Muon anomalous magnetic dipole moment in the $\mu$-problem solvable extra U(1) models

The recent measurement of the muon anomalous magnetic dipole moment shows 2.6$\sigma$ deviation of $a_\mu$ from the standard model prediction which can be explained by a chargino-sneutrino loop correction in the supersymmetric models. In this paper we consider extra U(1) models where the $\mu$ parameter is radiatively generated. This model predicts the sign of $\mu$ is positive in wide parameter regions. But even the 2$\sigma$ constraint causes a serious contradiction to the experimental bound of the extra neutral gauge boson mass. Although a minimal supergravity scenario is ruled out, a very small window is remained as an allowed region for a no-scale model with non-universal gaugino masses.