paper

Effective potential in ultraviolet completions for composite Higgs models

arXiv:1707.06033 · doi:10.1103/PhysRevD.97.095005

Abstract

We consider a class of composite Higgs models based on asymptotically free gauge theories with 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 or , whereas the top partners live in two-index representations of the relevant flavor group ( or ). 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 gauge theory and provides a different realization of the coset. The top partners of this model live in the fundamental representation of , and, as a result, the effective potential of this model is qualitatively different from the gauge theories. We also discuss the role of the isospin-triplet fields contained in the 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.

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