Exploring amplitude criteria for weak gravity in electroweak theory

Connections between weak gravity conjecture (WGC) bounds and scattering positivity have been extensively studied over the past decade. This work further explores these connections by proposing positivity as a potential amplitude criterion for weak gravity, with the aim of unifying various weak gravity bounds within a single framework. We illustrate this criterion by analyzing two-body elastic scatterings of photons and Higgs bosons in the forward limit of an electroweak (EW)-like theory. This leads to an amplitude-based criterion that extends magnetic WGC-type bounds to include not only the Abelian gauge coupling but also the non-Abelian gauge and the Yukawa coupling. Furthermore, a version of the species bound naturally emerges within this setup, suggesting that this amplitude criterion may extend to broader Swampland conjectures beyond the WGC.