Analytic helicity amplitudes for two-loop five-gluon scattering: the single-minus case

Abstract

We present a compact analytic expression for the leading colour two-loop five-gluon amplitude in Yang-Mills theory with a single negative helicity and four positive helicities. The analytic result is reconstructed from numerical evaluations over finite fields. The numerical method combines integrand reduction, integration-by-parts identities and Laurent expansion into a basis of pentagon functions to compute the coefficients directly from six-dimensional generalised unitarity cuts.

arXiv comment18 pages, 2 figures

References in corpus (54)

• One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits
• Fusing Gauge Theory Tree Amplitudes Into Loop Amplitudes
• Multiloop integrals in dimensional regularization made simple
• Differential Equations for Two-Loop Four-Point Functions
• Generalized Unitarity and One-Loop Amplitudes in N=4 Super-Yang-Mills
• The Singular Behaviour of QCD Amplitudes at Two-loop Order
• Reducing full one-loop amplitudes to scalar integrals at the integrand level
• CutTools: a program implementing the OPP reduction method to compute one-loop amplitudes
• One-Loop Amplitudes for e^+ e^- to Four Partons
• On the Structure of Infrared Singularities of Gauge-Theory Amplitudes
• Infrared singularities of scattering amplitudes in perturbative QCD
• The All-Loop Integrand For Scattering Amplitudes in Planar N=4 SYM
• FIRE5: a C++ implementation of Feynman Integral REduction
• Kira - A Feynman Integral Reduction Program
• Local Integrals for Planar Scattering Amplitudes
• One-Loop Corrections to Five-Gluon Amplitudes
• Factorization constraints for soft anomalous dimensions in QCD scattering amplitudes
• Automated One-Loop Calculations with GoSam
• Full one-loop amplitudes from tree amplitudes
• A novel approach to integration by parts reduction
• Scattering amplitudes over finite fields and multivariate functional reconstruction
• A Numerical Unitarity Formalism for Evaluating One-Loop Amplitudes
• Bootstrapping a Five-Loop Amplitude Using Steinmann Relations
• One-Loop Corrections to Two-Quark Three-Gluon Amplitudes
• Scattering AMplitudes from Unitarity-based Reduction Algorithm at the Integrand-level
• Uniqueness of two-loop master contours
• Amplitudes and Spinor-Helicity in Six Dimensions
• Heptagons from the Steinmann Cluster Bootstrap
• Analytic form of the two-loop planar five-gluon all-plus-helicity amplitude in QCD
• A Two-Loop Five-Gluon Helicity Amplitude in QCD
• Pentagon functions for massless planar scattering amplitudes
• Hepta-Cuts of Two-Loop Scattering Amplitudes
• A quasi-finite basis for multi-loop Feynman integrals
• Scattering Amplitudes from Multivariate Polynomial Division
• On the Integrand-Reduction Method for Two-Loop Scattering Amplitudes
• A first look at two-loop five-gluon scattering in QCD
• Bootstrapping the QCD soft anomalous dimension
• Integrand-Level Reduction of Loop Amplitudes by Computational Algebraic Geometry Methods
• Planar Two-Loop Five-Parton Amplitudes from Numerical Unitarity
• A Complete Two-Loop, Five-Gluon Helicity Amplitude in Yang-Mills Theory
• Azurite: An algebraic geometry based package for finding bases of loop integrals
• Bootstrapping pentagon functions
• Prescriptive Unitarity
• Complete integration-by-parts reductions of the non-planar hexagon-box via module intersections
• Optimizing the Reduction of One-Loop Amplitudes
• Differential equations from unitarity cuts: nonplanar hexa-box integrals
• Adaptive Integrand Decomposition in parallel and orthogonal space
• The Double Pentaladder Integral to All Orders
• Simplified differential equations approach for Master Integrals
• Multiloop Integrand Reduction for Dimensionally Regulated Amplitudes
• Two-loop six gluon all plus helicity amplitude
• Local integrands for two-loop all-plus Yang-Mills amplitudes
• An Integrand Reconstruction Method for Three-Loop Amplitudes
• Differential equations on unitarity cut surfaces

Cited by in corpus (59)

• FiniteFlow: multivariate functional reconstruction using finite fields and dataflow graphs
• Reconstructing Rational Functions with $\text{FireFly}$
• 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
• All master integrals for three-jet production at NNLO
• Analytic Form of the Planar Two-Loop Five-Gluon Scattering Amplitudes in QCD
• Pentagon Functions for Scattering of Five Massless Particles
• Decomposition of Feynman Integrals on the Maximal Cut by Intersection Numbers
• Analytic form of the full two-loop five-gluon all-plus helicity amplitude
• NNLO QCD corrections to three-photon production at the LHC
• Pentagon Functions for One-Mass Planar Scattering Amplitudes
• 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
• The two-loop five-point amplitude in $\mathcal{N}=8$ supergravity
• The Transverse Energy-Energy Correlator in the Back-to-Back Limit
• Leading-Color Two-Loop QCD Corrections for Three-Jet Production at Hadron Colliders
• Two-loop helicity amplitudes for diphoton plus jet production in full color
• Physical projectors for multi-leg helicity amplitudes
• 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
• Determine Arbitrary Feynman Integrals by Vacuum Integrals
• Integration-by-parts reductions of Feynman integrals using Singular and GPI-Space
• The two-loop five-particle amplitude in $\mathcal{N}=8$ supergravity
• Complete reduction of integrals in two-loop five-light-parton scattering amplitudes
• Di-photon amplitudes in three-loop Quantum Chromodynamics
• Two-loop leading colour QCD corrections to $q\bar{q}\to \gamma \gamma g$ and $qg\to \gamma \gamma q$
• Leading-Color Two-Loop QCD Corrections for Three-Photon Production at Hadron Colliders
• Two-loop leading-color helicity amplitudes for three-photon production at the LHC
• On loop celestial amplitudes for gauge theory and gravity
• Two-loop leading-colour QCD helicity amplitudes for two-photon plus jet production at the LHC
• The Two-Loop Four-Graviton Scattering Amplitudes
• Integrands of loop amplitudes within loop-tree duality
• Prescriptive Unitarity for Non-Planar Six-Particle Amplitudes at Two Loops
• 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 $pp\to t\bar{t}j$
• Locally finite two-loop amplitudes for off-shell multi-photon production in electron-positron annihilation
• Ansätze for Scattering Amplitudes from $p$-adic Numbers and Algebraic Geometry
• Color Dressed Unitarity and Recursion for Yang-Mills Two-Loop All-Plus Amplitudes
• Extracting analytical one-loop amplitudes from numerical evaluations
• Two-Loop Five-Parton Leading-Colour Finite Remainders in the Spinor-Helicity Formalism
• 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
• Two- and Three-Loop Data for Groomed Jet Mass
• Bootstrapping a Two-Loop Four-Point Form Factor
• Full-colour double-virtual amplitudes for associated production of a Higgs boson with a bottom-quark pair at the LHC
• Hidden Analytic Relations for Two-Loop Higgs Amplitudes in QCD
• An $n$-point QCD two-loop amplitude
• One-loop hexagon integral to higher orders in the dimensional regulator
• Computational challenges for multi-loop collider phenomenology
• Complete Form Factors in Yang-Mills from Unitarity and Spinor Helicity in Six Dimensions
• Conformally Regulated Direct Integration of the Two-Loop Heptagon Remainder
• The dimension-shift conjecture for one-loop amplitudes
• 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
• Symmetric reduction of high-multiplicity one-loop integrals and maximal cuts
• Two-loop tensor integral coefficients in OpenLoops
• Recent progress for five-particle two-loop scattering amplitudes with an off-shell leg