Quasi-5.5PN TaylorF2 approximant for compact binaries: point-mass phasing and impact on the tidal polarizability inference

We derive a point-mass (nonspinning) frequency-domain TaylorF2 phasing approximant at quasi-5.5 post-Newtonian (PN) accuracy for the gravitational wave from coalescing compact binaries. The new approximant is obtained by Taylor-expanding the effective-one-body (EOB) resummed energy and angular momentum flux along circular orbits with all the known test-particle information up to 5.5PN. The - yet uncalculated - terms at 4PN order and beyond entering both the energy flux and the energy are taken into account as free parameters and then set to zero. We compare the quasi-5.5PN and 3.5PN approximants against full EOB waveforms using gauge-invariant phasing diagnostics Qω=ω^2/ω^, where ω^ is the dimensionless gravitational-wave frequency. The quasi-5.5PN phasing is found to be systematically closer to the EOB one than the 3.5PN one. Notably, the quasi-5.5PN (3.5PN) approximant accumulates a EOB-PN dephasing of ΔψEOBPN∼10-3 rad (0.13 rad) up to frequency ω^≃0.06, 6 orbits to merger, (ω^≃0.086, 2 orbits to merger) for a fiducial binary neutron star system. We explore the performance of the quasi-5.5PN approximant on the measurement of the tidal polarizability parameter Λ using injections of EOB waveforms hybridized with numerical relativity merger waveforms. We prove that the quasi-5.5PN point-mass approximant augmented with 6PN-accurate tidal terms allows one to reduce (and in many cases even eliminate) the biases in the measurement of Λ that are instead found when the standard 3.5PN point-mass baseline is used. Methodologically, we demonstrate that the combined use of Qω analysis and of the Bayesian parameter estimation offers a new tool to investigate the impact of systematics on gravitational-wave inference.