Effective-one-body waveform model for noncircularized, planar, coalescing black hole binaries. II. High accuracy by improving logarithmic terms in resummations

Effective-one-body (EOB) models are based on analytical building blocks that, mathematically, are truncated Taylor series with logarithms. These functions are usually resummed using Pad\'e approximants obtained first assuming that the logarithms are constant, and then replacing them back into the resulting rational functions. A recent study [A. Nagar et al., Effective-one-body waveform model for non-circularized, planar, coalescing black hole binaries: The importance of radiation reaction, Phys. Rev. D 110, 084001 (2024)] pointed out that this procedure introduces spurious logarithmic terms when the resummed functions are reexpanded. We therefore explore analytically more consistent resummation schemes. Here we update the TEOBResumS-Dal\'{\i} waveform model for spin-aligned, noncircularized coalescing black hole binaries by systematically implementing new (still Pad\'e based) resummations for all EOB functions (that is, the metric potentials $A$, $D$ and the residual waveform amplitude corrections ${\ensuremath{\rho}}_{\ensuremath{\ell}m}$ up to $\ensuremath{\ell}=8$). Once the model is informed by 50 numerical relativity (NR) simulations (with the usual two flexibility parameters, one in the orbital and one in the spin sector), this new approach proves key in lowering the maximum effective-one-body (EOB)/numerical relativity (NR) unfaithfulness ${\overline{\mathcal{F}}}_{\mathrm{EOBNR}}^{\mathrm{max}}$ for the $\ensuremath{\ell}=m=2$ mode (with the Advanced LIGO noise in the total mass range $10--200{M}_{\ensuremath{\bigodot}}$) over 530 spin-aligned waveforms of the Simulating eXtreme Spacetimes catalog. A median unfaithfulness equal to $3.09\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ is achieved, which is a marked improvement over the previous value, $1.06\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$. The largest value, $\mathrm{Max}[{\overline{\mathcal{F}}}_{\mathrm{EOBNR}}^{\mathrm{max}}]=6.80\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$, is found for an equal-mass, equal-spin simulation with dimensionless spins $\ensuremath{\sim}+0.998$; only five configurations have ${\overline{\mathcal{F}}}_{\mathrm{EOBNR}}^{\mathrm{max}}>5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ (four of which equal mass and with equal spins larger than $\ensuremath{\sim}+0.98$). Results for eccentric binaries are similarly excellent (well below ${10}^{\ensuremath{-}2}$ and mostly around ${10}^{\ensuremath{-}3}$). For scattering configurations, we find an unprecedented EOB/NR agreement ($\ensuremath{\lesssim}1%$) for relatively small values of the scattering angle, though differences progressively increase as the threshold of immediate capture is approached. Our results thus prove that an improved treatment of (apparently) minor analytical details is crucial to obtain highly accurate waveform models for next generation detectors.