Effective potential in ultraviolet completions for composite Higgs models

Abstract

We consider a class of composite Higgs models based on asymptotically free SOðdÞ gauge theories with d odd, with fermions in two irreducible representations, and in which the Higgs field arises as a pseudo-NambuGoldstone boson and the top quark is partially composite. The Nambu-Goldstone coset containing the Higgs field, or Higgs coset, is either SUð4Þ=Spð4Þ or SUð5Þ=SOð5Þ, whereas the top partners live in two-index representations of the relevant flavor group [SUð4Þ or SUð5Þ]. 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 pseudoNambu-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 lowenergy 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 SUð4Þ gauge theory and provides a different realization of the SUð5Þ=SOð5Þ coset. The top partners of this model live in the fundamental representation of SUð5Þ, and, as a result, the effective potential of this model is qualitatively different from the SOðdÞ gauge theories. We also discuss the role of the isospin-triplet fields contained in the SUð5Þ=SOð5Þ coset, and show that, without further constraints on the four-fermion couplings, an expectation value for the Higgs field will trigger the subsequent condensation of an isospin-triplet field.

Phase ambiguity of the measure for continuum Majorana fermions

“…IV A carries over. 13 We next consider the case where N Dirac fermions are traded with 2N Majorana fermions. In the initial Dirac-fermion lattice formulation we again set θ W = 0.…”

Radiative contribution to the composite-Higgs potential in a two-representation lattice model

“…Realization of the Higgs phenomenon requires V eff to have a negative curvature at Σ = 1. This is expected to arise from coupling to the top quark [7,8,11,12,16], which we do not treat here. For phenomenological use of C LR , see for example Ref.…”

Partial compositeness and baryon matrix elements on the lattice

“…Appendix A describes the matching of the effective low-energy theory at the electroweak scale to the hypercolor theory in Ferretti's model [16,17]. Resulting from the calculation are the following expressions for the Yukawa coupling and mass of the top quark,…”