Perturbiner Methods for Effective Field Theories and the Double Copy

TL;DR

This paper develops perturbiner methods for various effective field theories, deriving new formulas for amplitudes, exploring double-copy relations, and extending the approach to theories like NLSM, special Galileon, and Born-Infeld.

Contribution

It introduces perturbiner expansions for multiple effective field theories and establishes double-copy relations without additional field redefinitions.

Findings

Derived perturbiner formulas for NLSM, bi-adjoint scalar, Galileon, and Born-Infeld theories.

Proposed a Cachazo-He-Yuan formula for multi-trace bi-adjoint scalar amplitudes.

Found double-copy relations hold up to gauge terms without extra redefinitions.

Abstract

Perturbiner expansion provides a generating function for all Berends-Giele currents in a given quantum field theory. We apply this method to various effective field theories with and without color degrees of freedom. In the colored case, we study the U(N) non-linear sigma model of Goldstone bosons (NLSM) in a recent parametrization due to Cheung and Shen, as well as its extension involving a coupling to the bi-adjoint scalar. We propose a Lagrangian and a Cachazo-He-Yuan formula for the latter valid in multi-trace sectors and systematically calculate its amplitudes. Furthermore, we make a similar proposal for a higher-derivative correction to NLSM that agrees with the subleading order of the abelian Z-theory. In the colorless cases, we formulate perturbiner expansions for the special Galileon and Born-Infeld theories. Finally, we study Kawai-Lewellen-Tye-like double-copy relations for Berends-Giele currents between the above colored and colorless theories. We find that they hold up to pure gauge terms, but without the need for further field redefinitions.