Higgs criticality in and beyond the Standard Model

TL;DR

This paper explores the significance of Higgs potential parameters being near critical values, suggesting that such near-criticality could be a fundamental feature influencing the Standard Model and beyond, with implications for dynamical mechanisms and model building.

Contribution

It introduces the concept of near-criticality in Higgs parameters as a fundamental aspect, reviews mechanisms driving parameters to criticality, and discusses broader implications beyond the Standard Model.

Findings

Higgs parameters are close to critical values, indicating potential underlying dynamical mechanisms.

Mechanisms exist that can dynamically tune Higgs parameters towards criticality.

Near-criticality has significant implications for model building and understanding BSM physics.

Abstract

The properties of the Higgs potential are determined by three parameters: the mass parameter, the quartic self-coupling, and a constant term. Remarkably, all three of these parameters seem subject to a significant amount of fine-tuning. All these tunings can be seen as their corresponding parameters being close to critical values marking quantum phase transitions. While such behavior is surprising from a conventional particle physics perspective, it is a common feature of dynamical systems. This has motivated the conjecture that the values of the Higgs' parameters are the result of some dynamical mechanism. This possibility suggests the construction of mechanisms dynamically choosing sets of Higgs parameters. In these notes, I discuss a complementary approach. Taking seriously that such a mechanism could exist in nature, it is plausible to assume that it also influences Beyond-Standard-Model physics. This suggests considering near-criticality in any model of interest and investigating its consequences more generally, in particular independent of a concrete mechanism responsible for it. I first explain what it means for the parameters of the Higgs potential to be near-critical. This includes a discussion of the recently discovered "metastability bound" on the Higgs mass, which can be understood through a critical point. I then review two concrete examples of mechanisms in which the parameters of the Higgs potential are dynamically driven towards critical values. These mechanisms also serve as an important proof on concept for the feasibility of the assumptions at the foundation of these notes. Using a simple example for concreteness, the final part of these notes then explicitly demonstrates how to approach a given model in the light of the near-criticality conjecture.