The electroweak symmetry breaking Higgs boson in models with top-quark condensation

The top quark may get its large mass not from a fundamental scalar but a NambuJona-Lasinio mechanism involving a strongly coupled gauge sector that triggers topquark condensation. Forbidding a large hierarchy in the gap equation implies that top quark condensation is a spectator to electroweak symmetry breaking, which must be accomplished mainly by another sector. The properties of the electroweak symmetry breaking scalars are identified. Production mechanisms and decay modes are studied. Unlike the standard model, the scalar degree of freedom most relevant to electroweak symmetry breaking can only be produced by its gauge interactions. An e±e±μ∓ + μ ± μ ± e ∓ signal is proposed to help unambiguously detect the presence of such a gaugecoupled Higgs if it is light. Other useful modes of detection are also presented, and a summary is made of the search capabilities at LEPII, Tevatron and LHC. Work supported by the Department of Energy under contract DE-AC03-76SF00515. 1 Finetuning and the top-quark gap equation As it became clear that the top quark is very massive attention was naturally turned to top-quark condensate models [1, 2, 3] which rely on the gauged Nambu-Jona-Lasinio (NJL) model [4]. Starting with a four fermion interaction L = L‖〉\ + G ψL⊔R ⊔RψL where ψL = (⊔L, ⌊L) (1) a gap equation can be formulated for the dynamical top quark mass G−1 = Nc 8π2 ( Λ −mt log Λ mt ) . (2) Furthermore, in the fermion bubble approximation, with the above gap equation enforced, zeros of the inverse gauge boson propagators are found at non-zero momentum. This gives mass to the gauge bosons and corresponds [5, 3, 6] to a decay constant of f 2 πt ≃ Nc 16π2 mt log Λ mt . (3) This relation is often referred to as the Pagels-Stokar formula. In order for the top-quark condensate to account for all of electroweak symmetry breaking, fπt needs to be equal to v = 175GeV. The currently measured top quark mass is mt = 175±6GeV [7], which means that Λ would have to be about thirteen orders of magnitude above mW to account for all of electroweak symmetry breaking, an uninspiring result for pure top-quark condensate models. The Pagels-Stokar relation is logarithmically sensitive to the condensate scale, and provides only a relationship between the decay constant and dynamical quark mass, not the overall scale of these parameters. The gap equation, on the other hand, sets the overall scale of mt and therefore fπt . The quadratic sensitivity to the condensate scale induces a large hierarchy problem for the weak scale (mt and fπt) if Λ is above a few TeV. For large Λ the four-fermion coupling G must be tuned to one part in Λ/mt . For a condensate scale in the multi-TeV region, this finetuning is greater than one part in 10. It will be assumed here that finetunings much above this are unnatural, and are probably not maintained by nature [8]. Therefore, from the Pagels-Stokar relation the decay constant associated with top-quark condensation is fπt < ∼ 60GeV, implying that top-quark condensation is a spectator to electroweak symmetry breaking (EWSB). That is, top-quark condensation mainly