Peccei-Quinn extended gauge-mediation model with vector-like matter
  We construct a gauge-mediated SUSY breaking model with vector-like matters combined with the Peccei-Quinn mechanism to solve the strong CP problem. The Peccei-Quinn symmetry plays an essential role for generating sizable masses for the vector-like matters and the $\mu$-term without introducing dangerous CP angle. The model naturally explains both the 125GeV Higgs mass and the muon anomalous magnetic moment. The stabilization of the Peccei-Quinn scalar and the cosmology of the saxion and axino are also discussed. 
Kazunori Nakayama and Norimi Yokozaki
hep-ph