Local integrands for two-loop all-plus Yang-Mills amplitudes

Abstract

We express the planar five- and six-gluon two-loop Yang-Mills amplitudes with all positive helicities in compact analytic form using D-dimensional local integrands that are free of spurious singularities. The integrand is fixed from on-shell tree amplitudes in six dimensions using D-dimensional generalised unitarity cuts. The resulting expressions are shown to have manifest infrared behaviour at the integrand level. We also find simple representations of the rational terms obtained after integration in 4-2epsilon dimensions.

arXiv comment24 pages + refs + ancillary file; v3 published version

References in corpus (43)

• Direct Proof Of Tree-Level Recursion Relation In Yang-Mills Theory
• One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits
• Perturbative Gauge Theory As A String Theory In Twistor Space
• Fusing Gauge Theory Tree Amplitudes Into Loop Amplitudes
• New Recursion Relations for Tree Amplitudes of Gluons
• Generalized Unitarity and One-Loop Amplitudes in N=4 Super-Yang-Mills
• Reducing full one-loop amplitudes to scalar integrals at the integrand level
• Dimensionally Regulated Pentagon Integrals
• The All-Loop Integrand For Scattering Amplitudes in Planar N=4 SYM
• Local Integrals for Planar Scattering Amplitudes
• One-Loop Corrections to Five-Gluon Amplitudes
• Massive Loop Amplitudes from Unitarity
• Dimensionally Regulated One-Loop Integrals
• Full one-loop amplitudes from tree amplitudes
• FIESTA 4: optimized Feynman integral calculations with GPU support
• One-Loop Self-Dual and N=4 Super Yang-Mills
• One-loop Singular Behaviour of QCD and SUSY QCD Amplitudes with Massive Partons
• One-Loop N Gluon Amplitudes with Maximal Helicity Violation via Collinear Limits
• Supersymmetric Regularization, Two-Loop QCD Amplitudes and Coupling Shifts
• Uniqueness of two-loop master contours
• Amplitudes and Spinor-Helicity in Six Dimensions
• Analytic form of the two-loop planar five-gluon all-plus-helicity amplitude in QCD
• A Two-Loop Five-Gluon Helicity Amplitude in QCD
• FIESTA 3: cluster-parallelizable multiloop numerical calculations in physical regions
• Hepta-Cuts of Two-Loop Scattering Amplitudes
• On the Integrand-Reduction Method for Two-Loop Scattering Amplitudes
• Scattering Amplitudes from Multivariate Polynomial Division
• Integrand-Level Reduction of Loop Amplitudes by Computational Algebraic Geometry Methods
• On the Singularity Structure of Maximally Supersymmetric Scattering Amplitudes
• Evidence for a Nonplanar Amplituhedron
• One Loop Multiphoton Helicity Amplitudes
• A Complete Two-Loop, Five-Gluon Helicity Amplitude in Yang-Mills Theory
• Local Integrand Representations of All Two-Loop Amplitudes in Planar SYM
• The Pentabox Master Integrals with the Simplified Differential Equations approach
• Multiloop Integrand Reduction for Dimensionally Regulated Amplitudes
• Two-loop six gluon all plus helicity amplitude
• An Integrand Reconstruction Method for Three-Loop Amplitudes
• The classification of two-loop integrand basis in pure four-dimension
• Multivariate Residues and Maximal Unitarity
• Counting to one: reducibility of one- and two-loop amplitudes at the integrand level
• Unitarity Cuts of Integrals with Doubled Propagators
• Global Residues and Two-Loop Hepta-Cuts
• Massive Nonplanar Two-Loop Maximal Unitarity

Cited by in corpus (32)

• Scattering amplitudes over finite fields and multivariate functional reconstruction
• To $d$, or not to $d$: Recent developments and comparisons of regularization schemes
• Collider Physics at the Precision Frontier
• Analytic Form of the Planar Two-Loop Five-Gluon Scattering Amplitudes in QCD
• A first look at two-loop five-gluon scattering in QCD
• Two-Loop Four-Gluon Amplitudes with the Numerical Unitarity Method
• NNLO QCD corrections to three-photon production at the LHC
• Analytic helicity amplitudes for two-loop five-gluon scattering: the single-minus case
• Bootstrapping pentagon functions
• Maximal Cuts in Arbitrary Dimension
• Determine Arbitrary Feynman Integrals by Vacuum Integrals
• Direct Solution of Integration-by-Parts Systems
• On loop celestial amplitudes for gauge theory and gravity
• Subleading Poles in the Numerical Unitarity Method at Two Loops
• Multi-Quark Colour Decompositions from Unitarity
• Analytic all-plus-helicity gluon amplitudes in QCD
• Differential equations for loop integrals in Baikov representation
• Prescriptive Unitarity for Non-Planar Six-Particle Amplitudes at Two Loops
• Locally finite two-loop amplitudes for off-shell multi-photon production in electron-positron annihilation
• Two-loop master integrals for a planar topology contributing to $pp\to t\bar{t}j$
• Full Colour for Loop Amplitudes in Yang-Mills Theory
• Two-loop $\mathcal{N}=2$ SQCD amplitudes with external matter from iterated cuts
• The Full Color Two-Loop Six-Gluon All-Plus Helicity Amplitude
• A first look at the function space for planar two-loop six-particle Feynman integrals
• Non-factorisable contribution to $t$-channel single-top production
• Two-loop Feynman integrals for leading colour $t\bar{t}W$ production at hadron colliders
• Two-Loop Gravity amplitudes from four dimensional Unitarity
• Virtual QCD corrections to gluon-initiated diphoton plus jet production at hadron colliders
• Infrared and transcendental structure of two-loop supersymmetric QCD amplitudes
• Multi-loop calculations: numerical methods and applications
• Integrands of Less-Supersymmetric Yang-Mills at One Loop
• The integrand form of infrared singularities of two-loop QCD scattering amplitudes