From the confluent Heun equation to a new factorized and resummed gravitational waveform for circularized, nonspinning, compact binaries

We introduce a new factorized and resummed waveform for circularized, nonspinning, compact binaries that leverages on the solution of the Teukolsky equation once mapped into a confluent Heun equation. The structure of the solution allows one to identify new resummed factors that completely absorb all test-mass logarithms and transcendental numbers via exponentials and $\Gamma$-functions at any post-Newtonian (PN) order. The corresponding residual relativistic and phase corrections are thus polynomial with rational coefficients, that are in fact PN-truncated hypergeometric functions. Our approach complements the recent proposal of Ivanov et al. [Phys. Rev. Lett. 135 (2025) 14, 141401], notably recovering the corresponding renormalization group scaling of multipole moments from first principles and fixing the scaling constant. In the test mass limit, our approach (pushed up to 10PN) yields waveforms and fluxes that are globally more accurate than those obtained using the standard factorized approach of Damour et al. [Phys. Rev. D 79 (2009), 064004]. The method generalizes straightforwardly to comparable mass binaries implementing the new concept of universal anomalous dimension of multipole moments and might be eventually useful to improve current state of the art effective-one-body waveform models for coalescing binaries.