Scattering Equations and Factorization of Amplitudes II: Effective Field Theories

Abstract

We continue the program of extending the scattering equation framework by Cachazo, He and Yuan to a double-cover prescription. We discuss how to apply the double-cover formalism to effective field theories, with a special focus on the non-linear sigma model. A defining characteristic of the double-cover formulation is the emergence of new factorization relations. We present several factorization relations, along with a novel recursion relation. Using the recursion relation and a new prescription for the integrand, any non-linear sigma model amplitude can be expressed in terms of off-shell three-point amplitudes. The resulting expression is purely algebraic, and we do not have to solve any scattering equation. We also discuss soft limits, boundary terms in BCFW recursion, and application of the double-cover prescription to other effective field theories, like the special Galileon theory.

arXiv comment39+14 pages

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Cited by in corpus (7)

• Cosmological Scattering Equations at Tree-level and One-loop
• Scalar-Graviton Amplitudes
• Higher-order tree-level amplitudes in the nonlinear sigma model
• Exploring the Landscape for Soft Theorems of Nonlinear Sigma Models
• Transmuting off-shell CHY integrals in the double-cover framework
• Note on scalar-graviton and scalar-photon-graviton amplitudes
• Factorizations for tree amplitudes in the double-cover framework: from gravity to other theories