PolyLogTools - Polylogs for the masses

Abstract

We review recent developments in the study of multiple polylogarithms, including the Hopf algebra of the multiple polylogarithms and the symbol map, as well as the construction of single valued multiple polylogarithms and discuss an algorithm for finding fibration bases. We document how these algorithms are implemented in the Mathematica package PolyLogTools and show how it can be used to study the coproduct structure of polylogarithmic expressions and how to compute iterated parametric integrals over polylogarithmic expressions that show up in Feynman integal computations at low loop orders.

Package URL: https://gitlab.com/pltteam/plt

References in corpus (22)

• Higgs boson gluon-fusion production in N3LO QCD
• Classical Polylogarithms for Amplitudes and Wilson Loops
• Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals
• Bootstrapping a Five-Loop Amplitude Using Steinmann Relations
• Higgs boson gluon-fusion production at threshold in N3LO QCD
• Bootstrapping an NMHV amplitude through three loops
• The massless higher-loop two-point function
• The two-loop five-point amplitude in $\mathcal{N}=4$ super-Yang-Mills theory
• All master integrals for three-jet production at NNLO
• Analytic Form of the Planar Two-Loop Five-Gluon Scattering Amplitudes in QCD
• Bootstrapping the QCD soft anomalous dimension
• Analytic result for a two-loop five-particle amplitude
• Multi-Regge kinematics and the moduli space of Riemann spheres with marked points
• Elliptic polylogarithms and Feynman parameter integrals
• Cluster adjacency and the four-loop NMHV heptagon
• Two-loop splitting amplitudes and the single-real contribution to inclusive Higgs production at N3LO
• Calculating Massive 3-loop Graphs for Operator Matrix Elements by the Method of Hyperlogarithms
• The two-loop five-point amplitude in $\mathcal{N}=8$ supergravity
• The two-loop five-particle amplitude in $\mathcal{N}=8$ supergravity
• Multi-Loop Positivity of the Planar $\mathcal{N}=4$ SYM Six-Point Amplitude
• Manifestly Dual-Conformal Loop Integration
• A massive momentum-subtraction scheme

Cited by in corpus (153)

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• Collider Physics at the Precision Frontier
• Radiation-Reaction in the Effective Field Theory Approach to Post-Minkowskian Dynamics
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• Charged Current Drell-Yan Production at N3LO
• Multiple polylogarithms with algebraic arguments and the two-loop EW-QCD Drell-Yan master integrals
• Pentagon Functions for One-Mass Planar Scattering Amplitudes
• Higgs production in bottom-quark fusion to third order in the strong coupling
• Two-loop helicity amplitudes for diphoton plus jet production in full color
• The gluon-fusion production of Higgs boson pair: N${}^3$LO QCD corrections and top-quark mass effects
• Mixed strong$-$electroweak corrections to the Drell$-$Yan process
• Analytic representation of all planar two-loop five-point Master Integrals with one off-shell leg
• The SAGEX Review on Scattering Amplitudes, Chapter 3: Mathematical structures in Feynman integrals
• Higgs production in bottom quark fusion: Matching the 4- and 5-flavour schemes to third order in the strong coupling
• Di-photon amplitudes in three-loop Quantum Chromodynamics
• Gravitational scattering at the seventh order in $G$: nonlocal contribution at the sixth post-Newtonian accuracy
• Folding Amplitudes into Form Factors: An Antipodal Duality
• Lifting Heptagon Symbols to Functions
• Black hole perturbation theory and multiple polylogarithms
• Cosmology meets cohomology
• The ice cone family and iterated integrals for Calabi-Yau varieties
• Two-loop Octagons, Algebraic Letters and $\bar{Q}$ Equations
• Mixed QCD-electroweak corrections to W-boson production in hadron collisions
• Soft gluon emission at two loops in full color
• Disentangling the Regge cut and Regge pole in perturbative QCD
• Three-loop helicity amplitudes for diphoton production in gluon fusion
• Loop-by-loop Differential Equations for Dual (Elliptic) Feynman Integrals
• N-jettiness beam functions at N3LO
• On next to soft corrections to Drell-Yan and Higgs Boson productions
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• The Two-Loop Four-Graviton Scattering Amplitudes
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• Two-loop leading colour QCD helicity amplitudes for top quark pair production in the gluon fusion channel
• Two-loop master integrals for a planar topology contributing to $pp\to t\bar{t}j$
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• Linear power corrections to $e^{+}{e}^{-}$ shape variables in the three-jet region
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• First look at the evaluation of three-loop non-planar Feynman diagrams for Higgs plus jet production
• Analytic Computation of Three-point Energy Correlator in QCD
• Two-loop mixed QCD-EW corrections to $gg\to Hg$
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• Two-loop helicity amplitudes for $H+$jet production to higher orders in the dimensional regulator
• The Wilson-loop $d\log$ representation for Feynman integrals
• The Two-Loop Remainder Function for Eight and Nine Particles
• AdS super gluon scattering up to two loops: A position space approach
• Polarized semi-inclusive deep-inelastic scattering at NNLO in QCD
• Fully exclusive heavy quark-antiquark pair production from a colourless initial state at NNLO in QCD
• Pentagon integrals to arbitrary order in the dimensional regulator
• Beam functions for $N$-jettiness at N${}^3$LO in perturbative QCD
• The width difference in the $B-\bar{B}$ system at next-to-next-to-leading order of QCD
• High Energy String Scattering in AdS
• One-loop hexagon integral to higher orders in the dimensional regulator
• The Compton Scattering Total Cross Section at Next-to-Leading Order
• Revisiting the double-soft asymptotics of one-loop amplitudes in massless QCD
• Cutting-Edge Tools for Cutting Edges
• Quark and gluon two-loop beam functions for leading-jet $p_T$ and slicing at NNLO
• The type IIA Virasoro-Shapiro amplitude in AdS${}_4$ $\times$ CP${}^3$ from ABJM theory
• Two-loop running effects in Higgs physics in Standard Model Effective Field Theory
• Neutral and Charged Current Semi-Inclusive Deep-Inelastic Scattering at NNLO QCD
• Two-loop massive QCD and QED helicity amplitudes for light-by-light scattering
• Towards Analytic Structure of Feynman Parameter Integrals with Rational Curves
• Resummation methods for Master Integrals
• Form factors with two operator insertions and the principle of maximal transcendentality
• Three-point Energy Correlators in Hadronic Higgs Decays
• The SAGEX Review on Scattering Amplitudes, Chapter 5: Analytic Bootstraps for Scattering Amplitudes and Beyond
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• The Kaluza-Klein AdS Virasoro-Shapiro Amplitude near Flat Space
• Non-planar elliptic vertex
• Quark mass effects in two-loop Higgs amplitudes
• Analytic two-loop amplitudes for $tW$ production: leading color and light fermion-loop contributions
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• A Note on Kinematic Flow and Differential Equations for Two-Site One-Loop Graph in FRW Spacetime
• Single-inclusive hadron production in electron-positron annihilation at next-to-next-to-next-to-leading order in QCD
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• Analytic two-loop master integrals for $tW$ production at hadron colliders. Part II
• Asymptotic behavior of angular integrals in the massless limit
• Differential equations for tree--level cosmological correlators with massive states
• A Two-Loop Four-Point Form Factor at Function Level
• The analytic leading color contribution to the Higgs-gluon form factor in QCD at NNLO
• Heptagon Functions and Seven-Gluon Amplitudes in Multi-Regge Kinematics
• A first computation of three-loop master integrals for the production of two off-shell vector bosons with different masses
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• Two-Loop Four-Fermion Scattering Amplitude in QED
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• Integrated Unitarity for Scattering Amplitudes
• Mixed QCD-electroweak corrections to dilepton production at the LHC in the high invariant mass region
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• Three-loop helicity amplitudes for four-quark scattering in massless QCD
• Next-to-next-to-leading order threshold soft function for $tW$ production
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• Three-Loop QCD corrections to the production of a Higgs boson and a Jet
• Hemisphere mass up to four-loops with generalised $k_t$ algorithms
• On multi-propagator angular integrals
• Pseudoscalar Higgs boson decay to three parton amplitudes at NNLO to higher orders in the dimensional regulator
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• Dihadron Angular Correlations in the $e^{+}{e}^{-}$ Collision
• Chaos and moduli space volumes in unorientable JT gravity
• Two-loop mixed QCD-EW corrections to $q\overline{q}\to Hg$, $qg\to Hq$, and $\overline{q}g\to H\overline{q}$
• On Solving Dual Conformal Integrals in Coulomb-branch Amplitudes and Their Periods
• Two-loop scattering amplitude for heavy-quark pair production through light-quark annihilation in QCD
• Two-loop non-planar hexa-box integrals with one massive leg
• Higgs-boson production in top-quark fragmentation
• Energy-Energy Correlator from the AdS Virasoro-Shapiro Amplitude
• $\text{history}$: A tool for fully-differential cross sections at next-to-next-to-leading order
• Integral of the double-emission eikonal function for a massive and a massless emitter at an arbitrary angle
• Estimating power corrections for the Drell-Yan Process
• The integrand form of infrared singularities of two-loop QCD scattering amplitudes
• The Hopf Algebra Structure of the Two Loop Three Mass Non-Planar Feynman Diagram
• Boomerang webs up to three-loop order
• Transition Form-Factor for ${\eta }_Q$ at NNLO in the strong coupling ${\alpha }_s$ and with all-order $v^2$ resummation
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• Two-loop mixed QCD-EW corrections to neutral current Drell-Yan
• The analytic two-loop soft function for leading-jet $p_T$
• Mixed QCD-EW corrections to $W$-pair production at electron-positron colliders
• Analytic results for two-loop planar master integrals for Bhabha scattering
• Hyper-Mahler measures via Goncharov-Deligne cyclotomy