Higher-order logarithmic soft terms

Establish the extension to n\geq 3 of the non-analytic classical gravitational soft terms proportional to \(\omega^{n-1}(\ln\omega)^n\) beyond the explicitly derived case \(n=2\), thereby determining whether the conjectured tower holds in the general case.

Background

The paper organizes the classical low-frequency waveform as a joint expansion in the gravitational coupling and emitted frequency. In this expansion, logarithmic terms encode long-range gravitational effects such as tails and acceleration. The authors note that terms of the form ωn−1(ln⁡ω)n\omega^{n-1}(\ln\omega)^n have been derived explicitly only for n=2n=2 in generic classical gravitational scattering, while the corresponding higher-order extension remains conjectural. Resolving this issue would clarify the all-orders infrared structure of gravitational radiation and support the proposed tower of leading infrared logarithms.

References

The non-analytic terms of the form \omega{n-1} (\ln \omega)n have been derived explicitly for n=2 in the generic classical gravitational scattering, while their extension to n\geq 3 is presently conjectural in the general case.

— An Effective $S$-Matrix Approach to Low-Frequency Waveforms from Black Hole Mergers  (2609.10329 - Aoki et al., 9 Sep 2026) in Section 2.3, subsection “Perturbative organization of the soft expansion”