Advancing the Effective-One-Body Framework in the Test-Mass Limit

Abstract

We present SEOB-TML, an enhanced effective-one-body (EOB) framework for the test-mass limit, optimized for quasi-circular, spin-aligned binary black holes. On the dynamical side, we introduce a quadrupole-factorized (Q-factorized) prescription that maps the total energy flux-including horizon absorption-onto a single (2,2) mode baseline. This approach effectively captures higher-order multipole contributions without explicit mode summation, while simultaneously leading to a dramatic reduction in fractional flux errors. To ensure a smooth transition to the post-merger stage, we replace traditional next-to-quasicircular corrections with a phenomenological ansatz, enabling a flexible, mode-dependent attachment prescription. For the merger-ringdown stage, we utilize quasi-normal mode coefficients extracted from numerical waveforms via qnmfinder to explicitly model mode-mixing effects. These enhancements lead to a substantial reduction in residuals, capturing the complex physical modulations prominent in retrograde configurations. Additionally, we implement the (2,0) mode across the full waveform, further extending the model's physical coverage and accuracy. Overall, our framework generates highly accurate late inspiral-merger-ringdown waveforms for extreme-mass-ratio systems, significantly reducing dephasing and improving the near-merger reconstruction. We demonstrate the performance of SEOB-TML against the current state-of-the-art SEOBNRv5HM model, highlighting how our specialized developments extend the reliability of the EOB framework into the test-mass limit.