All Split Helicity Tree-Level Gluon Amplitudes

Abstract

Recently a new recursion relation for tree-level gluon amplitudes in gauge theory has been discovered. We solve this recursion to obtain explicit formulas for the closed set of amplitudes with arbitrarily many positive and negative helicity gluons in a split helicity configuration. The solution admits a simple diagrammatic expansion in terms of zigzag diagrams. We comment on generalizations of this result.

15 pages, harvmac, v2: typos corrected

References in corpus (34)

• 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
• MHV Vertices And Tree Amplitudes In Gauge Theory
• Higher Order Corrections to Jet Cross Sections in Hadron Colliders
• One-Loop Amplitudes for e^+ e^- to Four Partons
• Calculating Scattering Amplitudes Efficiently
• Massive Loop Amplitudes from Unitarity
• Progress in One-Loop QCD Computations
• On the Tree-Level S-Matrix of Yang-Mills Theory
• On-Shell Recurrence Relations for One-Loop QCD Amplitudes
• All Non-Maximally-Helicity-Violating One-Loop Seven-Gluon Amplitudes in N=4 Super-Yang-Mills Theory
• A Googly Amplitude from the B-model in Twistor Space
• Singular terms of helicity amplitudes at one-loop in QCD and the soft limit of the cross sections of multi-parton processes
• Next-to-Maximal Helicity Violating Amplitudes in Gauge Theory
• Twistor-Space Recursive Formulation of Gauge-Theory Amplitudes
• Computing One-Loop Amplitudes From The Holomorphic Anomaly Of Unitarity Cuts
• All Next-to-Maximally-Helicity-Violating One-Loop Gluon Amplitudes in N=4 Super-Yang-Mills Theory
• The Googly Amplitudes in Gauge Theory
• Tree Level Recursion Relations In General Relativity
• Recursion Relations for Tree Amplitudes in Super Gauge Theories
• Dissolving N=4 loop amplitudes into QCD tree amplitudes
• Twistor-Inspired Construction of Electroweak Vector Boson Currents
• Loops in Twistor Space
• Holomorphic Anomaly Of Unitarity Cuts And One-Loop Gauge Theory Amplitudes
• Compact Formulas for Tree Amplitudes of Six Partons
• All Googly Amplitudes from the B-model in Twistor Space
• MHV Vertices and Scattering Amplitudes in Gauge Theory
• Unitarity-based Techniques for One-Loop Calculations in QCD
• Twistor diagram recursion for all gauge-theoretic tree amplitudes
• Equivalence of twistor prescriptions for super Yang-Mills

Cited by in corpus (49)

• Iteration of Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory at Three Loops and Beyond
• Dual superconformal symmetry of scattering amplitudes in N=4 super-Yang-Mills theory
• On-Shell Methods in Perturbative QCD
• A note on dual superconformal symmetry of the N=4 super Yang-Mills S-matrix
• A direct proof of the CSW rules
• Recursion Relations for Gauge Theory Amplitudes with Massive Particles
• Bootstrapping Multi-Parton Loop Amplitudes in QCD
• Bootstrapping One-Loop QCD Amplitudes with General Helicities
• All tree-level amplitudes in N=4 SYM
• The Last of the Finite Loop Amplitudes in QCD
• Recursion Relations for Gauge Theory Amplitudes with Massive Vector Bosons and Fermions
• Harmony of Super Form Factors
• Recursive Calculation of One-Loop QCD Integral Coefficients
• Two-Loop Amplitudes of Gluons and Octa-Cuts in N=4 Super Yang-Mills
• Tree-level gluon amplitudes on the celestial sphere
• All tree-level amplitudes in massless QCD
• MHV-Vertices for Gravity Amplitudes
• All One-loop Maximally Helicity Violating Gluonic Amplitudes in QCD
• All-Multiplicity Amplitudes with Massive Scalars
• Amplitudes in the beta-deformed Conformal Yang-Mills
• Recursive Construction of Higgs-Plus-Multiparton Loop Amplitudes: The Last of the Phi-nite Loop Amplitudes
• On-shell recursion relations for all Born QCD amplitudes
• Multi-parton Cross Sections at Hadron Colliders
• An Introduction to On-shell Recursion Relations
• Tree-Level Amplitudes in N=8 Supergravity
• The rational parts of one-loop QCD amplitudes I: The general formalism
• Structure of the MHV-rules Lagrangian
• Complete Six-Gluon Disk Amplitude in Superstring Theory
• Susy Theories and QCD: Numerical Approaches
• Supersymmetric Ward Identities and NMHV Amplitudes involving Gluinos
• S-Matrix Equivalence Theorem Evasion and Dimensional Regularisation with the Canonical MHV Lagrangian
• Soft theorems in maximally supersymmetric theories
• One-Loop NMHV Amplitudes involving Gluinos and Scalars in N=4 Gauge Theory
• N=4 SYM NMHV Loop Amplitude in Superspace
• Conformal anomaly of super Wilson loop
• Massive Quark-Gluon Scattering Amplitudes at Tree Level
• Tree-level amplitudes and dual superconformal symmetry
• General Split Helicity Gluon Tree Amplitudes in Open Twistor String Theory
• Recursion relations, Helicity Amplitudes and Dimensional Regularization
• On-Shell Unitarity Bootstrap for QCD Amplitudes
• The MHV Lagrangian for a spontaneously broken gauge theory
• Recursion relations for the general tree-level amplitudes in QCD with massive dirac fields
• Multigluon tree amplitudes with a pair of massive fermions
• Spinor formalism for massive fields with half-integral spin
• Generating MHV super-vertices in light-cone gauge
• Exploiting Twistor Techniques for One-loop QCD Amplitudes
• The MHV lagrangian vertices and the Parke-Taylor formula
• On perturbative field theory and twistor string theory
• Tree-level Split Helicity Amplitudes in Ambitwistor Space