Analytic Form of the Planar Two-Loop Five-Gluon Scattering Amplitudes in QCD

Abstract

We present the analytic form of the two-loop five-gluon scattering amplitudes in QCD for a complete set of independent helicity configurations of external gluons. These include the first analytic results for five-point two-loop amplitudes relevant for the computation of next-to-next-to-leading-order QCD corrections at hadron colliders. The results were obtained by reconstructing analytic expressions from numerical evaluations. The complexity of the computation is reduced by exploiting physical and analytical properties of the amplitudes, employing a minimal basis of so-called pentagon functions that have recently been classified.

arXiv commentAncillary files with analytic expressions can be downloaded from https://www.qft.physik.uni-freiburg.de/ScatteringAmplitudes

References in corpus (50)

• One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits
• Fusing Gauge Theory Tree Amplitudes Into Loop Amplitudes
• 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
• Classical Polylogarithms for Amplitudes and Wilson Loops
• Numerical evaluation of multiple polylogarithms
• An Automated Implementation of On-Shell Methods for One-Loop Amplitudes
• Infrared singularities of scattering amplitudes in perturbative QCD
• Multi-loop Amplitudes and Resummation
• One-Loop Corrections to Five-Gluon Amplitudes
• Factorization constraints for soft anomalous dimensions in QCD scattering amplitudes
• Full one-loop amplitudes from tree amplitudes
• A novel approach to integration by parts reduction
• From polygons and symbols to polylogarithmic functions
• Hopf algebras, coproducts and symbols: an application to Higgs boson amplitudes
• A Numerical Unitarity Formalism for Evaluating One-Loop Amplitudes
• Scattering amplitudes over finite fields and multivariate functional reconstruction
• Two-Loop Helicity Amplitudes for Gluon-Gluon Scattering in QCD and Supersymmetric Yang-Mills Theory
• Two-loop Integrand Decomposition into Master Integrals and Surface Terms
• Two-loop QCD corrections to gluon-gluon scattering
• 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
• The two-loop five-point amplitude in $\mathcal{N}=4$ super-Yang-Mills theory
• Planar Two-Loop Five-Gluon Amplitudes from Numerical Unitarity
• Scattering Amplitudes from Multivariate Polynomial Division
• A first look at two-loop five-gluon scattering in QCD
• Integrand-Level Reduction of Loop Amplitudes by Computational Algebraic Geometry Methods
• Two-Loop Four-Gluon Amplitudes with the Numerical Unitarity Method
• One-loop radiative corrections to the helicity amplitudes of QCD processes involving four quarks and one gluon
• Planar Two-Loop Five-Parton Amplitudes from Numerical Unitarity
• Two-Loop Helicity Amplitudes for Quark-Quark Scattering in QCD and Gluino-Gluino Scattering in Supersymmetric Yang-Mills Theory
• Transforming differential equations of multi-loop Feynman integrals into canonical form
• Analytic result for a two-loop five-particle amplitude
• A Complete Two-Loop, Five-Gluon Helicity Amplitude in Yang-Mills Theory
• Analytic helicity amplitudes for two-loop five-gluon scattering: the single-minus case
• The two-loop five-point amplitude in $\mathcal{N}=8$ supergravity
• Two-loop QCD helicity amplitudes for massless quark-quark scattering
• Differential equations from unitarity cuts: nonplanar hexa-box integrals
• Two-loop five-point all plus helicity Yang-Mills amplitude
• The Pentabox Master Integrals with the Simplified Differential Equations approach
• Two-loop six gluon all plus helicity amplitude
• Local integrands for two-loop all-plus Yang-Mills amplitudes
• Subleading Poles in the Numerical Unitarity Method at Two Loops
• Multi-Quark Colour Decompositions from Unitarity
• Analytic all-plus-helicity gluon amplitudes in QCD
• NLO QCD Predictions for $Wb\bar{b}$ Production in Association with up to Three Light Jets at the LHC
• The four-dimensional helicity scheme and dimensional reconstruction
• Modular SIMD arithmetic in Mathemagix

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