Berends-Giele currents in Bern-Carrasco-Johansson gauge for $F^3$- and $F^4$-deformed Yang-Mills amplitudes

TL;DR

This paper develops new recursive methods to compute tree-level gauge theory amplitudes with higher-dimensional operators, revealing dualities and enabling local double-copy constructions for gravity amplitudes.

Contribution

It introduces Bern-Carrasco-Johansson gauge for organizing deformed Yang-Mills amplitudes and constructs explicit double-copy representations for gravity involving higher-derivative operators.

Findings

Compact tensor structures for deformed amplitudes

Manifest color-kinematics duality in new representations

Explicit local double-copy formulas for gravity amplitudes

Abstract

We construct new representations of tree-level amplitudes in D-dimensional gauge theories with deformations via higher-mass-dimension operators $\alpha' F^3$ and $\alpha'^{2} F^4$. Based on Berends-Giele recursions, the tensor structure of these amplitudes is compactly organized via off-shell currents. On the one hand, we present manifestly cyclic representations, where the complexity of the currents is systematically reduced. On the other hand, the duality between color and kinematics due to Bern, Carrasco and Johansson is manifested by means of non-linear gauge transformations of the currents. We exploit the resulting notion of Bern-Carrasco-Johansson gauge to provide explicit and manifestly local double-copy representations for gravitational amplitudes involving $\alpha' R^2$ and $\alpha'^2 R^3$ operators.