The seeds of EFT double copy

TL;DR

This paper advances the understanding of the double copy construction in effective field theories by developing systematic methods to generate scalar numerators and KLT kernels, applicable to higher multiplicities and connecting color-kinematics and KLT formalisms.

Contribution

It introduces a systematic construction of scalar numerators satisfying Jacobi identities from seed functions and relates generalized KLT and color-kinematics formalisms for EFTs.

Findings

Constructed scalar numerators up to 6-point with trace-like properties.

Produced KLT kernels at arbitrary order in EFT expansion.

Confirmed that EFT kernels generate double-copy amplitudes consistent with traditional KLT at 4-point, with initial checks at 5-point.

Abstract

We explore the double copy of effective field theories (EFTs), in the recently proposed generalized color-kinematics and Kawai-Lewellen-Tye (KLT) approaches. In the former, we systematically construct scalar numerators satisfying the Jacobi identities from simpler numerator "seeds" with trace-like permutation properties. This construction has the advantage of being easily applicable to any multiplicity, which we exemplify up to 6-point. It employs the linear map between color factors formed by single traces of generators and by products of the structure constants, which 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.