Muon anomalous magnetic moment, $B\to X_s γ$ and dark matter detection in the string models with dilaton domination

We consider the muon anomalous magnetic moment $a_{\mu}$ in the string models with dilaton domination with two different string scales : the usual GUT scale and the intermediate scale. After imposing the direct search limits on the lightest neutral Higgs and SUSY particle masses and the lightest neutralino LSP, the $a_{\mu}^{\rm SUSY}$ is predicted to be less than $ 65~ (55) \times 10^{-10}$ for $M_{string} = 2 \times 10^{16}$ GeV ($3 \times 10^{11}$ GeV). If we further impose the $B\to X_s \gamma$ branching ratio, the predicted $a_{\mu}$ becomes lower : $ 30 ~(20) \times 10^{-10}$ for two different string scales, respectively. The resulting LSP - proton scattering cross section is not larger than $\sim 2.5 ~(6.5) \times 10^{-8}$ pb, which is far below the DAMA sensitivity.