Top quark effects on the scalar sector of the minimal Standard Model

Abstract

We study effects of the heavy top quark ($m_t\approx 180GeV$) on the scalar sector of the minimal Standard Model. We construct the effective potential for the scalar doublet, by first taking into account the leading contributions of the top quark loops. Minimizing this potential gives us a condition analogous to the leading-Nc gap equation of the standard $\bar{t}t$-condensation model (Top-mode standard model). This essentially nonperturbative condition leads to a low ultraviolet cutoff $\text{L}=O(1TeV)$ in the case when the bare mass $\mu$ of the scalar doublet in the tree level potential satisfies ${\mu }^2=-M_0^2\le 0$ and the scalar doublet there is selfinteracting ($\lambda >0$). We demand that the scalar selfinteraction behave perturbatively -- in the sense that its 1-loop contributions influence the effective poten- tial distinctly less than those of the Yukawa coupling of the heavy top quark. When we subsequently include the 1-loop contributions of the scalar and the gauge bosonic sectors in a perturbative manner, the results change numerically, but the cutoff $\text{L}$ remains $O(1TeV)$. The resulting Higgs mass $M_H$ is then in the range 150-250 GeV. Furthermore, the results of the paper survive even in the case when the square of the bare mass ${\mu }^2$ is positive, as long as ${\mu }^2\le O(\lambda v^2)$, where $\lambda /4!$ is the usual bare coupling parameter of the quartic selfinteraction of the scalars and $v$ is the vacuum expectation value ($v=246.2\text{GeV}$, $M_H^2\approx \lambda v^2/3$).

Comments: standard LaTex, 24 pages, 3 ps figures; references updated; reference [4] pointed out in Introduction; reference [11] added; no other changes; to appear in Int.J.Mod.Phys.A