Higgs potential criticality beyond the Standard Model

Both parameters in the Higgs field's potential, its mass and quartic coupling, appear fine-tuned to nearcritical values, which gives rise to the hierarchy problem and the metastability of the electroweak vacuum. Whereas such behavior appears puzzling in the context of particle physics, it is a common feature of dynamical systems, which has led to the suggestion that the parameters of the Higgs potential could be set through some dynamical process. In this article, we discuss how this notion could be extended to physics beyond the Standard Model (SM). We first review in which sense the SM Higgs parameters can be understood as near-critical and show that this notion can be extrapolated in a unique way for a generic class of SM extensions. Our main result is a prediction for the parameters of such models in terms of their corresponding Standard Model effective field theory Wilson coefficients and corresponding matching scale. For generic models, our result suggests that the scale of new (bosonic) physics lies close to the instability scale. We explore the potentially observable consequences of this connection, and illustrate aspects of our analysis with a concrete example. Lastly, we discuss implications of our results for several mechanisms of dynamical vacuum selection associated with various beyond-the-Standard-Model constructions.