Origin of Neutrino Masses on the Convex Cone of Positivity Bounds

We exhibit the geometric structure of the convex cone in the linear space of the Wilson coefficients for the dimension-8 operators involving the left-handed lepton doublet L and the Higgs doublet H in the Standard Model effective field theory (SMEFT). The boundary of the convex cone gives rise to the positivity bounds on the Wilson coefficients, while the extremal ray corresponds to the unique particle state in the theory of ultraviolet completion.