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

Motivated by the recently measured muon 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 dilaton or modulus-mediated models in heterotic string or M theory, gauge-mediated model, no-scale or gaugino-mediated models, and also the minimal and deflected anomaly-mediated models. For each model, the range of $a_{\mu }^{\mathrm{SUSY}}$ allowed by other experimental constraints, e.g., $\overrightarrow{b}s\gamma$ and the collider bounds on superparticle masses, is obtained together with the corresponding parameter region of the model. Gauge-mediated models with a low messenger scale can give any $a_{\mu }^{\mathrm{SUSY}}$ within the $2\sigma$ bound. In many other models, $\overrightarrow{b}s\gamma$ favors $a_{\mu }^{\mathrm{SUSY}}$ smaller than either the $-1\sigma$ value $(26\mathrm{}\times {10}^{-10})$ or the central value $(42\mathrm{}\times {10}^{-10}).\mathrm{}$