The Quantum Critical Higgs

TL;DR

This paper investigates models where the Higgs boson emerges near a quantum critical point, exhibiting non-mean-field behavior, and explores how collider processes can reveal properties of such critical Higgs scenarios.

Contribution

It introduces models of a quantum critical Higgs with non-mean-field behavior and proposes methods to extract Higgs properties from collider data using form factors.

Findings

Models based on generalized free fields and AdS duals illustrate non-mean-field Higgs behavior.

Processes $gg\to ZZ$ and $gg\to hh$ can probe the Higgs scaling dimension.

Experimental data can reveal the IR transition scale and critical properties.

Abstract

The appearance of the light Higgs boson at the LHC is difficult to explain, particularly in light of naturalness arguments in quantum field theory. However light scalars can appear in condensed matter systems when parameters (like the amount of doping) are tuned to a critical point. At zero temperature these quantum critical points are directly analogous to the finely tuned standard model. In this paper we explore a class of models with a Higgs near a quantum critical point that exhibits non-mean-field behavior. We discuss the parametrization of the effects of a Higgs emerging from such a critical point in terms of form factors, and present two simple realistic scenarios based on either generalized free fields or a 5D dual in AdS space. For both of these models we consider the processes $gg\to ZZ$ and $gg\to hh$, which can be used to gain information about the Higgs scaling dimension and IR transition scale from the experimental data.