Top-quark mass and isospin breaking in the dynamical symmetry-breaking scenario

We consider a scenario where the top-quark mass is generated dynamically, and study the implications of the present experimental values for [Formula presented] and the [Formula presented] parameter. We assume a technicolorlike scenario for inducing the [Formula presented] mass and an effective four-Fermi operator for inducing the top-quark mass. We also assume that only this four-Fermi operator is relevant at low energy. Then we estimate in detail the strength [Formula presented] and the intrinsic mass scale [Formula presented] of the four-Fermi operator. A unitarity bound is used to quantify the strength of [Formula presented]. We find that [Formula presented] and that [Formula presented] is of the order of [Formula presented] TeV or less. Namely the four-Fermi operator cannot be treated as "pointlike" around the electroweak scale. Furthermore we estimate the contribution of the four-Fermi operator to the [Formula presented] parameter. We find that the QCD correction to the top-quark mass function reduces the contribution to the [Formula presented] parameter by about 40%. By comparing the results with the present experimental bound, we obtain another upper bound on [Formula presented] which is typically in the several to 10 TeV region.