Effective field theory of vacuum tilting

Abstract

Simple models of topcolor and topcolor-assisted technicolor rely on a relatively strong U (1) gauge interaction to "tilt" the vacuum. This tilting is necessary to produce a top-condensate, thereby naturally obtaining a heavy top-quark, and to avoid producing a bottom-condensate. We identify some peculiarities of the Nambu-JonaLasinio (NJL) approximation often used to analyze the topcolor dynamics. We resolve these puzzles by constructing the low-energy effective field theory appropriate to a mass-independent renormalization scheme. We construct the power-counting rules for such an effective theory. By requiring that the Landau pole associated with the U (1) gauge theory be sufficiently above the topcolor gauge boson scale, we derive an upper bound on the strength of the U (1) gauge-coupling evaluated at the topcolor scale. The upper bound on the U (1) coupling implies that these interactions can shift the composite Higgs boson mass-squared by only a few per cent and, therefore, that the topcolor coupling must be adjusted to equal the critical value for chiral symmetry breaking to within a few per cent.

Top quark seesaw theory of electroweak symmetry breaking

“…(2.9). Furthermore, the LL and RR interactions do not affect the low-energy effective potential in the large N c limit [8], so we will ignore them (one should keep in mind that these interactions may have other effects, such as contributions to the custodial symmetry violation parameter T [9,8], but these effects are negligible if the topcolor scale is in the multi-TeV range).…”

Electroweak symmetry breaking as a consequence of compact dimensions

“…The important feature here is that the chiral phase transition is second order as c is varied. This property is expected to remain true beyond the large-N c approximation [10]. In the absence of excessive fine-tuning, i.e.…”

Top condensation as a motivated explanation of the top forward-backward asymmetry

“…This bound state should be present in the effective Lagrangian [28] and may be light (of order the top-higgs mass). We will not discuss the bottom-Higgs further simply because it is unrelated to A t F B .…”