Probing the messenger of supersymmetry breaking by the muon anomalous magnetic moment

Motivated by the recently measured muon's anomalous magnetic moment $a_{\mu}$, we examine the supersymmetry contribution to $a_{\mu}$ in various mediation models of supersymmetry breaking which lead to predictive flavor conserving soft parameters at high energy scale. The studied models include the dilaton/modulus-mediated model in heterotic string/$M$ theory, gauge-mediated model, no-scale or gaugino-mediated model, and also the minimal and deflected anomaly-mediated models. When other experimental constraints, e.g. $b -> s\gamma$ and the collider bounds on superparticle masses, are taken into account, only a small fraction of the parameter space of the model can give $a^{\rm SUSY}_{\mu}$ which is {\it not} smaller than the $-2\sigma$ value ($10\times 10^{-10}$) except for the gauge mediation model with a relatively low messenger scale. It is pointed out that a more involved analysis of $b -> s\gamma$ can make the allowed value of $a^{\rm SUSY}_{\mu}$ even smaller.