The quantum criticality of the Standard Model and the hierarchy problem

A bstract The naturalness principle has long guided efforts to understand physics beyond the Standard Model, with the hierarchy problem as the central issue. We revisit the role of quantum corrections in the fine-tuning of the low-energy effective description and its phase structure. We implement, for the first time in the context of the full Standard Model, the Wilsonian functional renormalization group. Crucially, this method captures conveniently both logarithmic and quadratic scalings, which must both be considered in the tuning, and allows us to provide a new generic and quantitative study of fine-tuning and its interpretation in terms of critical phenomena. We emphasize on the connection between the hierarchy problem and the near-criticality of the Standard Model and extract scheme-independent information on the infrared Higgs phases and the associated quantum phase transition as well as discuss a related enhanced fine-tuning usually not considered in tuning estimates. Finally, we illustrate the framework’s versatility by exploring new physics coupled to the Higgs sector that can soften high-scale sensitivity, recovering also the large-anomalous-dimension solution to the hierarchy problem.