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 $a_{\mu}^{\rm SUSY}$ becomes lower to $35 \times 10^{-10}$ for intermediate string scale. The resulting LSP - proton scattering cross section is less than $\sim 10^{-7}$ pb, which is below the sensitivity of the current direct dark matter search experiments, but could be covered by future experiments.