Quantum Critical Higgs

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 anti–de Sitter 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.

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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. The discovery of the Higgs boson in 2012 revolutionized particle physics and turned the long-standing puzzle about its existence into an experimentally accessible question at the Large Hadron Collider (LHC): Why is the Higgs boson light? Why is the standard model of particle physics near a critical point? Despite the Higgs boson being consistent with the standard model of particle physics, the origin of the mass of the elementary particles and the lightness of the Higgs boson remain a mystery.

Some theories have put forth the idea that light scalars can be realized by tuning parameters close to a critical value. Here, we search for low-energy manifestations of these theories consistent with a light Higgs boson particle. As part of our work, we propose experimental observations associated with our theories that might be measureable at the LHC. We explore a class of models with a Higgs boson near a quantum critical point that exhibits non-mean-field behavior. We discuss the parametrization of the effects of a Higgs boson emerging from such a critical point in terms of form factors, and we present two simple realistic scenarios based on either generalized free fields or a 5D dual in anti–de Sitter space. We additionally study how the production of pairs of Higgs bosons might inform our knowledge of these particles.

We expect that our findings will motivate novel analyses of future LHC data to better understand the Higgs boson.

Figure 1

Form factor for the cubic Higgs coupling, Eq. (44), for $\mu =400$, plotted as a function of an off-shell Higgs momentum $p=\sqrt{p_{\mu }{p}^{\mu }}$. The solid lines correspond to the real part of the form factor, and the dashed lines correspond to the imaginary part. On the top, we keep only one Higgs on shell. We take $\mathrm{\Delta }=1.5$, and the three colors correspond to three different values of the off-shell Higgs momentum: 200 GeV (red), 400 GeV (blue), and 600 GeV (green). On the bottom, only one of the external Higgs fields are taken to be off shell, and the colors correspond to $\mathrm{\Delta }=1.2$ (red), 1.4 (blue), and 1.6 (green).

Figure 2

The effects of including the quantum critical Higgs two-point function in the production of on-shell $Z$-boson pairs. The effects of varying $\mathrm{\Delta }$ (top two plots) and $\mu$ (bottom two plots) are shown. On the right-hand side, data are shown as a fraction of the SM result. The effect of the cut associated with the nonstandard two-point function is to dramatically enhance the production of $Z$ pairs far away from the Higgs pole. In each plot, for comparison purposes, the effect of a second heavy 500-GeV Higgs with a 100-GeV width is included.

Figure 3

Potential deviations in double Higgs production at the 14-TeV LHC. We consider two different cases. The first (dashed lines) is when only the Higgs two-point function is modified, as when the strong sector that mixes with the Higgs has vanishing $n$-point correlators for $n\ge 2$. The second (solid lines) is when the Higgs quartic coupling (and, hence, the cubic form factor) comes purely from a four-point correlator in a large $N$ CFT, and thus both the two- and three-point functions for the Higgs boson carry nontrivial momentum dependence. We vary $\mathrm{\Delta }$ and $\mu$ for both cases, as shown.