Factorization and resummation: A new paradigm to improve gravitational wave amplitudes

We introduce a new resummed analytical form of the post-Newtonian (PN), factorized, multipolar amplitude corrections f_m of the effective-one-body (EOB) gravitational waveform of spinning, nonprecessing, circularized, coalescing black hole binaries (BBHs). This stems from the following two-step paradigm: (i) the factorization of the orbital (spin-independent) terms in f_m; (ii) the resummation of the residual spin (or orbital) factors. We find that resumming the residual spin factor by taking its inverse resummed (iResum) is an efficient way to obtain amplitudes that are more accurate in the strong-field, fast-velocity regime. The performance of the method is illustrated on the =2 and $m=(1,2)$ waveform multipoles, both for a test mass orbiting around a Kerr black hole and for comparable-mass BBHs. In the first case, the iResum f_m's are much closer to the corresponding ``exact'' functions (obtained by numerically solving the Teukolsky equation) up to the light ring than the nonresummed ones, especially when the black-hole spin is nearly extremal. The iResum paradigm is also more efficient than including higher post-Newtonian terms (up to 20PN order): the resummed 5PN information yields per se a rather good numerical or analytical agreement at the last stable orbit and a well-controlled behavior up to the light ring. For comparable mass binaries (including the highest PN-order information available, 3.5PN), comparing EOB with numerical relativity (NR) data shows that the EOB/NR fractional disagreement at merger, without NR calibration of the EOB waveform, is generically reduced by iResum, from 40% of the usual approach to just a few percent. This suggests that EOBNR waveform models for coalescing BBHs may be improved by using iResum amplitudes.