Scattering angle at 3PM in scalar-tensor theories using the PM-EFT formalism

TL;DR

The paper extends the post-Minkowskian EFT framework to massless scalar-tensor gravity to derive the conservative two-body dynamics of non-spinning binaries. By computing the effective action from two-loop (3PM) diagrams, it delivers an analytic expression for the scattering angle up to $3PM$, including scalar exchanges and their coupling to worldline degrees of freedom. The results are shown to reproduce the post-Newtonian limit and agree with GR in the binary black hole limit, providing a consistent cross-check with PN and GR literature and offering a path toward scalar-tensor waveform templates. This work thus broadens the applicability of PM-EFT methods to modified gravity and paves the way for connecting PM coefficients to PN coefficients and to EFT-based waveform modeling in scalar-tensor theories.

Abstract

In this work, we derive the conservative dynamics of non-spinning binaries in the massless scalar-tensor theories using the post-Minkowskian Effective Field Theory (EFT) approach. Our main result is an analytic expression of the scattering angle, computed up to third Post-Minkowskian order via two-loop Feynman diagrams. Our results are in perfect agreement with previous literature, in particular within the post-Newtonian limit.

Figures (6)

• Figure 1: Feynman diagrams needed for the computation of the effective action up to 2PM order. The wavy lines represent the graviton propagator, dashed lines represents the scalar propagator and the black dots represent the external sources.
• Figure 2: Feynman diagrams due to four-scalar bulk vertices.
• Figure 3: Feynman diagrams due to four-graviton bulk vertices.
• Figure 4: Feynman diagrams due to three-scalar one-graviton bulk vertices.
• Figure 5: Feynman diagrams due to two-scalar two-graviton bulk vertices.