  In general, we can propose the hybrid supersymmetry breakings and hybrid
mediations in the Supersymmetric Standard Models (SSMs). In this paper, we
study the hybrid mediation for supersymmetry (SUSY) breaking. In particular, we
study how to keep the good properties of gravity mediation, gauge mediation,
and anomaly mediation, while solve their problems simultaneously. As an
example, we consider the anomaly-gravity mediation, where all the
supersymmetric particles (sparticles) obtain the SUSY breaking soft terms from
the traditional gravity mediation while gauge mediation gives dominant
contributions to the soft terms in the colored sector due to the splitted
messengers. Thus, we can realize the electroweak supersymmetry naturally where
the sleptons, sneutrinos, and electroweakinos are light within one TeV while
the squarks and gluino are heavy around a few TeVs. And then we can explain 125
GeV Higgs mass, satisfy the LHC SUSY search bounds, and explain the anomalous
magnetic momement of muon, etc. Moreover, the gluino and squarks are well
beyond the current LHC Run II searches.
