Effective-one-body Hamiltonian in scalar-tensor gravity at third post-Newtonian order

We determine the general local-in-time effective-one-body (EOB) Hamiltonian for massless scalar-tensor (ST) theories at third post-Newtonian (PN) order. Starting from the Lagrangian derived in Bernard [Phys. Rev. D 99, 044047 (2019)], we map it to the corresponding ordinary Hamiltonian describing the two-body interaction in ST theories at 3PN level. Using a canonical transformation, we then map this onto an EOB Hamiltonian so as to determine the ST corrections to the 3PN-accurate EOB potentials $(A,B,{Q}_{e})$ at 3PN. We then focus on circular orbits and compare the effect of the newly computed 3PN terms, also completed with finite-size and nonlocal-in-time contributions, on predictions for the frequency at the innermost stable circular orbit. Our results will be useful to build high-accuracy waveform models in ST theory, which could be used to perform precise tests against general relativity using gravitational wave data from coalescing compact binaries.