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By post-Newtonian (PN) expanding the well-known, factorized and resummed,effective-one-body energy flux for circularized binaries we show that: (i)because of the presence of the resummed tail factor, the 4.5PN-accuratetails-of-tails-of-tails contribution to the energy flux recently computed byMarchand et al. [Class. Q. Grav. 33 (2016) 244003] is actually contained in theresummed expression; this is also the case of the the next-to-leading-ordertail-induced spin-orbit term of Marsat et al. [Class. Q. Grav. 31 (2014)025023]; (ii) in performing this expansion, we also obtain, for the first time,the explicit 3.5PN leading-order tail-induced spin-spin flux term; (iii)pushing the PN expansion of the (nonspinning) EOB flux up to 5.5PN order, wecompute 4PN, 5PN and 5.5PN contributions to the energy flux, though in a formthat explicitly depends on, currently unknown, 4PN and 5PN non-test-masscorrections to the factorized waveform amplitudes. Within this (parametrized)4.5PN accuracy, we calculate the TaylorF2 approximant. Focusing for simplicityon the nonspinning case and using the numerical-relativity calibratedIMRPhenomD waveform model as benchmark, we demonstrate that it is possible toreproduce the derivative of the IMRPhenomD phase (say up to the frequency ofthe Schwarzschild last-stable-orbit) by flexing only a 4PN "effective" waveformamplitude parameter. A preliminary analysis also illustrates that similarresults can be obtained for the spin-aligned case provided only theleading-order spin-orbit and spin-spin terms are kept. Our findings suggestthat this kind of, EOB-derived, (parametrized), higher-order, PN approximantsmay serve as promising tools to construct Inspiral-Merger-Ringdownphenomenological models or even to replace the standardly used 3.5PN-accurateTaylorF2 approximant in searches of small-mass binaries.

Parametrized-4.5PN TaylorF2 approximant(s) and tail effects to quartic nonlinear order from the effective one body formalism