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.
Highlights
The Higgs boson mass has been measured to be around 125 GeV by the LHC experiments
If the system approaches a trivial fixed point, we find “mean-field” critical exponents associated with the Landau-Ginzburg effective theory, and a light scalar excitation
The purpose of this paper is to present a general class of theories describing a Higgs field near a nonmean-field quantum phase transitions (QPTs) and explore the observable consequences
Summary
The Higgs boson mass has been measured to be around 125 GeV by the LHC experiments. The appearance of a light scalar degree of freedom is quite unusual both in particle physics and in condensed matter systems [1]. This is just as in the SM supplemented by higher-dimensional operators, with the extra information that the states of the QPT are expected to couple strongly to the Higgs field and, because of the Higgs’s large anomalous dimension, a generic operator with a given number of Higgs insertions will be more irrelevant than the analog one in the weakly coupled case The phenomenology of these models will share some features with scenarios where the Higgs is involved with a conformal sector [9,10,11,12,13]; here we try to formulate a general low-energy effective theory consistent with a QPT and no new massless particles. The paper is organized as follows: we first discuss the general phenomenology of Higgs form factors, we present two general classes of models for a Higgs near a QPT, and, we discuss observable signals at the LHC that can allow us to extract the Higgs scaling dimension and IR transition scale
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