The quantum criticality of the Standard Model and the hierarchy problem

TL;DR

This paper investigates the hierarchy problem in the Standard Model through a novel Wilsonian renormalization group approach, revealing connections to quantum criticality and phase transitions that influence fine-tuning and naturalness.

Contribution

It introduces the first full Standard Model implementation within the Wilsonian functional renormalization group, capturing both logarithmic and quadratic scalings to analyze fine-tuning and critical phenomena.

Findings

Identifies the near-criticality of the Standard Model as related to the hierarchy problem.

Provides scheme-independent insights into Higgs phase structure and quantum phase transitions.

Explores new physics scenarios that reduce high-scale sensitivity and address fine-tuning.

Abstract

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 this context, the full Standard Model within 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.