Bootstrap-ready scattering observables with soft photons and gravitons
In plain words
In four dimensions, every scattering of charged particles or gravitons emits unlimited numbers of very low-energy photons or gravitons, so the usual scattering amplitude is ill-defined. A replacement object with the properties bootstrap methods need has not been established.
Precise statement
For 4D theories with massless gauge bosons or gravitons, define nonperturbatively asymptotic observables (dressed amplitudes, Faddeev-Kulish states, or inclusive cross sections) that are infrared finite and obey unitarity, analyticity and crossing in a form usable for numerical bootstrap. An answer is such a definition with proofs of these properties, or a demonstration that one of them must fail.
What would settle it
A definition with nonperturbative proofs of unitarity, analyticity and crossing, used in a working numerical bootstrap.
Status in the literature
Generalized crossing relations between different asymptotic observables were proven at tree level in 2023 (Caron-Huot, Giroux, Hannesdottir, Mizera, arXiv:2310.12199).