Analytic form of the two-loop planar five-gluon all-plus-helicity amplitude in QCD

Abstract

Virtual two-loop corrections to scattering amplitudes are a key ingredient to precision physics at collider experiments. We compute the full set of planar master integrals relevant to five-point functions in massless QCD, and use these to derive an analytical expression for the two-loop five-gluon all-plus-helicity amplitude. After subtracting terms that are related to the universal infrared and ultraviolet pole structure, we obtain a remarkably simple and compact finite remainder function, consisting only of dilogarithms.

Corrected typo in eq.(9), 5 pages, 2 figures

References in corpus (8)

• Reducing full one-loop amplitudes to scalar integrals at the integrand level
• Classical Polylogarithms for Amplitudes and Wilson Loops
• Algorithm FIRE -- Feynman Integral REduction
• Sector Decomposition
• Iterative structure of finite loop integrals
• Two-Loop Iteration of Five-Point N=4 Super-Yang-Mills Amplitudes
• New differential equations for on-shell loop integrals
• Iterative Structure Within The Five-Particle Two-Loop Amplitude

Cited by in corpus (98)

• Jet Substructure at the Large Hadron Collider: A Review of Recent Advances in Theory and Machine Learning
• Scattering amplitudes over finite fields and multivariate functional reconstruction
• Feynman Integrals and Intersection Theory
• Algorithmic transformation of multi-loop master integrals to a canonical basis with CANONICA
• Two-loop planar master integrals for Higgs$\to 3$ partons with full heavy-quark mass dependence
• Pentagon functions for massless planar scattering amplitudes
• Collider Physics at the Precision Frontier
• 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
• Cuts of Feynman Integrals in Baikov representation
• All master integrals for three-jet production at NNLO
• Elliptic Feynman integrals and pure functions
• Analytic Form of the Planar Two-Loop Five-Gluon Scattering Amplitudes in QCD
• Planar Two-Loop Five-Gluon Amplitudes from Numerical Unitarity
• A first look at two-loop five-gluon scattering in QCD
• Decomposition of Feynman Integrals on the Maximal Cut by Intersection Numbers
• Two-Loop Four-Gluon Amplitudes with the Numerical Unitarity Method
• 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
• Transforming differential equations of multi-loop Feynman integrals into canonical form
• Evidence for a Nonplanar Amplituhedron
• Analytic result for a two-loop five-particle amplitude
• Analytic helicity amplitudes for two-loop five-gluon scattering: the single-minus case
• Multiple polylogarithms with algebraic arguments and the two-loop EW-QCD Drell-Yan master integrals
• Pentagon Functions for One-Mass Planar Scattering Amplitudes
• Bootstrapping pentagon functions
• Prescriptive Unitarity
• Complete integration-by-parts reductions of the non-planar hexagon-box via module intersections
• Analytic result for the nonplanar hexa-box integrals
• Two-loop QCD corrections to $Wb\bar{b}$ production at hadron colliders
• Cluster algebras for Feynman integrals
• Complete sets of logarithmic vector fields for integration-by-parts identities of Feynman integrals
• The two-loop five-point amplitude in $\mathcal{N}=8$ supergravity
• Leading-Color Two-Loop QCD Corrections for Three-Jet Production at Hadron Colliders
• The Transverse Energy-Energy Correlator in the Back-to-Back Limit
• Differential equations from unitarity cuts: nonplanar hexa-box integrals
• Two-loop helicity amplitudes for diphoton plus jet production in full color
• Two-loop five-point all plus helicity Yang-Mills amplitude
• Two-loop leading-colour QCD helicity amplitudes for Higgs boson production in association with a bottom-quark pair at the LHC
• Two-Loop Hexa-Box Integrals for Non-Planar Five-Point One-Mass Processes
• On the reduction of generalized polylogarithms to ${\text{Li}}_n$ and ${\text{Li}}_{2,2}$ and on the evaluation thereof
• The Pentabox Master Integrals with the Simplified Differential Equations approach
• Integration-by-parts reductions of Feynman integrals using Singular and GPI-Space
• The two-loop five-particle amplitude in $\mathcal{N}=8$ supergravity
• Two-loop six gluon all plus helicity amplitude
• Overcoming Obstacles to Colour-Kinematics Duality at Two Loops
• On loop celestial amplitudes for gauge theory and gravity
• Local integrands for two-loop all-plus Yang-Mills amplitudes
• Bootstrapping two-loop Feynman integrals for planar N=4 sYM
• Two-loop five-point massless QCD amplitudes within the IBP approach
• Multi-Quark Colour Decompositions from Unitarity
• Analytic all-plus-helicity gluon amplitudes in QCD
• Dual Conformal Structure Beyond the Planar Limit
• Two-Loop Master Integrals for Leading-Color $pp\to t\bar{t}H$ Amplitudes with a Light-Quark Loop
• Differential equations on unitarity cut surfaces
• Implications of nonplanar dual conformal symmetry
• Differential equations for loop integrals in Baikov representation
• Lepton-pair scattering with an off-shell and an on-shell photon at two loops in massless QED
• Analytic Two-Loop Higgs Amplitudes in Effective Field Theory and the Maximal Transcendentality Principle
• Three-loop helicity amplitudes for quark-gluon scattering in QCD
• Prescriptive Unitarity for Non-Planar Six-Particle Amplitudes at Two Loops
• Two-loop master integrals for a planar topology contributing to $pp\to t\bar{t}j$
• The two-loop n-point all-plus helicity amplitude
• Full Colour for Loop Amplitudes in Yang-Mills Theory
• Two-loop $\mathcal{N}=2$ SQCD amplitudes with external matter from iterated cuts
• Color Dressed Unitarity and Recursion for Yang-Mills Two-Loop All-Plus Amplitudes
• Amplitudes from superconformal Ward identities
• Two-Loop Five-Parton Leading-Colour Finite Remainders in the Spinor-Helicity Formalism
• Internal Reduction method for computing Feynman Integrals
• One-loop QCD helicity amplitudes for $pp\to t\bar{t}j$ to $O({\epsilon }^2)$
• The Full Color Two-Loop Six-Gluon All-Plus Helicity Amplitude
• Bootstrapping a Two-Loop Four-Point Form Factor
• A first look at the function space for planar two-loop six-particle Feynman integrals
• Full-colour double-virtual amplitudes for associated production of a Higgs boson with a bottom-quark pair at the LHC
• Numerical evaluation of two-loop QCD helicity amplitudes for $gg\to t\bar{t}g$ at leading colour
• Hidden Analytic Relations for Two-Loop Higgs Amplitudes in QCD
• One-loop hexagon integral to higher orders in the dimensional regulator
• An $n$-point QCD two-loop amplitude
• Locally finite two-loop QCD amplitudes from IR universality for electroweak production
• Two-loop Feynman integrals for leading colour $t\bar{t}W$ production at hadron colliders
• The SAGEX Review on Scattering Amplitudes, Chapter 5: Analytic Bootstraps for Scattering Amplitudes and Beyond
• Conformally Regulated Direct Integration of the Two-Loop Heptagon Remainder
• Two-Loop Gravity amplitudes from four dimensional Unitarity
• Systematic approximation of multi-scale Feynman integrals
• Les Houches 2023 -- Physics at TeV Colliders: Report on the Standard Model Precision Wishlist
• The dimension-shift conjecture for one-loop amplitudes
• All Two-Loop Feynman Integrals for Five-Point One-Mass Scattering
• Double virtual QCD corrections to $t\bar{t}+$jet production at the LHC
• Virtual QCD corrections to gluon-initiated diphoton plus jet production at hadron colliders
• Two-loop all-plus helicity amplitudes for self-dual Higgs boson with gluons via unitarity cut constraints
• Monte Carlo evaluation of divergent one-loop integrals without contour deformation
• Symmetric reduction of high-multiplicity one-loop integrals and maximal cuts
• Three-loop helicity amplitudes for four-quark scattering in massless QCD
• One-loop Feynman integrals for $2\to 3$ scattering involving many scales including internal masses
• Analytic Four-Point Lightlike Form Factors and OPE of Null-Wrapped Polygons
• Top-Yukawa contributions to $pp\to b\bar{b}H$: two-loop leading-colour amplitudes
• One-Loop QCD Corrections to $\bar{u}d\to t\bar{t}W$ at $\mathcal{O}({\epsilon }^2)$