HPL, a Mathematica implementation of the harmonic polylogarithms

Abstract

In this paper, we present an implementation of the harmonic polylogarithm of Remiddi and Vermaseren for Mathematica. It contains an implementation of the product algebra, the derivative properties, series expansion and numerical evaluation. The analytic continuation has been treated carefully, allowing the user to keep the control over the definition of the sign of the imaginary parts. Many options enables the user to adapt the behavior of the package to his specific problem.

24 pages, Latex, the package can be downloaded at http://krone.physik.unizh.ch/~maitreda/HPL/, typos corrected, one example changed

References in corpus (15)

• Iteration of Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory at Three Loops and Beyond
• Numerical evaluation of multiple polylogarithms
• The Longitudinal Structure Function at the Third Order
• The Standard Model Prediction of the Muon Anomalous Magnetic Moment
• Two-loop QCD Corrections to the Heavy Quark Form Factors: the Vector Contributions
• Two-Loop QCD Corrections to the Heavy Quark Form Factors: Anomaly Contributions
• Two-Loop Corrections to Bhabha Scattering
• Master integrals for massive two-loop Bhabha scattering in QED
• Two-Loop QCD Corrections to the Heavy Quark Form Factors: Axial Vector Contributions
• Analytic Continuation of the Harmonic Sums for the 3--Loop Anomalous Dimensions
• Analytical Evaluation of Dimensionally Regularized Massive On-Shell Double Boxes
• Master Integrals For Massless Two-Loop Vertex Diagrams With Three Offshell Legs
• Master integrals for the two-loop light fermion contributions to $gg\to H$ and $H\to \gamma \gamma$
• Two-Loop N_F =1 QED Bhabha Scattering: Soft Emission and Numerical Evaluation of the Differential Cross-section
• Two-Loop Bhabha Scattering in QED

Cited by in corpus (282)

• NNLO corrections to top-pair production at hadron colliders: the all-fermionic scattering channels
• The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory
• Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals
• Quest for precision in hadronic cross sections at low energy: Monte Carlo tools vs. experimental data
• HypExp, a Mathematica package for expanding hypergeometric functions around integer-valued parameters
• From polygons and symbols to polylogarithmic functions
• Bootstrapping the three-loop hexagon
• PolyLogTools - Polylogs for the masses
• HypExp 2, Expanding Hypergeometric Functions about Half-Integer Parameters
• Hopf algebras, coproducts and symbols: an application to Higgs boson amplitudes
• Bootstrapping rapidity anomalous dimension for transverse-momentum resummation
• Higgs Boson Production at Hadron Colliders at N3LO in QCD
• NNLO corrections to event shapes in $e^{+}{e}^{-}$ annihilation
• Polylogarithms, Multiple Zeta Values and Superstring Amplitudes
• The Two-Loop Hexagon Wilson Loop in N = 4 SYM
• Two-loop amplitudes and master integrals for the production of a Higgs boson via a massive quark and a scalar-quark loop
• Feynman Diagrams and Differential Equations
• Analytic result for the two-loop six-point NMHV amplitude in N=4 super Yang-Mills theory
• Testing new physics with the electron g-2
• Analytic Results for Virtual QCD Corrections to Higgs Production and Decay
• Soft triple-real radiation for Higgs production at N3LO
• Two-Loop QCD Corrections to the Helicity Amplitudes for $H\to$ 3 partons
• Antenna subtraction at NNLO with hadronic initial states: initial-final configurations
• Space-time S-matrix and Flux tube S-matrix II. Extracting and Matching Data
• Magnus and Dyson Series for Master Integrals
• Threshold Resummation for Top-Pair Hadroproduction to Next-to-Next-to-Leading Log
• Extension of HPL to complex arguments
• A Computer Algebra Toolbox for Harmonic Sums Related to Particle Physics
• Theory of the tau lepton anomalous magnetic moment
• Towards a fitting procedure for deeply virtual Compton scattering at next-to-leading order and beyond
• Leading singularities and off-shell conformal integrals
• Single-valued harmonic polylogarithms and the multi-Regge limit
• Infrared structure of e+e- --> 3 jets at NNLO
• Master Integrals for Four-Loop Massless Propagators up to Transcendentality Weight Twelve
• Five-Loop Anomalous Dimension of Twist-Two Operators
• Higgs boson production at the LHC using the $q_T$ subtraction formalism at N${}^3$LO QCD
• Quark Transverse Parton Distribution at the Next-to-Next-to-Next-to-Leading Order
• Two-Loop Fermionic Corrections to Heavy-Quark Pair Production: the Quark-Antiquark Channel
• epsilon: A tool to find a canonical basis of master integrals
• The 3-Loop Non-Singlet Heavy Flavor Contributions and Anomalous Dimensions for the Structure Function $F_2(x,Q^2)$ and Transversity
• The 3-Loop Pure Singlet Heavy Flavor Contributions to the Structure Function $F_2(x,Q^2)$ and the Anomalous Dimension
• FeynCalc 10: Do multiloop integrals dream of computer codes?
• The three-loop cusp anomalous dimension in QCD
• Evaluating single-scale and/or non-planar diagrams by differential equations
• The Energy-Energy Correlation at Next-to-Leading Order in QCD, Analytically
• The cusp anomalous dimension at three loops and beyond
• The three-loop cusp anomalous dimension in QCD and its supersymmetric extensions
• Two-Loop Four-Gluon Amplitudes with the Numerical Unitarity Method
• On the Generalized Harmonic Polylogarithms of One Complex Variable
• Inclusive Heavy Flavor Hadroproduction in NLO QCD: the Exact Analytic Result
• Production of scalar and pseudo-scalar Higgs bosons to next-to-next-to-leading order at hadron colliders
• Two-Loop Planar Corrections to Heavy-Quark Pair Production in the Quark-Antiquark Channel
• Four-loop photon quark form factor and cusp anomalous dimension in the large-$N_c$ limit of QCD
• Analytic continuation and numerical evaluation of the kite integral and the equal mass sunrise integral
• Two-loop QCD helicity amplitudes for $q\bar{q}\to W^{\pm }\gamma$ and $q\bar{q}\to Z^0\gamma$
• Solving differential equations for Feynman integrals by expansions near singular points
• Transverse Parton Distribution and Fragmentation Functions at NNLO: the Quark Case
• Fragmentation in Jets at NNLO
• NNLO BFKL Pomeron eigenvalue in N=4 SYM
• Precise mass-dependent QED contributions to leptonic g-2 at order alpha^2 and alpha^3
• Bootstrapping pentagon functions
• Matter dependence of the four-loop cusp anomalous dimension
• Two-loop QCD correction to differential semi-leptonic b --> u decays in the shape-function region
• Real-Virtual contributions to the inclusive Higgs cross-section at N3LO
• The two-loop electroweak bosonic corrections to ${\sin }^2{\theta }_{\mathrm{eff}}^{\mathrm{b}}$
• HandyG -- rapid numerical evaluation of generalised polylogarithms in Fortran
• Analytic calculation of two-loop QCD corrections to b\to s\ell^+\ell^- in the high q^2 region
• The quark and gluon form factors to three loops in QCD through to O(eps^2)
• Adjoint BFKL at finite coupling: a short-cut from the collinear limit
• Iterative Structure Within The Five-Particle Two-Loop Amplitude
• Energy-energy correlations at next-to-next-to-leading order
• Analytic Next-To-Leading Order Calculation of Energy-Energy Correlation in Gluon-Initiated Higgs Decays
• The four-loop cusp anomalous dimension in N=4 super Yang-Mills and analytic integration techniques for Wilson line integrals
• NNLO corrections to inclusive semileptonic B decays in the shape-function region
• Two-Loop Leading Color Corrections to Heavy-Quark Pair Production in the Gluon Fusion Channel
• Heavy-to-heavy quark decays at NNLO
• Nine-Propagator Master Integrals for Massless Three-Loop Form Factors
• The Two Loop Crossed Ladder Vertex Diagram with Two Massive Exchanges
• Two-body non-leptonic heavy-to-heavy decays at NNLO in QCD factorization
• Non-global Logarithms at 3 Loops, 4 Loops, 5 Loops and Beyond
• The AdS Virasoro-Shapiro Amplitude
• Two-loop matching factors for light quark masses and three-loop mass anomalous dimensions in the RI/SMOM schemes
• Numerical evaluation of loop integrals
• Quantum Spectral Curve for a Cusped Wilson Line in N=4 SYM
• The Complete $O({\alpha }_s^2)$ Non-Singlet Heavy Flavor Corrections to the Structure Functions $g_{1,2}^{ep}(x,Q^2)$, $F_{1,2,L}^{ep}(x,Q^2)$, $F_{1,2,3}^{\nu (\bar{\nu })}(x,Q^2)$ and the Associated Sum Rules
• NNLO phase space master integrals for two-to-one inclusive cross sections in dimensional regularization
• Quantum Spectral Curve at Work: From Small Spin to Strong Coupling in N=4 SYM
• On the reduction of generalized polylogarithms to ${\text{Li}}_n$ and ${\text{Li}}_{2,2}$ and on the evaluation thereof
• Quark--anti-quark potential in N=4 SYM
• NLO Antenna Subtraction with Massive Fermions
• The QCD form factor of heavy quarks at NNLO
• Master Integrals for Fermionic Contributions to Massless Three-Loop Form Factors
• Extending Precision Perturbative QCD with Track Functions
• The $n_f^2$ contributions to fermionic four-loop form factors
• Four-loop quark form factor with quartic fundamental colour factor
• Light quark mass effects in the on-shell renormalization constants
• Transverse Parton Distribution and Fragmentation Functions at NNLO: the Gluon Case
• Fragmentation Functions at Next-to-Next-to-Leading Order Accuracy
• Analytic Epsilon Expansions of Master Integrals Corresponding to Massless Three-Loop Form Factors and Three-Loop g-2 up to Four-Loop Transcendentality Weight
• Exact Correlation Functions in Conformal Fishnet Theory
• Light-quark two-loop corrections to heavy-quark pair production in the gluon fusion channel
• Single-top-quark production in the $t$-channel at NNLO
• Decays of Scalar and Pseudoscalar Higgs Bosons into Fermions: Two-loop QCD Corrections to the Higgs-Quark-Antiquark Amplitude
• Fermionic pentagons and NMHV hexagon
• Hexagon Wilson Loop OPE and Harmonic Polylogarithms
• Matter dependence of the four-loop QCD cusp anomalous dimension: from small angles to all angles
• Higgs boson production at the LHC: NNLO partonic cross sections through order $\epsilon$ and convolutions with splitting functions to N${}^3$LO
• Scale dependence and collinear subtraction terms for Higgs production in gluon fusion at N3LO
• Hadronic corrections to $\mu$-$e$ scattering at NNLO with space-like data
• One-Loop Single-Real-Emission Contributions to $pp\to H+X$ at Next-to-Next-to-Next-to-Leading Order
• Fiducial Higgs and Drell-Yan distributions at N${}^3$LL${}^{\prime }$+NNLO with RadISH
• Introducing SummerTime: a package for high-precision computation of sums appearing in DRA method
• Gluon-fusion Higgs production in the Standard Model Effective Field Theory
• Multi-Loop Positivity of the Planar $\mathcal{N}=4$ SYM Six-Point Amplitude
• Gravitational scattering at the seventh order in $G$: nonlocal contribution at the sixth post-Newtonian accuracy
• Four-point Amplitudes in N=8 Supergravity and Wilson Loops
• NNLO corrections to B --> X_u l nu in the shape-function region
• Numerical Implementation of Harmonic Polylogarithms to Weight w = 8
• Double-real corrections at O(alpha alpha_s) to single gauge boson production
• Mixed QCD-electroweak corrections to W-boson production in hadron collisions
• Small-mass effects in heavy-to-light form factors
• Generalised ladders and single-valued polylogarithms
• Four-graviton scattering to three loops in $\mathcal{N}=8$ supergravity
• Evaluating `elliptic' master integrals at special kinematic values: using differential equations and their solutions via expansions near singular points
• Analytic Computing Methods for Precision Calculations in Quantum Field Theory
• Renormalization Group Flows for Track Function Moments
• The double-soft integral for an arbitrary angle between hard radiators
• Six-Loop Anomalous Dimension of Twist-Three Operators in N=4 SYM
• Small Flux Superpotentials for Type IIB Flux Vacua Close to a Conifold
• Massive three-loop form factor in the planar limit
• Two-loop QCD helicity amplitudes for $gg\to Zg$ and $gg\to Z\gamma$
• Matching QCD and HQET heavy-light currents at three loops
• The electron self-energy in QED at two loops revisited
• Three-loop on-shell Feynman integrals with two masses
• Loop-by-loop Differential Equations for Dual (Elliptic) Feynman Integrals
• Electron, muon and tau magnetic moments: a theoretical update
• Two-loop QED radiative corrections to the decay pi0 -> e+ e- : The virtual corrections and soft-photon bremsstrahlung
• Moments of heavy quark correlators with two masses: exact mass dependence to three loops
• MPL - a program for computations with iterated integrals on moduli spaces of curves of genus zero
• The three-loop single mass polarized pure singlet operator matrix element
• Semi-inclusive deep-inelastic scattering at NNLO in QCD
• MT: a Mathematica package to compute convolutions
• Massive planar and non-planar double box integrals for light Nf contributions to gg->tt
• The real radiation antenna function for $S\to Q\bar{Q}q\bar{q}$ at NNLO QCD
• Adequate bases of phase space master integrals for $gg\to h$ at NNLO and beyond
• The NNLO soft function for the pair invariant mass distribution of boosted top quarks
• Systematics of the cusp anomalous dimension
• Hexagon OPE Resummation and Multi-Regge Kinematics
• Three-loop helicity amplitudes for quark-gluon scattering in QCD
• Anomalous dimensions at twist-3 in the sl(2) sector of N=4 SYM
• Three loop anomalous dimension of the non-singlet transversity operator in QCD
• NumExp: Numerical epsilon expansion of hypergeometric functions
• RG stability of integrable fishnet models
• Massless two-loop self-energy diagram: Historical review
• Next-to-Next-to-Leading-Order QCD Prediction for the Photon-Pion Form Factor
• Unpolarized Quark and Gluon TMD PDFs and FFs at N${}^3$LO
• Calculation of the Two-Loop Heavy-Flavor Contribution to Bhabha Scattering
• Wilson loop OPE, analytic continuation and multi-Regge limit
• Chromomagnetic Dipole-Operator Corrections in Bbar -> X_sgamma at O(beta_0 alpha_s^2)
• All loop structures in Supergravity Amplitudes on $Ad{S}_5\times S^5$ from CFT
• Subleading Regge limit from a soft anomalous dimension
• Two-loop amplitudes for processes $gg\to Hg,qg\to Hq$ and $q\bar{q}\to Hg$ at large Higgs transverse momentum
• Virtual Hadronic and Heavy-Fermion O(alpha^2) Corrections to Bhabha Scattering
• Two-Parton Contribution to the Heavy-Quark Forward-Backward Asymmetry in NNLO QCD
• Two-loop anomalous dimension for the resummation of non-global observables
• Two-loop coefficient function for DVCS: Vector contributions
• Two-loop QCD Corrections to $B_c$ Meson Leptonic Decays
• Testing high-energy factorization beyond the next-to-leading-logarithmic accuracy
• Quark beam function at next-to-next-to-next-to-leading order in perturbative QCD in the generalized large-$N_c$ approximation
• Integrated correlators from integrability: Maldacena-Wilson line in $\mathcal{N}=4$ SYM
• Searching for new spin-0 resonances at LHCb
• High-Energy Expansion of Two-Loop Massive Four-Point Diagrams
• Three-loop vacuum integrals with arbitrary masses
• Reciprocity of gauge operators in N=4 SYM
• The LBK theorem to all orders
• Analytic approximations of $2\to 2$ processes with massive internal particles
• On a two-loop crossed six-line master integral with two massive lines
• The Polarized Two-Loop Massive Pure Singlet Wilson Coefficient for Deep-Inelastic Scattering
• Master Integrals for two-loop QCD corrections to Quasi PDFs
• Complete $N_f^2$ contributions to four-loop pure-singlet splitting functions
• Analytic three-loop QCD corrections to top-quark and semileptonic $b\to u$ decays
• Two-Loop Massive Quark Jet Functions in SCET
• Two-Loop integrals for CP-even heavy quarkonium production and decays: Elliptic Sectors
• Four-particle scattering amplitudes in QCD at NNLO to higher orders in the dimensional regulator
• Polarized semi-inclusive deep-inelastic scattering at NNLO in QCD
• Hard Matching for Boosted Tops at Two Loops
• A matrix model for the latitude Wilson loop in ABJM theory
• IR divergences and Regge limits of subleading-color contributions to the four-gluon amplitude in N=4 SYM Theory
• Higher loop mixed correlators in N=4 SYM
• Exact scattering amplitudes in conformal fishnet theory
• The light-fermion contribution to the exact Higgs-gluon form factor in QCD
• Beam functions for $N$-jettiness at N${}^3$LO in perturbative QCD
• Two-loop master integrals for non-leptonic heavy-to-heavy decays
• Towards three-loop QCD corrections to the time-like splitting functions
• On Epsilon Expansions of Four-loop Non-planar Massless Propagator Diagrams
• The unpolarized two-loop massive pure singlet Wilson coefficients for deep-inelastic scattering
• $\epsilon$-Expansion of Multivariable Hypergeometric Functions Appearing in Feynman Integral Calculus
• Two-Loop QCD Helicity Amplitudes for (2+1)-Jet Production in Deep Inelastic Scattering
• Revisiting the double-soft asymptotics of one-loop amplitudes in massless QCD
• The Full-Color Two-Loop Four-Gluon Amplitude in $\mathcal{N}=2$ Super-QCD
• A planar four-loop form factor and cusp anomalous dimension in QCD
• Conformal Regge Theory at Finite Boost
• Antenna subtraction at NNLO with identified hadrons
• Infrared singularities of multi-leg QCD amplitudes with a massive parton at three loops
• Master integrals for splitting functions from differential equations in QCD
• A double copy from twisted (co)homology at genus one
• Two-Loop integrals for CP-even heavy quarkonium production and decays
• Top-quark pair production at next-to-next-to-leading order QCD in electron positron collisions
• High-precision muon decay predictions for ALP searches
• NNLO corrections to B --> X_u l nu and the determination of |V_ub|
• The inverse Mellin transform via analytic continuation
• Neutral and Charged Current Semi-Inclusive Deep-Inelastic Scattering at NNLO QCD
• Double-logs, Gribov-Lipatov reciprocity and wrapping
• Exact N${}^3$LO results for $q{q}^{\prime }\to H+X$
• Decays of polarized top quarks to lepton, neutrino and jets at NLO QCD
• Two-Loop master integrals for heavy-to-light form factors of two different massive fermions
• Heavy quark form factors in the large ${\beta }_0$ limit
• A $QQ\to QQ$ planar doublebox in canonical form
• The real-virtual antenna functions for $S\to Q\bar{Q}X$ at NNLO QCD
• Recoil corrections to the energy levels of hydrogenic atoms
• Heavy-quark pair production in polarized photon-photon collisions at next-to-leading order: Fully integrated total cross sections
• Position-space cuts for Wilson line correlators
• A Surprise in the Amplitude/Wilson Loop Duality
• Quark mass effects in two-loop Higgs amplitudes
• Positivity of the Hypergeometric Coon Amplitude
• Double -- photon exclusive processes with heavy quark -- heavy antiquark pairs in high-energy Pb-Pb collisions at LHC
• Evaluating the three-loop static quark potential
• An explicit calculation of pseudo-goldstino mass at the leading three-loop level
• Matching the heavy-quark fields in QCD and HQET at four loops
• Single-inclusive hadron production in electron-positron annihilation at next-to-next-to-next-to-leading order in QCD
• Multiple soft-photon emission at next-to-leading power to all orders
• Coon unitarity via partial waves or: how I learned to stop worrying and love the harmonic numbers
• Amplitudes in fishnet theories in diverse dimensions and Box ladder diagrams
• QCD cusp anomalous dimension: current status
• Special Values of Generalized Log-sine Integrals
• Three-loop planar master integrals for heavy-to-light form factors
• Master integrals for bipartite cuts of three-loop photon self energy
• Double-Real-Virtual and Double-Virtual-Real Corrections to the Three-Loop Thrust Soft Function
• Reflection identities of harmonic sums of weight four
• Generalized Polylogarithms in Maple
• A Novel Algorithm for Nested Summation and Hypergeometric Expansions
• Disc partition function of 2d $R^2$ gravity from DWG matrix model
• Applications of Diagrammatic Renormalization Methods in QCD Sum-Rules
• N${}^3$LL + $\mathcal{O}({\alpha }_s^2)$ predictions of lepton-jet azimuthal angular distribution in deep-inelastic scattering
• New results for loop integrals: AMBRE, CSectors, hexagon
• Harmonic polylogarithms for massive Bhabha scattering
• Automated calculations for multi-leg processes
• BFKL Eigenvalue and Maximal Alternation of Harmonic Sums
• NNLO electron structure functions (PDFs) from SCET
• The analytic structure of the BFKL equation and reflection identities of harmonic sums at weight five
• Analytic calculation of doubly heavy hadron spectral density in coordinate space
• Correlation functions of determinant operators in conformal fishnet theory
• Bootstrability in Defect CFT: Integrated Correlators and Sharper Bounds
• Master integrals for mixed QCD-QED corrections to charged-current Drell-Yan production of a massive charged lepton
• Hypergeometric functions with rational arguments
• Two-Loop QED Heavy-Flavor Contribution to Bhabha Scattering
• Infrared and transcendental structure of two-loop supersymmetric QCD amplitudes
• Wilson Loops with Lagrangians: Large Spin OPE and Cusp Anomalous Dimension Dictionary
• HQET vertex diagram: $\epsilon$ expansion
• On-shell renormalisation constants including two different nonzero masses
• New Evaluations of Inverse Binomial Series via Cyclotomic Multiple Zeta Values
• The real radiation antenna functions for $S\to Q\bar{Q}gg$ at NNLO QCD
• Exact Results in Supersymmetric Gauge Theories
• Bhabha Scattering at NNLO
• Three-Loop QCD corrections to the production of a Higgs boson and a Jet
• Three-loop helicity amplitudes for four-quark scattering in massless QCD
• Unitarity methods for Mellin moments of Drell-Yan cross sections
• Higgs-boson production in top-quark fragmentation
• Integral of the double-emission eikonal function for a massive and a massless emitter at an arbitrary angle
• Evaluating Feynman Integrals through differential equations and series expansions
• 12 loops and triple wrapping in ABJM theory from integrability
• Two-parton contribution to the heavy-quark A_FB at NNLO QCD in e+e- collisions
• An Operator Product Expansion for Form Factors II. Born level
• Universal structure of radiative QED amplitudes at one loop
• Hyper-Mahler measures via Goncharov-Deligne cyclotomy
• Mixed QCD-EW corrections to $W$-pair production at electron-positron colliders
• Higher-Order Corrections to Higgs Boson Amplitudes with Full Quark Mass Dependence in Quantum Chromodynamics
• Analytic calculation of Energy-Energy Correlation in $e^{+}{e}^{-}$ annihilation at NLO
• QCD factorization for the $B\to \gamma \ell {\nu }_{\ell }$ decay beyond leading power
• The canonical form has got baubles
• Higher-order corrections to the splitting functions from differential equations in QCD
• Anomalous Ward identities for on-shell amplitudes at the conformal fixed point