Comparing second-order gravitational self-force and effective-one-body waveforms from inspiralling, quasicircular black hole binaries with a nonspinning 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 nonspinning 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 ${G}_{S}$, ${G}_{{S}_{*}}$ entering the spin-orbit sector within the EOB dynamics. In particular, we consider the usual gauge of teobresums, where ${G}_{S}$ and ${G}_{{S}_{*}}$ 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 ${G}_{{S}_{*}}$ the complete expression ${G}_{{S}_{*}}^{K}$ 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 first postadiabatic 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.