A Proof of the Explicit Minimal-basis Expansion of Tree Amplitudes in Gauge Field Theory

Abstract

In last couple years, an important relation (BCJ relation) between color-ordered tree-level scattering amplitudes of gauge theory has inspired many studies. This relation implies that the minimal basis for the color-ordered tree-level amplitudes is $(n-3)!$ and other amplitudes can be expanded into a particular chosen basis. In this paper we will prove the conjectured explicit minimal basis expansion. For this purpose we will write down general BCJ relation of gauge theory by taking the field theory limit of BCJ relation in string theory. Then we prove these general BCJ relations using BCFW on-shell recursion relation. Using these general BCJ relations, we prove the conjectured explicit minimal-basis expansion of gauge theory tree amplitudes inductively.

22 pages, no figure

References in corpus (15)

• New Relations for Gauge-Theory Amplitudes
• The All-Loop Integrand For Scattering Amplitudes in Planar N=4 SYM
• Minimal Basis for Gauge Theory Amplitudes
• The Momentum Kernel of Gauge and Gravity Theories
• Gauge Amplitude Identities by On-shell Recursion Relation in S-matrix Program
• Consistency Conditions on the S-Matrix of Massless Particles
• Taming Tree Amplitudes In General Relativity
• Gravity and Yang-Mills Amplitude Relations
• Tree Level Recursion Relations In General Relativity
• New Identities among Gauge Theory Amplitudes
• On BCFW shifts of integrands and integrals
• On-shell Recursion in String Theory
• New Relations for Gauge-Theory Amplitudes with Matter
• U(1)-decoupling, KK and BCJ relations in $\mathcal{N}=4$ SYM
• Pomerons and BCFW recursion relations for strings on D-branes

Cited by in corpus (25)

• Scattering amplitudes in N=2 Maxwell-Einstein and Yang-Mills/Einstein supergravity
• The Five-Loop Four-Point Integrand of N=8 Supergravity as a Generalized Double Copy
• Scattering equations and BCJ relations for gauge and gravitational amplitudes with massive scalar particles
• Multiparticle SYM equations of motion and pure spinor BRST blocks
• Two-loop supersymmetric QCD and half-maximal supergravity amplitudes
• Double Copy from Homotopy Algebras
• Einstein-Yang-Mills from pure Yang-Mills amplitudes
• Manifesting Color-Kinematics Duality in the Scattering Equation Formalism
• BRST-Lagrangian Double Copy of Yang-Mills Theory
• Color-kinematics duality and Sudakov form factor at five loops for N=4 supersymmetric Yang-Mills theory
• Expansion of All Multitrace Tree Level EYM Amplitudes
• Tree-level amplitudes from the pure spinor superstring
• Kaluza-Klein from Colour-Kinematics Duality for Massive Fields
• Correlation functions of local composite operators from generalized unitarity
• A Lie bracket for the momentum kernel
• Gauge $\times$ Gauge $=$ Gravity on Homogeneous Spaces using Tensor Convolutions
• BCJ relations from a new symmetry of gauge-theory amplitudes
• Group-theoretic relations for amplitudes in gauge theories with orthogonal and symplectic groups
• Expansion of EYM Amplitudes in Gauge Invariant Vector Space
• Next-to-MHV Yang-Mills kinematic algebra
• Note on graph-based BCJ relation for Berends-Giele currents
• Note on off-shell relations in nonlinear sigma model
• Scattering amplitudes in gauge theories with and without supersymmetry
• Color-factor symmetry of the amplitudes of Yang-Mills and biadjoint scalar theory using perturbiner methods
• Color-factor symmetry and BCJ relations for QCD amplitudes