Top Mass and Isospin Breaking in Dynamical Symmetry Breaking Scenario

We consider a scenario where the top-quark mass is generated dynamically, and study the implication of the present experimental values for $m_t$ and the $T$ parameter. We assume technicolor-like scenario for inducing the $W$ 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 $G$ and the intrinsic mass scale $M$ of the four fermi operator. Unitarity bound is used to quantify the strength of $G$. We find that $G/4\pi \sim {\cal O}(1)$ and that $M$ is of the order of $\Lambda_{TC} \simeq 1 \sim 2$~TeV or less. Namely the four fermi operator cannot be treated as `point-like' around the electroweak scale. Furthermore we estimate the contribution of the four fermi operator to the $T$ parameter. We find that the QCD correction to the top-quark mass function reduces the contribution to the $T$ parameter by about 40\%. By comparing the results with the present experimental bound, we obtain another upper bound on $M$ which is typically in several to 10~TeV region.