Comparing second-order gravitational self-force and effective-one-body waveforms from inspiralling, quasi-circular black hole binaries with a non-spinning primary and a spinning secondary

We present the first comparison of waveforms evaluated using the effective-one-body (EOB) approach and gravitational self-force (GSF) theory for inspiralling black hole binaries with a non-spinning primary and a spinning secondary. This paper belongs to a series of papers comparing the EOB model TEOBResumS to GSF results, where the latter are used to benchmark the EOB analytical choices in the large-mass-ratio regime. In this work, we explore the performance of two gauge choices for the gyro-gravitomagnetic functions GS, GS* entering the spin-orbit sector within the EOB dynamics. In particular, we consider the usual gauge of TEOBResumS, where GS and GS* only depend on the inverse radius and the radial momentum, and a different gauge where these functions also depend on the azimuthal momentum. The latter choice allows us to exploit as prefactor in GS* the complete expression GKS* for a spinning particle on Kerr. As done previously, we employ both waveform alignments in the time domain and a gauge-invariant frequency-domain analysis to gain a more complete understanding of the impact of the new analytical choice. The frequency-domain analysis is particularly useful in confirming that the gyro-gravitomagnetic functions in the new chosen gauge bring the EOB spin contribution at 1st post-adiabatic order closer to the GSF one. We finally implement the improved functions within the public code for TEOBResumS-Dal\'i, which already incorporates eccentricity. In this way, we upgrade the EOB model for extreme-mass-ratio inspirals presented in our previous work.