2PM waveform from loop corrected soft theorems

We introduce a classical version of the loop corrected soft graviton theorem and we use it to compute the universal part of the one-loop (2PM) waveform up to sub-subleading order in the energy ω of the emitted graviton for spinless black-hole scattering. In particular, we compute the action of the soft operators on the classically resummed four-point amplitude, that can be written in terms of the exponential of the eikonal phase (and is therefore non-perturbative in the Newton's constant GN) and then we perform the usual PM expansion in powers of GN . We find perfect agreement with the existing 2PM literature at the orders logω and ωlog²ω, which are universal. Furthermore, we use this method to compute the universal part of the ωlogω contribution to the 2PM waveform. Our approach, based on the resummed eikonal amplitude, gives a unified picture of the various computations of the classical soft graviton behaviour that are present in the literature since the seminal paper by Weinberg in 1965.