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 polynomials 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 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-Dali waveform model for spin-aligned, noncircularized, coalescing black hole binaries by systematically implementing new (still Pad\'e based) resummations for all EOB functions. Once the model is informed by 51 Numerical Relativity simulations this new approach proves key in lowering the maximum EOB/NR unfaithfulness F̄EOBNRᵐᵃˣ for the =m=2 mode (with the Advanced LIGO noise in the total mass range 10-200M_) over the whole Simulating eXtreme Spacetimes catalog of 534 waveforms. A median mismatch of 3.418× 10⁻⁴ is achieved, which is a marked improvement on the previous value, 1.06× 10⁻³. The largest value, F̄ᵐᵃˣEOBNR~ 10⁻², is found for an equal-mass, equal-spin simulation with dimensionless spins ~ +0.994; only six configurations (all equal-mass, and with equal spins larger than $+0.97$) are above 5× 10⁻³. Results for eccentric binaries are similarly excellent (well below 10⁻² and mostly around 10⁻³). For scattering configurations, we find an unprecedented EOB/NR agreement ($<1%$) for relatively small values of the scattering angle, though differences progressively increase as the threshold of immediate capture is approached.