New mechanism for the top-bottom mass hierarchy

We propose a mechanism to generate hierarchy between masses of the top and bottom quarks without fine tuning of the Yukawa coupling constants in the context of the two Higgs doublet model (THDM). In the THDM with a discrete symmetry, there exists the vacuum where only the top quark receives the mass of the order of the electroweak symmetry breaking scale $v(\simeq 246 GeV)$, while the bottom quark remains massless. By introducing a small soft-breaking parameter $m_3^2$ of the discrete symmetry, the bottom quark perturbatively acquires a nonzero mass. We show a model in which the small $m_3^2 [\sim v^2/(4\pi)^2]$ is generated by the dynamics above the cutoff scale of the THDM. The ratio $\tan\beta$ of the two vacuum expectation values is necessarily very large; i.e., $\tan \beta \sim m_t/m_b$. We also find a salient relation, $1/\tan\beta \simeq m_3^2/m_H^2$, where $m_H$ is the mass of the extra CP-even Higgs boson. Our scenario yields some specific features that can be tested in future collider experiments.