SUSY breaking mediation mechanisms and (g-2)_μ, B -> X_s γ, B -> X_{s} l^+ l^- and B_s -> μ^+ μ^-

Abstract

We show that there are qualitative differences in correlations among $(g-2)_μ$, $B\to X_s γ$, $B \to X_{s} l^+ l^-$ and $B_s \to μ^+ μ^-$ in various SUSY breaking mediation mechanisms: minimal supergravity (mSUGRA), gauge mediation (GMSB), anomaly mediation (AMSB), gaugino mediation ($\tilde{g}$MSB), weakly and strongly interacting string theories, and $D$ brane models. After imposing the direct search limits on the Higgs boson and SUSY particle search limits and $B\to X_s γ$ branching ratio, we find all the scenarios can accommodate the $a_μ\equiv (g-2)_μ/2 $ in the range of (a few tens)$\times 10^{-10}$, and predict that the branching ratio for $B\to X_s l^+ l^-$ can differ from the standard model (SM) prediction by $\pm 20 %$ but no more. On the other hand, the $B_s \to μ^+ μ^-$ is sensitive to the SUSY breaking mediation mechanisms through the pseudoscalar and stop masses ($m_A$ and $m_{\tilde{t}_1}$), and the stop mixing angle. In the GMSB with a small messenger number, the AMSB, the $\tilde{g}$MSB and the noscale scenarios, one finds that $B(B_s \to μ^+ μ^-) \lesssim 2 \times 10^{-8}$, which is below the search limit at the Tevatron Run II. Only the mSUGRA or string inspired models can generate a large branching ratio for this decay.