New mechanism for the top-bottom mass hierarchy

Abstract

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 $v(\ensuremath{\simeq}246\text{ }\text{ }\mathrm{G}\mathrm{e}\mathrm{V})$, 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 ${m}_{3}^{2}[\ensuremath{\sim}{v}^{2}/(4\ensuremath{\pi}{)}^{2}]$ is generated by the dynamics above the cutoff scale of the THDM. The ratio $\mathrm{tan}\ensuremath{\beta}$ of the two vacuum expectation values is necessarily very large, i.e., $\mathrm{tan}\ensuremath{\beta}\ensuremath{\sim}{m}_{t}/{m}_{b}$. We also find a salient relation, $1/\mathrm{tan}\ensuremath{\beta}\ensuremath{\simeq}{m}_{3}^{2}/{m}_{H}^{2}$, 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.