CHY formula and MHV amplitudes

Abstract

In this paper, we study the relation between the Cachazo-He-Yuan (CHY) formula and the maximal-helicity-violating (MHV) amplitudes of Yang-Mills and gravity in four dimensions. We prove that only one special rational solution of the scattering equations found by Weinzierl support the MHV amplitudes. Namely, localized at this solution, the integrated CHY formula reproduces the Parke-Taylor formula for Yang-Mills amplitudes as well as the Hodges formula for gravitational amplitudes. This is achieved by developing techniques, in a manifestly Möbius covariant formalism, to explicitly compute relevant reduced Pfaffians/determinants. We observe and prove two interesting properties (or identities), which facilitate the computations. We also check that all the other $(n-3)!-1$ solutions to the scattering equations do not support the MHV amplitudes, and prove analytically that this is indeed true for the other special rational solution proposed by Weinzierl, that actually supports the anti-MHV amplitudes.

28 pages, 4 figures, published version

References in corpus (13)

• Einstein-Yang-Mills Scattering Amplitudes From Scattering Equations
• One-loop amplitudes on the Riemann sphere
• Scattering equations and BCJ relations for gauge and gravitational amplitudes with massive scalar particles
• One-Loop Corrections from Higher Dimensional Tree Amplitudes
• Scattering Equations and String Theory Amplitudes
• CHY representations for gauge theory and gravity amplitudes with up to three massive particles
• A simple formula for gravitational MHV amplitudes
• Elimination and recursions in the scattering equations
• On the solutions of the scattering equations
• General Solution of the Scattering Equations
• Color structures and permutations
• Minimal Basis in Four Dimensions and Scalar Blocks
• CHY-construction of Planar Loop Integrands of Cubic Scalar Theory

Cited by in corpus (10)

• Twin Supergravities from Yang-Mills Squared
• Cross-ratio Identities and Higher-order Poles of CHY-integrand
• Ambitwistor formulations of $R^2$ gravity and $(DF{)}^2$ gauge theories
• The Polynomial Form of the Scattering Equations is an H-Basis
• Understanding the Cancelation of Double Poles in the Pfaffian of CHY-formulism
• Feynman Rules of Higher-order Poles in CHY Construction
• A Combinatoric Shortcut to Evaluate CHY-forms
• Direct Evaluation of $n$-point single-trace MHV amplitudes in 4d Einstein-Yang-Mills theory using the CHY Formalism
• CHY Theory for Several Fields
• A note on multi-trace EYM amplitudes in four dimensions