A Mechanism for the Top-Bottom Mass Hierarchy

Abstract

We discuss a mechanism to generate hierarchy between masses of the top and bottom quarks without fine-tuning of the Yukawa coupling constants. In the framework of the two-Higgs-doublet model (THDM) with a discrete $Z_2$ 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. We show a model in which a small sofb-breaking mass $m_3^2 [\sim v^2/(4π)^2]$ for the $Z_2$ symmetry is generated by the dynamics above the cutoff scale of the THDM. The appearance of $m_3^2$ gives the small mass for the bottom quark, and explain the hierarchy $m_b/m_t \ll 1$.