Composite Higgses

Abstract

We present an overview of composite Higgs models in light of the discovery of the Higgs boson. The small value of the physical Higgs mass suggests that the Higgs quartic is likely loop generated, thus models with tree-level quartics will generically be more tuned. We classify the various models (including bona fide composite Higgs, little Higgs, holographic composite Higgs, twin Higgs and dilatonic Higgs) based on their predictions for the Higgs potential, review the basic ingredients of each of them, and quantify the amount of tuning needed, which is not negligible in any model. We explain the main ideas for generating flavor structure and the main mechanisms for protecting against large flavor violating effects, and present a summary of the various coset models that can result in realistic pseudo-Goldstone Higgses. We review the current experimental status of such models by discussing the electroweak precision, flavor and direct search bounds, and comment on UV completions and on ways to incorporate dark matter.We start by explaining the consequences of the recent measurement of the value of the Higgs mass on the parameters of the Higgs potential: both the mass and quartic self coupling are independently fixed. A light Higgs mass of 125 GeV implies a small quartic, which is more likely to point toward a loop induced quartic rather than a tree-level one. We present a simple parametrization of the potential suitable for pseudo-Goldstone composite Higgs models, and the tuning necessary to obtain this potential. In Sec. 3 we classify the various types of composite Higgs models based on their predictions for the Higgs potential and quantify the expected amount of tuning in these models. Sec. 4 contains the discussion of the various possible mechanisms for generating the Yukawa couplings, and for protecting from large flavor changing effects. We review the various coset models that can give rise to realistic patterns of symmetry breaking with SM-like Higgs bosons in Sec. 5. The signals and constraints on the composite Higgs models are summarized in Sec. 6, and we finally comment on UV completions in Sec. 7. The Higgs Potential of Composite Higgs Models and TuningOne can nicely classify the various types of composite Higgs models by the size of the Higgs potential and also by the mechanism that generates the Yukawa couplings, in particular for the top quark. We will first focus on the generic features of the potential, in order to categorize in Sec. 3 composite Higgs models based on the particulars of such a potential, and finally in Sec. 4 we will discuss the various mechanisms for the generation of the Yukawa couplings.While the numerical values of the parameters in the Higgs potential (1.1) are now fixed, there are several different dynamical ways in which one can arrive at this potential. We will make the following assumptions regarding the dynamics responsible for generating the potential:• The Higgs is a composite with a scale of compositeness given by f .

Goldstone inflation

“…A useful trick is to take the whole SO(N ) global symmetry to be gauged, and only at the end of the calculation setting the unphysical SO(N )/SO(N − 1) gauge fields to zero [26,27]. The most general effective Lagrangian involving couplings between Σ and SO(N ) gauge bosons, in momentum space and up to quadratic order in the gauge fields, is where A µ = A a µ T a (a = 1, .…”

“…This result can be understood as the sum over the series of diagrams: As discussed in [26,27], Π 1 can be thought of as an order parameter, which goes to zero in the symmetry-preserving phase at high momenta. Provided the ratio Π A 1 /Π A 0 decreases fast enough, the integral in (2.8) will converge.…”

“…which now has a pole at p 2 = 0, since the broken SO(N )/SO(N − 1) currents can excite the Goldstones from the vacuum [26,27]. We approximate the Π 0 form factors with their tree level values.…”

Partially composite dark matter

“…The spin independent cross section per nucleon is given by 11) where m N (N = p, n) is the nucleon mass and A and Z are the mass and atomic number of the target nucleus, respectively. The factor f N q are matrix elements, f N q = (m q /m N ) N |qq|N .…”

“…In particular, the coupling to electroweak gauge bosons can be measured with a good accuracy. It has been studied that the sensitivity can reach to ∼ 0.1 (0.01) at the LHC (ILC) [11]. 6 In the m DM < m h /2 region, the invisible branching ratio of the Higgs boson decay is also expected.…”