Classical effective action of dilaton-gravity from the double copy

We compute the classical effective action of color charges moving along worldlines 
by integrating out the Yang-Mills gauge field to next-to-leading order in the coupling. 
An adapted version of the Bern-Carrasco-Johansson (BCJ) double-copy construction 
known from quantum scattering amplitudes is then applied to the Feynman integrands, 
yielding the prediction for the classical effective action of point masses in dilaton gravity. 
We check the validity of the result by independently constructing the effective action 
in dilaton gravity employing field redefinitions and gauge choices that greatly simplify 
the perturbative construction. Complete agreement is found at next-to-leading order. 
Finally, upon performing the post-Newtonian expansion of our result, we find agreement 
with the corresponding action of scalar-tensor theories known from the literature. 
Our results represent a proof of concept for the classical double-copy construction 
of the gravitational effective action and provides another application of a BCJ-like 
double copy beyond scattering amplitudes. Comments on the ongoing 2PN computation will be made.

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