yielding finite or evanescent massless pentabox integrals, gives compact generators via momentum basis and Gram determinants, and evaluates lowest-rank cases in polylogarithms and pentagon functions.
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 new open FORM package implements parametric hyperlogarithm integration, demonstrated on zigzag Feynman integrals up to six loops.
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.
Graphical functions, defined as massless three-point position-space integrals, serve as a powerful tool for evaluating multi-loop Feynman integrals, with extensions to conformal field theory and recent algorithmic computability.
citing papers explorer
-
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.
-
Conformal moments of the two-loop coefficient functions in DVCS
Conformal moments of the two-loop DVCS coefficient functions have been computed with a new technique.
-
The type IIA Virasoro-Shapiro amplitude in AdS$_4$ $\times$ CP$^3$ from ABJM theory
Fixes the leading AdS curvature corrections to the type IIA Virasoro-Shapiro amplitude in AdS4 x CP3 by matching resonances in the ABJM stress-tensor correlator to a single-valued polylog worldsheet ansatz.
-
All-loop four-quark Bethe-Salpeter kernel
The all-loop bare perturbative part of the four-quark Bethe-Salpeter kernel is computed analytically in the large-Nf limit of massless QCD.
-
Pseudo-Evanescent Feynman Integrals from Local Subtraction
Local subtraction reduces pseudo-evanescent Feynman integrals to products of one-loop integrals or one-fold integrals, with the finite part of the two-loop all-plus five-point amplitude arising solely from ultraviolet regions after infrared cancellations.
-
LinApart3: efficient algorithm for multivariate partial fraction decomposition with linear denominators
LinApart3 performs multivariate partial fraction decomposition for linear-denominator rational functions using linear algebra and residue extraction on hyperplane arrangements, with guarantees on term structure, no spurious singularities, ordering independence, and spectator-variable insensitivity.
-
Five legs @ three loops: slightly off-shell dual conformal integrals
Three-loop five-point dual conformal master integrals on the Coulomb branch of N=4 SYM are computed via DCI-preserving regularization, cross-ratio factorization, and HyperInt for residual regions.
-
Fano and Reflexive Polytopes from Feynman Integrals
Quasi-finite Feynman integrals produce sparse Fano and reflexive polytopes that encode degenerate Calabi-Yau varieties and link to del Pezzo surfaces, K3 surfaces, and Calabi-Yau threefolds.
-
Planar master integrals for two-loop NLO electroweak light-fermion contributions to $g g \rightarrow Z H$
Analytic expressions for the planar master integrals in two-loop NLO EW light-fermion contributions to gg → ZH are derived via canonical differential equations and expressed using Goncharov polylogarithms or one-fold integrals over them.
-
Finite Massless Pentaboxes
Characterizes numerators yielding finite or evanescent massless pentabox integrals, gives compact generators via momentum basis and Gram determinants, and evaluates lowest-rank cases in polylogarithms and pentagon functions.
-
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.
-
HyperFORM -- a FORM package for parametric integration with hyperlogarithms
A new open FORM package implements parametric hyperlogarithm integration, demonstrated on zigzag Feynman integrals up to six loops.
-
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.
-
Graphical Functions by Examples
Graphical functions, defined as massless three-point position-space integrals, serve as a powerful tool for evaluating multi-loop Feynman integrals, with extensions to conformal field theory and recent algorithmic computability.