The seeds of EFT double copy

Abstract

We explore the double copy of effective field theories (EFTs), both in the (generalized) color-kinematics and Kawai-Lewellen-Tye (KLT) approaches. In the former, we define the linear map between color factors formed by single traces of generators and by products of the structure constants. It enables us to systematically construct scalar numerators satisfying the Jacobi identities from simpler numerator seeds with trace-like permutation properties, with the advantage that this construction easily applies to any multiplicity. This map also relates the generalized KLT and color-kinematics formalisms, allowing to produce KLT kernels at arbitrary order in the EFT expansion. At 4-point, we show that all EFT kernels are generated and that they only yield double-copy amplitudes which can also be obtained from the traditional KLT kernel. We perform initial checks suggesting that the same conclusions also hold at 5-point. We focus on single-trace massless scalar EFTs which however also control the higher-derivative corrections to gauge and gravity theories.