(The) several bounds on the Higgs Boson mass

Abstract

As one of the last remnant of the particles which the SM predicts the Higgs boson is important. And the discovery of the Higgs boson will give us a hint of the origin of the mass and the symmetry breaking mechanism. The forecoming higher energy experiments like as LEP2 and LHC give us the hope for finding this particle if the mass of this particle $M_H$ is within the reach of these experiments. Therefore the study of the bounds on the Higgs boson mass is one of the most important problems now. We consider three kinds of theoretical bounds. There are two bounds on the Higgs boson mass from the SM. One is the lower bound from the requirement of the stability of the electroweak vacuum. The other bound from the SM is the upper bound from the requirement of perturbativity of $\lambda$. One of the extensions of the SM, the MSSM is one of the most important expansion. The upper bound on the lightest CP-even scalar mass can be obtained under the conditions of $M_A~M_{SUSY}$, maximal stop mixing and large β. There are experimental bounds on the Higgs boson mass. The failures of the direct searchs at LEP1 have set a lower bound : $M_H^{Direct}$ > 65.2 GeV. Besides these direct searches, there is an indirect estimation of the Higgs boson mass from the high precision LEP data. Recently $R_b$ and $R_c$ show important discrepancies from the predictions of the SM. The estimation of $M_H$ from the LEP precision data heavily depends on $R_b$. We fit to the LEP data with prescriptions of the nonuniversal interactions acting on only the b-, c-, and s-quark to explain $R_b$-$R_c$ crisis.