Infrared regularization for non-local interactions in cutoff computations

Develop and justify an appropriate infrared regularization scheme for cutoff-regularized de Sitter loop correlators with inverse-Laplacian (non-local) interactions, and apply it to resolve the IR divergences observed in the 1-loop bispectrum calculation for Diagram 32.

Background

For certain contractions in Diagram 32 involving inverse-Laplacian operators, the loop integral is divergent both in the ultraviolet and infrared. While a time-dependent physical cutoff implements the UV regularization, the authors note that the suitable IR regularization in de Sitter is subtle and not clear.

They therefore explicitly defer a detailed treatment of IR regularization for such non-local interactions to future work.

References

However, it is not very clear what the analogous appropriate regularization is in the IR (for related discussions, see and references therein). A detailed analysis involving regularization of IR divergences, such as the one arising in the above case of Diagram 32, is left for a future work.

— Singularities in Cosmological Loop Correlators II : Non Local Interactions and Flat Space limits  (2512.11040 - Ansari et al., 11 Dec 2025) in Section 3 (Results at 1-loop), Diagram 32