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Register a new userThe Natural Composite Higgs
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Authors
Luca Vecchi
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The discovery of the Higgs boson has put considerable pressure on theories that aim to solve the hierarchy problem. Scenarios in which the Higgs is a pseudo Nambu-Goldstone boson (NGB) of some new strong dynamics must possess a number of non-generic features in order to pass the progressively stringent collider bounds and simultaneously meet our naturalness criteria. Among these features are the existence of light fermionic partners of the top quark and an efficient collective breaking of the Nambu-Goldstone symmetry. The top partners have to be not only parametrically lighter than the other composites, but also weakly coupled to them in order to suppress unwanted flavor-violating effects. A Natural pseudo-NGB Higgs model should also be able to fit the LHC Higgs data without fine-tuning. Among theories with comparable compositeness scales, those that predict smaller corrections in the Higgs couplings to the standard model particles are therefore preferred. A concrete implementation of these ingredients is discussed in a scenario based on the coset SU(5)/SO(5). The fit to the current LHC Higgs data is significantly improved compared to the minimal scenarios, and a fully natural explanation of both the weak scale and the Higgs boson mass can be attained. An important role is played by an independent quartic Higgs coupling generated by UV-sensitive loops involving electroweak doublets mixing with the top partners. The collider signature of this framework is shown to be rather model-dependent; in particular, the exotic scalars can alter the phenomenology of the top partners at a qualitative level.
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Composite Higgs models provide an attractive solution to the hierarchy problem. However, many realistic models suffer from tuning problems in the Higgs potential. There are often large contributions from the UV dynamics of the composite resonances to the Higgs potential, and tuning between the quadratic term and the quartic term is required to separate the electroweak breaking scale and the compositeness scale. We consider a composite Higgs model based on the $SU(6)/Sp(6)$ coset, where an enhanced symmetry on the fermion resonances can minimize the Higgs quadratic term. Moreover, a Higgs quartic term from the collective symmetry breaking of the little Higgs mechanism can be realized by the partial compositeness couplings between elementary Standard Model fermions and the composite operators, without introducing new elementary fields beyond the Standard Model and the composite sector. The model contains two Higgs doublets, as well as several additional pseudo-Nambu-Goldstone bosons. To avoid tuning, the extra Higgs bosons are expected to be relatively light and may be probed in the future LHC runs. The deviations of the Higgs couplings and the weak gauge boson couplings also provide important tests as they are expected to be close to the current limits in this model.
We consider composite two-Higgs doublet models based on gauge-Yukawa theories with strongly interacting fermions generating the top-bottom mass hierarchy. The model features a single universal Higgs-Yukawa coupling, $ g $, which is identified with the top quark $ gequiv g_t sim mathcal{O}(1) $. The top-bottom mass hierarchy arises by soft breaking of a $ mathbb{Z}_2 $ symmetry by a condensate of strongly interacting fermions. A mass splitting between vector-like masses of the confined techni-fermions controls this top-bottom mass hierarchy. This mechanism can be present in a variety of models based on vacuum misalignment. For concreteness, we demonstrate it in a composite two-Higgs scheme.
We consider a composite Higgs model based on the $SU(6)/Sp(6)$ coset, where an $U(1)$ subgroup of $Sp(6)$ is identified as the flavor symmetry. A complex scalar field $s$, which is a pseudo-Nambu-Goldstone boson of the broken symmetry, carries a flavor charge and plays the role of a flavon field. The $U(1)_F$ flavor symmetry is then broken by a VEV of the flavon field, which leads to a small parameter and generates the mass hierarchy between the top and bottom quarks. A light flavon below the TeV scale can be naturally introduced, which provides a fully testable model for the origin of flavor hierarchy. A light flavon also leads to substantial flavor changing neutral currents, which are strongly constrained by the flavor precision tests. The direct search of additional scalar bosons can also be conducted in HL-LHC and future hadron colliders.
Most of the analysis of composite Higgs have focussed on the Minimal Composite Higgs Model, based on the coset SO(5)$times$U(1)$_X$/SO(4)$times$U(1)$_X$. We consider a model based on the coset of simple groups SO(7)/SO(6), with SO(4)$times$U(1)$_X$ embedded into SO(6). This extension of the minimal model leads to a new complex pNGB that has hypercharge and is a singlet of SU(2)$_L$, with properties mostly determined by the pattern of symmetry breaking and a mass of order TeV. Composite electroweak unification also leads to new bosonic and fermion resonances with exotic charges, not present in the minimal model. The lightest of these resonances is stable, and in some cases could provide candidates for dark matter. A new rich phenomenology is expected at LHC.
Composite Higgs models can be extended to the Planck scale by means of the partially unified partial compositeness (PUPC) framework. We present in detail the Techni-Pati-Salam model, based on a renormalizable gauge theory $SU(8)_{PS}times SU(2)_Ltimes SU(2)_R$. We demonstrate that masses and mixings for all generations of standard model fermions can be obtained via partial compositeness at low energy, with four-fermion operators mediated by either heavy gauge bosons or scalars. The strong dynamics is predicted to be that of a confining $Sp(4)_{rm HC}$ gauge group, with hyper-fermions in the fundamental and two-index anti-symmetric representations, with fixed multiplicities. This motivates for Lattice studies of the Infra-Red near-conformal walking phase, with results that may validate or rule out the model. This is the first complete and realistic attempt at providing an Ultra-Violet completion for composite Higgs models with top partial compositeness. In the baryon-number conserving vacuum, the theory also predicts a Dark Matter candidate, with mass in the few TeV range, protected by semi-integer baryon number.
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