Dynamical symmetry breaking and the top-quark mass

Dynamical symmetry breaking by fermion condensates is assumed to be the source of gauge-boson masses in the ${\mathrm{SU}\mathrm{}\left(3\right)\mathrm{}}_C\times {\mathrm{SU}\mathrm{}\left(2\right)\mathrm{}}_L\times \mathrm{U}\mathrm{}\left(1\right)\mathrm{}$ model. For the minimal case of $t\overline{t}$ condensation alone, the predicted $m_t$ ranges from about 98 to 450 GeV as the scale of "new physics," responsible for $m_t$, $\Lambda$, goes from $\infty$ to ∼1 TeV. The lighter values, $m_t\lesssim 200$ GeV, all correspond to "great desert" scenarios with $\Lambda \gtrsim m_{\mathrm{Planck}}\simeq 2\times {10}^{19}$ GeV. Including a fourth generation of fermion condensates can lower $m_t$. In the case of maximal $t-t^{\prime }$ mixing, we find $m_t\simeq m_{t^{\prime }}\simeq \left(\frac{\sqrt{3}}{2}\right)m_{b^{\prime }}$ with $m_t$ ranging from about 90 to 250 GeV, and $m_t\simeq 140$ GeV for $\Lambda \simeq {10}^{15}-{10}^{19}$ GeV. For smaller mixing, $m_{t^{\prime }}$ is lowered and $m_{b^{\prime }}$ approaches $m_t\lesssim 200$. We speculate as to how, using strong-coupling unitarity conditions, one might have $\Lambda$ GeV with $\Lambda$ far below $m_{\mathrm{Planck}}$. Phenomenological constraints and consequences are also discussed.