Natural $μ$-term with Peccei-Quinn Symmetry

The generalized Higgs mass term $NH_1H_2$ of the supersymmetric standard model is used to implement the Peccei-Quinn Symmetry to solve the strong-CP problem. Then supersymmetry breaking can generate the Higgs mass parameter $\mu$ of order $m_{3/2}$ through soft-breaking parameters. This kind of extension contains extra light fields of the axion supermultiplet whose dominant coupling may come from the supersymmetric axion-Higgs-Higgs coupling. We present a working example and discuss the cosmological implications of the model.