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The Supersymmetric Standard Models with a Pseudo-Dirac Gluino from Hybrid $F-$ and $D-$Term Supersymmetry Breakings

We propose the Supersymmetric Standard Models (SSMs) with a pseudo-Dirac gluino from hybrid $F-$ and $D-$term supersymmetry (SUSY) breakings. Similar to the SSMs before the LHC, all the supersymmetric particles in the Minimal SSM (MSSM) obtain the SUSY breaking soft terms from the traditional gravity mediation and have masses within about 1 TeV except gluino. To evade the LHC SUSY search constraints, the gluino also has a heavy Dirac mass above 3 TeV from $D-$term SUSY breaking. Interestingly, such a heavy Dirac gluino mass will not induce the electroweak fine-tuning problem. We realize such SUSY breakings via an anomalous $U(1)_X$ gauge symmetry inspired from string models. To maintain the gauge coupling unification and increase the Higgs boson mass, we introduce extra vector-like particles. We study the viable parameter space which satisfies all the current experimental constraints, and present a concrete benchmark point. This kind of models not only preserves the merits of pre-LHC SSMs such as naturalness, dark matter, etc, but also solves the possible problems in the SSMs with Dirac gauginos due to the $F$-term gravity mediation.