Generic EFT-motivated beyond General Relativity gravitational wave tests and their curvature dependence: from observation to interpretation

We present a "dictionary" to expedite the identification of potential deviations in gravitational waveforms from those predicted by General Relativity (GR) during the inspiral phase of black hole binaries. Assuming deviations from GR can be described by a local Effective Field Theory (EFT) formulated in terms of curvature operators (and possibly additional scalar fields), this dictionary characterizes how deviations scale with the masses of the binary components and identifies the leading order Post-Newtonian corrections in generic theories constructed within the EFT framework. By establishing a direct connection between observations and candidate theories beyond GR, this dictionary also aids in distinguishing genuine physical effects from systematic errors. These results can be readily incorporated into essentially all existing tests for the inspiral regime and, in particular, facilitate a more efficient combination of data from multiple events.