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 pointed out that this procedure introduces spurious logarithmic terms when the resummed functions are reexpanded. 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 $\rho_{\ell m}$ up to $\ell=8$). Once the model is informed by 50 Numerical Relativity simulations, this new approach proves key in lowering the maximum EOB/NR unfaithfulness $\bar{F}_{\rm EOBNR}^{\rm max}$ for the $\ell=m=2$ mode (with the Advanced LIGO noise in the total mass range $10-200M_{\odot}$) over 530 spin-aligned waveforms of the Simulating eXtreme Spacetimes catalog. A median unfaithfulness equal to $3.09\times 10^{-4}$ is achieved, which is a marked improvement over the previous value, $1.06\times 10^{-3}$. The largest value, ${\rm Max}[\bar{F}^{\rm max}_{\rm EOBNR}]= 6.80\times 10^{-3}$, is found for an equal-mass, equal-spin simulation with dimensionless spins $\sim +0.998$; only five configurations have $\bar{F}^{\rm max}_{\rm EOBNR} > 5\times 10^{-3}$ (four of which equal-mass and with equal spins larger than $\sim +0.98$). Results for eccentric binaries are similarly excellent (well below $10^{-2}$ and mostly around $10^{-3}$).