Bounds on four-dimensional gravitational couplings free of infrared logarithms
In plain words
In four dimensions, the known bounds that account for gravity depend, through a logarithm, on an arbitrary largest distance, because gravity's pull falls off too slowly. A version free of this dependence is not known.
Precise statement
Dispersive bounds on 4D gravitational EFT coefficients (for example $R^3$ and $R^4$ corrections to Einstein gravity) obtained from smeared impact-parameter sum rules hold only up to a factor $\log(b_{\mathrm{IR}} M)$, where $b_{\mathrm{IR}}$ is an infrared impact-parameter cutoff and $M$ the EFT cutoff (Caron-Huot, Li, Parra-Martinez, Simmons-Duffin, JHEP 05 (2023) 122). Find an infrared-safe observable whose sum rules give bounds independent of $b_{\mathrm{IR}}$, or prove that the logarithm cannot be removed.
What would settle it
A 4D sum rule built from infrared-finite quantities that yields cutoff-independent bounds, or a no-go theorem.
Status in the literature
Bounds valid up to the infrared logarithm were derived in 2022; cutoff-independent versions are not established.