Generalized Unitarity and Six-Dimensional Helicity

Abstract

We combine the unitarity method with the six-dimensional helicity formalism of Cheung and O'Connell to construct loop-level scattering amplitudes. As a first example, we construct dimensionally regularized QCD one-loop four-point amplitudes. As a nontrivial multiloop example, we confirm that the recently constructed four-loop four-point amplitude of N=4 super-Yang-Mills theory, including nonplanar contributions, is valid for dimensions less than or equal to six. We comment on the connection of our approach to the recently discussed Higgs infrared regulator and on dual conformal properties in six dimensions.

38 pages, 7 figures, typos corrected

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• Gluon scattering amplitudes at strong coupling
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• Generating Tree Amplitudes in N=4 SYM and N=8 SG
• Bootstrapping One-Loop QCD Amplitudes with General Helicities
• The Complete Four-Loop Four-Point Amplitude in N=4 Super-Yang-Mills Theory
• Direct Extraction Of One Loop Rational Terms
• W+3 jet production at the Tevatron
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• Closed-Form Decomposition of One-Loop Massive Amplitudes
• Recursion Relations, Generating Functions, and Unitarity Sums in N=4 SYM Theory
• Leading Singularities of the Two-Loop Six-Particle MHV Amplitude
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Cited by in corpus (69)

• Bootstrapping the three-loop hexagon
• Scattering amplitudes over finite fields and multivariate functional reconstruction
• Simplifying Multiloop Integrands and Ultraviolet Divergences of Gauge Theory and Gravity Amplitudes
• A Two-Loop Five-Gluon Helicity Amplitude in QCD
• Ultraviolet Properties of N = 8 Supergravity at Five Loops
• To $d$, or not to $d$: Recent developments and comparisons of regularization schemes
• Basics of Generalized Unitarity
• One-loop four-point amplitudes in pure and matter-coupled N <= 4 supergravity
• Maximal Unitarity at Two Loops
• The Five-Loop Four-Point Integrand of N=8 Supergravity as a Generalized Double Copy
• Scattering Amplitudes
• Scattering Amplitudes For All Masses and Spins
• Loop amplitudes in gauge theories: modern analytic approaches
• Evidence for a Nonplanar Amplituhedron
• Spinor Helicity and Dual Conformal Symmetry in Ten Dimensions
• New differential equations for on-shell loop integrals
• Dual Conformal Properties of Six-Dimensional Maximal Super Yang-Mills Amplitudes
• Massive amplitudes on the Coulomb branch of N=4 SYM
• D = 5 maximally supersymmetric Yang-Mills theory diverges at six loops
• Duals of Feynman Integrals, I: Differential Equations
• Simple superamplitudes in higher dimensions
• Duals of Feynman Integrals, 2: Generalized Unitarity
• Two-Loop Maximal Unitarity with External Masses
• Gauge and Gravity Amplitude Relations
• Conformal Field Theories in Six-Dimensional Twistor Space
• Scattering Amplitudes in Quantum Field Theory
• Dual conformal symmetry at loop level; massive regularization
• Little String Amplitudes (and the Unreasonable Effectiveness of 6D SYM)
• The S Matrix of 6D Super Yang-Mills and Maximal Supergravity from Rational Maps
• Multivariate Residues and Maximal Unitarity
• Amplitudes for Multiple M5 Branes
• The polarized scattering equations for 6d superamplitudes
• Exact coefficients for higher dimensional operators with sixteen supersymmetries
• Maximal Unitarity for the Four-Mass Double Box
• Review of AdS/CFT Integrability, Chapter V.2: Dual Superconformal Symmetry
• On-shell supersymmetry for massive multiplets
• Non-Chiral S-Matrix of N=4 Super Yang-Mills
• From Six to Four and More: Massless and Massive Maximal Super Yang-Mills Amplitudes in 6d and 4d and their Hidden Symmetries
• Amplitudes for massive vector and scalar bosons in spontaneously-broken gauge theory from the CHY representation
• Interpolating the Coulomb Phase of Little String Theory
• Chiral Squaring
• A unitarity compatible approach to one-loop amplitudes with massive fermions
• Cross-Order Integral Relations from Maximal Cuts
• One-Loop QCD and Higgs to Partons Processes Using Six-Dimensional Helicity and Generalized Unitarity
• Beyond the standard model with six-dimensional spinors
• Review of AdS/CFT Integrability, Chapter V.1: Scattering Amplitudes - a Brief Introduction
• Supervertices and Non-renormalization Conditions in Maximal Supergravity Theories
• Spinor-helicity formalism for massive and massless amplitudes in five dimensions
• Global Poles of the Two-Loop Six-Point N=4 SYM integrand
• Three particle superstring amplitudes with massive legs
• The Coulomb-branch S-matrix from massless amplitudes
• Consistency conditions from generalized-unitarity
• Challenges of D=6 N=(1,1) SYM Theory
• Complete Form Factors in Yang-Mills from Unitarity and Spinor Helicity in Six Dimensions
• Anomalies without an action
• One-loop N = 4 super Yang-Mills scattering amplitudes in d dimensions, relation to open strings and polygonal Wilson loops
• Yangian Symmetry in N=4 super Yang-Mills
• The dimension-shift conjecture for one-loop amplitudes
• Scattering Amplitudes and BCFW in $\mathcal{N}=2^{\ast }$ Theory
• Massive Scattering Amplitudes in Six Dimensions
• Logarithmic Singularities and Maximally Supersymmetric Amplitudes
• Generalized unitarity method for unstable particles
• Integral Reduction by Unitarity Method for Two-loop Amplitudes: A Case Study
• Infrared and transcendental structure of two-loop supersymmetric QCD amplitudes
• Perturbative Methods for Superconformal Quantum Field Theories in String - Gauge Theory Dualities
• Higher-dimensional invariants in $6D$ super Yang-Mills theory
• Divergences in maximal supersymmetric Yang-Mills theories in diverse dimensions
• The canonical form has got baubles
• Leading singularities in higher-derivative Yang-Mills theory and quadratic gravity