Damped $\sin (\beta -\alpha )$ of Higgs couplings and the lightest Higgs production at $\gamma \gamma$ colliders in MSSM

In the decoupling limit, $M_{A^0}^2\gg M_Z^2$, the heavy CP-even, CP-odd and charged Higgs boson masses are nearly degenerate, $\sin (\beta -\alpha )$ approaches 1, and the lightest CP-even Higgs boson almost displays the same properties as the Standard Model Higgs boson. But the stop and sbottom sector can change this pattern through radiative corrections. We find that there are parameter regions at small, moderate and large $\tan \beta$ in MSSM under experimental constraints of $(g-2{)}_{\mu }$ and $b\to s\gamma$, where ${\sin }^2(\beta -\alpha )$ is damped (say below 0.8), which has a significant effect on Higgs couplings $g_{h^{0}VV}(V=W^{\pm },Z^0)$ and $g_{h^0\gamma \gamma }$. We discuss its impact on the lightest CP-even Higgs production at $\gamma \gamma$ colliders.