Positivity and the electroweak hierarchy

We point out that an unnatural hierarchy between certain higher -dimensional operator coefficients in a low -energy effective field theory (EFT) would automatically imply that the Higgs' vacuum expectation value is hierarchically smaller than the EFT cutoff, assuming the EFT emerged from a unitary, causal and local UV completion. Future colliders may have the sensitivity to infer such a pattern of coefficients for a little hierarchy with an EFT cutoff up to O(10) TeV.