Simple models of top-color and top-color-assisted technicolor rely on a relatively strong $\mathrm{U}\mathrm{}\left(1\right)\mathrm{}$ 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–Jona-Lasinio approximation often used to analyze the top-color 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 $\mathrm{U}\mathrm{}\left(1\right)\mathrm{}$ gauge theory be sufficiently above the top-color gauge boson scale, we derive an upper bound on the strength of the $\mathrm{U}\mathrm{}\left(1\right)\mathrm{}$ gauge coupling evaluated at the top-color scale. The upper bound on the $\mathrm{U}\mathrm{}\left(1\right)\mathrm{}$ coupling implies that these interactions can shift the composite Higgs boson mass-squared by only a few percent and, therefore, that the top-color coupling must be adjusted to equal the critical value for chiral symmetry breaking to within a few percent.

• Received 11 June 1998

DOI:https://doi.org/10.1103/PhysRevD.58.115009