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A recent study [Phys. Rev. D 106 (2022) 6, 064049] introduced a completeeffective-one-body (EOB) model for extreme-mass-ratio-inspirals (EMRIs), whichbuilds upon the TEOBResumS-Dali model, incorporates aligned spins (both on theprimary and on the secondary) as well as orbital eccentricity and cruciallyrelies on conservative first-order gravitational self-force (1GSF) resultsrecasted within the resummed EOB potentials. A comparison of thequasi-circular, nonspinning version of this model with recently obtainedwaveforms at 2GSF accuracy prompted the improvement of the analytical contentof the 0th-order post-adiabatic (0PA) EOB fluxes, both at infinity and throughthe black hole horizon, that enter the resummed radiation reaction force. Inparticular the infinity flux, including modes up to $\ell =8$, was extended to$3^{+19}$PN accuracy, meaning that 3PN comparable-mass terms are hybridizedwith higher PN test-particle terms up to 22PN relative order. Here, exploitingour gained awareness of the importance of the 0PA fluxes, we show that theEOB/GSF agreement can be further improved by also including the$3^{+19}$PN-accurate $\ell=9$ and $\ell=10$ modes in the flux at infinity. Fora standard EMRI with mass ratio $q \equiv m_1/m_2 = 5 \times 10^4$ and $m_2 =10 M_\odot$, the accumulated EOB/2GSF dephasing is $\lesssim $ rad for $\sim 1$yr of evolution. We finally provide an efficient implementation of the modelthat includes both spin and eccentricity, paving the way for the systematic useof TEOBResumS in the construction of physically complete and accurate waveformtemplates for EMRIs.

Tailoring an effective-one-body waveform model to extreme-mass-ratio  inspirals: achieving full consistency with second-order gravitational  self-force results and beyond