Pentagon Functions for Scattering of Five Massless Particles

Abstract

We complete the analytic calculation of the full set of two-loop Feynman integrals required for computation of massless five-particle scattering amplitudes. We employ the method of canonical differential equations to construct a minimal basis set of transcendental functions, pentagon functions, which is sufficient to express all planar and nonplanar massless five-point two-loop Feynman integrals in the whole physical phase space. We find analytic expressions for pentagon functions which are manifestly free of unphysical branch cuts. We present a public library for numerical evaluation of pentagon functions suitable for immediate phenomenological applications.

arXiv comment50 pages, 4 figures; v2: updated references and minor text changes, matches the published version; v3: fixed minor typo in equation (3.2); analytic results at https://gitlab.com/pentagon-functions/PentagonMI ; C++ code at https://gitlab.com/pentagon-functions/PentagonFunctions-cpp

References in corpus (56)

• Multiloop integrals in dimensional regularization made simple
• Collier: a fortran-based Complex One-Loop LIbrary in Extended Regularizations
• Differential Equations for Feynman Graph Amplitudes
• Classical Polylogarithms for Amplitudes and Wilson Loops
• Dimensionally Regulated Pentagon Integrals
• OneLOop: for the evaluation of one-loop scalar functions
• Fully differential NNLO computations with MATRIX
• A novel approach to integration by parts reduction
• From polygons and symbols to polylogarithmic functions
• Two-Loop Master Integrals for ${\gamma }^{\ast }\to 3$ Jets: The planar topologies
• Bootstrapping the three-loop hexagon
• Scattering amplitudes over finite fields and multivariate functional reconstruction
• FiniteFlow: multivariate functional reconstruction using finite fields and dataflow graphs
• Bootstrapping a Five-Loop Amplitude Using Steinmann Relations
• Two-loop Integrand Decomposition into Master Integrals and Surface Terms
• Two-Loop Master Integrals for ${\gamma }^{\ast }\to 3$ Jets: The non-planar topologies
• Reconstructing Rational Functions with $\text{FireFly}$
• Heptagons from the Steinmann Cluster Bootstrap
• Hexagon functions and the three-loop remainder function
• Elliptic polylogarithms and iterated integrals on elliptic curves I: general formalism
• Algorithmic transformation of multi-loop master integrals to a canonical basis with CANONICA
• Pentagon functions for massless planar scattering amplitudes
• Elliptic polylogarithms and iterated integrals on elliptic curves II: an application to the sunrise integral
• The two-loop five-point amplitude in $\mathcal{N}=4$ super-Yang-Mills theory
• Analytic Form of the Planar Two-Loop Five-Parton Scattering Amplitudes in QCD
• All master integrals for three-jet production at NNLO
• A GPU compatible quasi-Monte Carlo integrator interfaced to pySecDec
• Iterative structure of finite loop integrals
• Planar Two-Loop Five-Gluon Amplitudes from Numerical Unitarity
• A first look at two-loop five-gluon scattering in QCD
• Evaluating single-scale and/or non-planar diagrams by differential equations
• Constructing d-log integrands and computing master integrals for three-loop four-particle scattering
• Generalised power series expansions for the elliptic planar families of Higgs + jet production at two loops
• Analytic form of the full two-loop five-gluon all-plus helicity amplitude
• Planar Two-Loop Five-Parton Amplitudes from Numerical Unitarity
• NNLO QCD corrections to three-photon production at the LHC
• Analytic result for a two-loop five-particle amplitude
• Analytic helicity amplitudes for two-loop five-gluon scattering: the single-minus case
• Two-Loop Integrals for Planar Five-Point One-Mass Processes
• Bootstrapping pentagon functions
• Complete integration-by-parts reductions of the non-planar hexagon-box via module intersections
• Analytic result for the nonplanar hexa-box integrals
• The two-loop five-point amplitude in $\mathcal{N}=8$ supergravity
• Deriving canonical differential equations for Feynman integrals from a single uniform weight integral
• How to choose master integrals
• QCDLoop: a comprehensive framework for one-loop scalar integrals
• Differential equations from unitarity cuts: nonplanar hexa-box integrals
• Integration-by-parts reductions of Feynman integrals using Singular and GPI-Space
• Complete reduction of integrals in two-loop five-light-parton scattering amplitudes
• The two-loop five-particle amplitude in $\mathcal{N}=8$ supergravity
• Lifting Heptagon Symbols to Functions
• Four-graviton scattering to three loops in $\mathcal{N}=8$ supergravity
• Two-loop five-point massless QCD amplitudes within the IBP approach
• Multi-Regge Limit of the Two-Loop Five-Point Amplitudes in $\mathcal{N}=4$ Super Yang-Mills and $\mathcal{N}=8$ Supergravity
• Internal Reduction method for computing Feynman Integrals
• The Full Color Two-Loop Six-Gluon All-Plus Helicity Amplitude

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• Recent progress for five-particle two-loop scattering amplitudes with an off-shell leg