A natural solution for the μ problem with anomalous U(1)A gauge symmetry

Recently we proposed an attractive scenario of grand unified theories with anomalous U(1)A gauge symmetry, in which doublet–triplet splitting is naturally realized in SO(10) unification using Dimopoulos–Wilczek mechanism and realistic quark and lepton mass matrices can be obtained in a simple way. In this Letter we show that there is a mechanism in which the doublet Higgs obtains the supersymmetric mass which is proportional to the SUSY breaking parameters. This mechanism can be applied easily in the above scenario. The point is that the mass term, which is forbidden by SUSY zero mechanism, can be induced by SUSY breaking. The proportional coefficient is controlled by the anomalous U(1)A charges.