The Polynomial Form of the Scattering Equations is an H-Basis

Abstract

We prove that the polynomial form of the scattering equations is a Macaulay H-basis. We demonstrate that this H-basis facilitates integrand reduction and global residue computations in a way very similar to using a Gröbner basis, but circumvents the heavy computation of the latter. As an example, we apply the H-basis to prove the conjecture that the dual basis of the polynomial scattering equations must contain one constant term.

6 pages

References in corpus (10)

• Einstein-Yang-Mills Scattering Amplitudes From Scattering Equations
• Scattering equations and BCJ relations for gauge and gravitational amplitudes with massive scalar particles
• Scattering Equations and String Theory Amplitudes
• CHY representations for gauge theory and gravity amplitudes with up to three massive particles
• Elliptic scattering equations
• On the solutions of the scattering equations
• $\Lambda$ Scattering Equations
• Scattering equations, generating functions and all massless five point tree amplitudes
• Feynman Rules of Higher-order Poles in CHY Construction
• Cross-Order Integral Relations from Maximal Cuts

Cited by in corpus (25)

• Aspects of Scattering Amplitudes and Moduli Space Localization
• Two-Loop Scattering Amplitudes from the Riemann Sphere
• On the computation of intersection numbers for twisted cocycles
• Cross-ratio Identities and Higher-order Poles of CHY-integrand
• Relations for Einstein-Yang-Mills amplitudes from the CHY representation
• CHY Loop Integrands from Holomorphic Forms
• CHY-Graphs on a Torus
• Quadratic Feynman Loop Integrands From Massless Scattering Equations
• Polynomial reduction and evaluation of tree- and loop-level CHY amplitudes
• MultivariateResidues: a Mathematica package for computing multivariate residues
• One-loop Parke-Taylor factors for quadratic propagators from massless scattering equations
• Understanding the Cancelation of Double Poles in the Pfaffian of CHY-formulism
• Non-planar one-loop Parke-Taylor factors in the CHY approach for quadratic propagators
• Algebraic geometry and Bethe ansatz (I) the quotient ring for BAE
• Four dimensional ambitwistor strings and form factors of local and Wilson line operators
• Direct Evaluation of $n$-point single-trace MHV amplitudes in 4d Einstein-Yang-Mills theory using the CHY Formalism
• A Combinatoric Shortcut to Evaluate CHY-forms
• One-loop diagrams with quadratic propagators from the worldsheet
• Derivation of Feynman Rules for Higher Order Poles Using Cross-ratio Identities in CHY Construction
• Bootstrapping solutions of scattering equations
• BCJ Numerators from Differential Operator of Multidimensional Residue
• Ambitwistor strings and reggeon amplitudes in N=4 SYM
• Note on solutions of scattering equations
• Analytic expressions of amplitudes by the cross-ratio identity method
• Relations and representations of QCD amplitudes