Abstract
The composite Higgs models based on the top seesaw mechanism commonly possess an enhanced approximate chiral symmetry, which is spontaneously broken to produce the Higgs field as the pseudo-Nambu-Goldstone bosons. The minimal model with only one extra vector-like singlet quark that mixes with the top quark can naturally give rise to a 126 GeV Higgs boson. However, without having a custodial symmetry it suffers from the weak-isospin violation constraint, which pushes the chiral symmetry breaking scale above a few TeV, causing a substantial fine-tuning for the weak scale. We consider an extension to the minimal model to incorporate the custodial symmetry by adding a vector-like electroweak doublet of quarks with hypercharge +7/6. Such a setup also protects the $$ Zb\overline{b} $$ coupling which is another challenge for many composite Higgs models. With this addition, the chiral symmetry breaking scale can be lowered to around 1 TeV, making the theory much less fine-tuned. The Higgs is a pseudo-Nambu-Goldstone boson of the broken O(5) symmetry. For the Higgs mass to be 126 GeV, the hypercharge +7/6 quarks should be around or below the chiral symmetry breaking scale, and are likely to be the lightest new states. The 14 TeV LHC will significantly extend the search reach of these quarks. To probe the rest of the spectrum, on the other hand, would require a higher-energy future collider.
Highlights
Seesaw model fixes the problem of the top quark being too heavy in the top condensation model [14,15,16,17,18] by mixing the top quark with a new vector-like quark χ
Without having a custodial symmetry it suffers from the weak-isospin violation constraint, which pushes the chiral symmetry breaking scale above a few TeV, causing a substantial fine-tuning for the weak scale
The U(3)L symmetry does not contain the SU(2) custodial symmetry and we just recover the minimal model of ref. [7] in this limit, which makes the extension of the hypercharge +7/6 quarks (X and T ) and the corresponding composite scalars totally pointless! To solve this problem, we introduce the following mass terms
Summary
As in the usual composite Higgs models, we assume that at a scale Λ 1 TeV there are no fundamental scalars. (This guarantees that the VEV of triplet scalars are suppressed.) Matching at the scale Λ, the size of the tadpole terms are related to the fermion mass terms by CQ μQ ξ. This means that at scale μ < Λ we do not need to include the explicit fermion mass terms in eq (2.1) They will appear from the scalar VEVs in the low energy effective theory. Eq (3.1) has an U(5)L chiral symmetry which is explicitly broken by the heavy field VEVs w and ut and the tadpole term Cχχ. Without the explicit breaking terms, U(5)L is spontaneously broken to U(4)L due to a negative mass-squared MΦ2χ, and Φχ contains 9 NGBs which includes two massless Higgs doublets.
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