Is the Standard Model in the Swampland? Consistency Requirements from Gravitational Scattering

TL;DR

This paper investigates the compatibility of the Standard Model with gravity using gravitational positivity bounds, identifying a cutoff scale around 10^{16} GeV, which varies depending on QCD effects and electroweak considerations.

Contribution

It applies gravitational positivity bounds to determine the cutoff scale of the Standard Model coupled to gravity, linking scattering processes to fundamental consistency conditions.

Findings

Cutoff scale is approximately 10^{16} GeV with QCD effects included.

Without QCD, the cutoff scale drops to about 10^{13} GeV.

The results depend on the modeling of Pomeron effects in QCD.

Abstract

We study compatibility of the Standard Model of particle physics and General Relativity by means of gravitational positivity bounds, which provide a necessary condition for a low-energy gravitational theory to be UV completable within the weakly coupled regime of gravity. In particular, we identify the cutoff scale of the Standard Model coupled to gravity by studying consistency of light-by-light scattering. While the precise value depends on details of the Pomeron effects in QCD, the cutoff scale reads $10^{16}$GeV if the single-Pomeron exchange picture works well up to this scale. We also demonstrate that the cutoff scale is lowered to $10^{13}$GeV if we consider the electroweak theory without the QCD sector.