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Perturbiner Methods for Effective Field Theories and the Double Copy

Sebastian Mizera, Barbara Skrzypek

TL;DR

This work extends perturbiner techniques to a broad class of effective field theories, both colored (NLSM and its BA extension) and colorless (special Galileon and Born–Infeld), deriving explicit off-shell Berends–Giele currents and multi-point amplitudes. It develops color-stripped and color-dressed recursions, connects perturbiner currents to CHY representations, and demonstrates dimensional-reduction paths to subleading α′ corrections (Z-theory). A central result is that KLT-like double-copy relations extend to off-shell currents in several cases (with pure-gauge terms as the only caveat), enabling a unified view of the perturbiner calculus across theories. The paper provides concrete Recursion relations, explicit 4–6-point amplitudes, and systematic checks against CHY formulas and known double-copy structures, offering practical tools and guiding principles for off-shell double-copy in EFTs.

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.

Perturbiner Methods for Effective Field Theories and the Double Copy

TL;DR

This work extends perturbiner techniques to a broad class of effective field theories, both colored (NLSM and its BA extension) and colorless (special Galileon and Born–Infeld), deriving explicit off-shell Berends–Giele currents and multi-point amplitudes. It develops color-stripped and color-dressed recursions, connects perturbiner currents to CHY representations, and demonstrates dimensional-reduction paths to subleading α′ corrections (Z-theory). A central result is that KLT-like double-copy relations extend to off-shell currents in several cases (with pure-gauge terms as the only caveat), enabling a unified view of the perturbiner calculus across theories. The paper provides concrete Recursion relations, explicit 4–6-point amplitudes, and systematic checks against CHY formulas and known double-copy structures, offering practical tools and guiding principles for off-shell double-copy in EFTs.

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.

Paper Structure

This paper contains 30 sections, 148 equations.

Table of Contents

  1. Introduction
  2. Perturbiner Methods
  3. Color-Stripped Perturbiners
  4. Yang--Mills Theory
  5. Bi-Adjoint Scalar Theory
  6. Color-Dressed Perturbiners
  7. Yang--Mills Theory
  8. Bi-Adjoint Scalar Theory
  9. Effective Field Theories With Colors
  10. Non-Linear Sigma Model
  11. Four-Point Examples
  12. Five-Point Examples
  13. Six-Point Example
  14. Extended Non-Linear Sigma Model
  15. Low-Point Examples
  16. ...and 15 more sections