New probe of naturalness.

Any new scalar fields that perturbatively solve the hierarchy problem by stabilizing the Higgs boson mass also generate new contributions to the Higgs boson field-strength renormalization, irrespective of their gauge representation. These new contributions are physical, and in explicit models their magnitude can be inferred from the requirement of quadratic divergence cancellation; hence, they are directly related to the resolution of the hierarchy problem. Upon canonically normalizing the Higgs field, these new contributions lead to modifications of Higgs couplings that are typically great enough that the hierarchy problem and the concept of electroweak naturalness can be probed thoroughly within a precision Higgs boson program. Specifically, at a lepton collider this can be achieved through precision measurements of the Higgs boson associated production cross section. This would lead to indirect constraints on perturbative solutions to the hierarchy problem in the broadest sense, even if the relevant new fields are gauge singlets.