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We study compatibility of the Standard Model of particle physics and GeneralRelativity by means of gravitational positivity bounds, which provide anecessary condition for a low-energy gravitational theory to be UV completablewithin the weakly coupled regime of gravity. In particular, we identify thecutoff scale of the Standard Model coupled to gravity by studying consistencyof light-by-light scattering. While the precise value depends on details of thePomeron effects in QCD, the cutoff scale reads $10^{16}$GeV if thesingle-Pomeron exchange picture works well up to this scale. We alsodemonstrate that the cutoff scale is lowered to $10^{13}$GeV if we consider theelectroweak theory without the QCD sector.

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