Third post-Newtonian dynamics for eccentric orbits and aligned spins in the effective-one-body waveform model SEOBNRv5EHM

Accurate waveform models for coalescing binaries on eccentric orbits are crucial for avoiding biases in the analysis of eccentric gravitational-wave signals. The effective-one-body (EOB) formalism combines various analytical approximation methods with information derived from numerical-relativity simulations, and it has proven reliable in modeling the inspiral-merger-ringdown waveform of binaries on generic orbits. In this work, we derive new analytical results within the EOB formalism, specifically addressing eccentric, aligned-spin binaries. For the first time, we obtain EOB results for eccentric orbits that are accurate up to the third post-Newtonian (PN) order for the complete far-zone energy and angular-momentum fluxes, the radiation-reaction (RR) force, and waveform modes (including memory contributions). We obtain these results by deriving transformations from the harmonic to EOB coordinates and from the quasi-Keplerian to the Keplerian parametrization, that properly account for the spin-supplementary condition, post-adiabatic contributions, and the gauge freedom in the RR force. We employ these findings to build the inspiral part of the SEOBNRv5EHM waveform model, which includes the 3PN eccentricity contributions in the RR force and waveform modes using the Keplerian parametrization, and augments the EOB equations of motion with PN evolution equations for the Keplerian parameters. The new SEOBNR model achieves much better accuracy than its predecessor SEOBNRv4EHM and other eccentric models, even for eccentricities as high as $\lesssim 0.5$.