Abstract
We consider a class of composite Higgs models based on asymptotically free $SO(d)$ gauge theories with $d$ odd, with fermions in two irreducible representations, and in which the Higgs field arises as a pseudo Nambu-Goldstone boson and the top quark is partially composite. The Nambu-Goldstone coset containing the Higgs field, or Higgs coset, is either $SU(4)/Sp(4)$ or $SU(5)/SO(5)$, whereas the top partners live in two-index representations of the relevant flavor group ($SU(4)$ or $SU(5)$). In both cases, there is a large number of terms in the most general four-fermion lagrangian describing the interaction of third-generation quarks with the top partners. We derive the top-induced effective potential for the Higgs coset together with the singlet pseudo Nambu-Goldstone boson associated with the non-anomalous axial symmetry, to leading order in the couplings between the third-generation quarks and the composite sector. We obtain expressions for the low-energy constants in terms of top-partner two-point functions. We revisit the effective potential of another composite Higgs model that we have studied previously, which is based on an $SU(4)$ gauge theory and provides a different realization of the $SU(5)/SO(5)$ coset. The top partners of this model live in the fundamental representation of $SU(5)$, and, as a result, the effective potential of this model is qualitatively different from the $SO(d)$ gauge theories. We also discuss the role of the isospin-triplet fields contained in the $SU(5)/SO(5)$ coset, and show that, without further constraints on the four-fermion couplings, an expectation value for the the Higgs field will trigger the subsequent condensation of an isospin-triplet field.
Highlights
Among the mechanisms that have been proposed to keep the Higgs particle naturally light, the so-called composite Higgs paradigm [1,2] postulates the existence of a new strong sector, perhaps in the few TeV range, based on an asymptotically free gauge theory that we will call hypercolor
We revisit the effective potential of another composite Higgs model that we have studied previously, which is based on an SUð4Þ gauge theory and provides a different realization of the SUð5Þ=SOð5Þ coset
We studied in detail several concrete realizations of this approach as an asymptotically free gauge theory with fermionic matter
Summary
Among the mechanisms that have been proposed to keep the Higgs particle naturally light, the so-called composite Higgs paradigm [1,2] postulates the existence of a new strong sector, perhaps in the few TeV range, based on an asymptotically free gauge theory that we will call hypercolor. When we couple the Standard Model and the hypercolor theory, this breaks explicitly the flavor symmetry group of the hypercolor theory to a smaller group, thereby generating an effective potential for the pseudo-Nambu-Goldstone bosons (pNGBs). The effective potential induced by the coupling of electroweak gauge bosons to the hypercolor theory has its minimum at the origin for the Higgs field. The SUð5Þ=SOð5Þ effective potential will in general contain cubic terms of the form ∼h2φ, where h is the physical Higgs, and φ is one of the nine new pNGBs.. To shed more light on this issue we calculate the full potential in the case that all the SUð5Þ=SOð5Þ pNGBs are turned off except for h and φ, and we discuss whether, and if so, how, those problematic cubic terms might be avoided.
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