Solution for little hierarchy problem andb→sγ

We show that all the parameters which destabilize the weak scale can be taken around the weak scale in the MSSM without conflicting with the SM Higgs mass bound set by LEP experiment. The essential point is that if the lightest $CP$-even Higgs $h$ in the MSSM has only a small coupling to $Z$ boson, $g_{ZZh}$, LEP cannot generate the Higgs sufficiently. In the scenario, the SM Higgs mass bound constrains the mass of the heaviest $CP$-even Higgs $H$ which has the SM like $g_{ZZH}$ coupling. However, it is easier to make the heaviest Higgs heavy by the effect of off-diagonal elements of the mass matrix of the $CP$-even Higgs because the larger eigenvalue of $2\times 2$ matrix becomes larger by introducing off-diagonal elements. Thus, the smaller stop masses can be consistent with the LEP constraints. Moreover, the two excesses observed at LEP Higgs search can naturally be explained as the signals of the MSSM Higgs $h$ and $H$ in this scenario. One of the most interesting results in the scenario is that all the Higgs in the MSSM have the weak scale masses. For example, the charged Higgs mass should be around 130 GeV. This looks inconsistent with the lower bound obtained by the $b\to s\gamma$ process as $m_{H^{\pm }}>350\mathrm{GeV}$. However, we show that the amplitude induced by the charged Higgs can naturally be compensated by that of the chargino if we take the mass parameters by which the little hierarchy problem can be solved. The point is that the both amplitudes have the same order of magnitudes when all the fields in the both loops have the same order of masses.