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

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