Gauged Peccei-Quinn symmetry — A case of simultaneous breaking of SUSY and PQ symmetry

Recently, a simple prescription to embed the global Peccei-Quinn (PQ) symmetry into a gauged $U\left(1\right)$ symmetry has been proposed. There, explicit breaking of the global PQ symmetry expected in quantum gravity are highly suppressed due to the gauged PQ symmetry. In this paper, we apply the gauged PQ mechanism to models where the global PQ symmetry and supersymmetry (SUSY) are simultaneously broken at around $O\left({10}^{11-12}\right)$ GeV. Such scenario is motivated by an intriguing coincidence between the supersymmetry breaking scale which explains the observed Higgs boson mass by the gravity mediated sfermion masses, and the PQ breaking scale which evades all the astrophysical and the cosmological constraints. As a concrete example, we construct a model which consists of a simultaneous supersymmetry/PQ symmetry breaking sector based on $SU\left(2\right)$ dynamics and an additional PQ symmetry breaking sector based on $SU\left(N\right)$ dynamics. We also show that new vector-like particles are predicted in the TeV range in the minimum model, which can be tested by the LHC experiments.