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 $v(\simeq 246GeV)$, while the bottom quark remains massless. We show a model in which a small sofb-breaking mass $m_3^2[\sim v^2/(4\pi {)}^2]$ 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 $m_b/m_t\ll 1$.

Comments: Contribution to the 12th International Conference on Supersymmetry and Unification of Fundamental Interactions (SUSY 2004), June 17-23, 2004, Tsukuba, Japan, talk given by S.K., to appear in the Proceedings