MSSM with $m_{h}=125$ GeV in High-Scale Gauge Mediation

Abstract: After the discovery of SM-like Higgs with $m_{h}=125$ GeV, it is increasingly urgent to explore a solution to the hierarchy problem. In the context of MSSM from gauge-mediated SUSY breaking, the lower bound on gluino mass suggests that the messenger scale $M$ is probably large if the magnitude of $\Lambda\sim 100$ TeV. In this paper, we study $\overline{\mathbf{5}}+ \mathbf{5}$ model with $M\sim 10^{8}-10^{12}$ GeV and $\Lambda\simeq 100$ TeV. For moderate Higgs-messenger coupling, it will be shown a viable model with moderate fine tuning. In this model, $\mu\sim 800$ GeV and $B_{\mu}$ nearly vanishes at input scale, which can be constructed in microscopic model.