Composite Higgses

Abstract

For the closing article in this volume on supersymmetry, we consider the alternative options to SUSY theories: 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 we 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 we comment on the UV completions of such models and on ways to incorporate dark matter.

UV completions of partial compositeness: the case for a SU(4) gauge group

“…Attempts to derive this lagrangian from an underlying model have been mostly based on the idea of extra dimensions and holography. We will not discuss these approaches in this paper and instead will refer to the many reviews [10][11][12][13][14][15][16][17][18][19] and references therein for the original literature. (We have been mostly following [20].…”

“…Recalling that with our conventions v = f sin( h /f ), we get a relation between the fine-tuning parameter ξ and the terms in the Higgs potential 19) i.e. a factor of four improvement over the minimal coset.…”

Towards a no-lose theorem for naturalness

“…This is its ultimate fate in composite Higgs models including their 5D realizations (e.g. [9][10][11][12][13][79][80][81], though many of these models also have a perturbative top partner regime at low energies). Since the Higgs has electroweak charge, this would seem to require the existence of new electroweak-charged states at scale Λ BSM .…”

Holographic Twin Higgs Model

“…Specifically, to survive the severe bounds, a model has to account for a Higgs mass much lower than the new states which restore naturalness. The composite Higgs framework [2] is a class of models, which address this problem by realizing the Higgs as a pseudo NambuGoldstone boson (PNGB) of a broken global symmetry. Loop corrections to the Higgs mass are controlled by collective breaking mechanisms -for example in the "little Higgs" [3] scenario and in holographic Higgs models [4][5][6].…”