Anomalous U(1) symmetry and missing doublet SU(5) model

We present the supersymmetric SU(5) models which provide a simple “all order” solution to the doublet-triplet splitting problem through the missing doublet mechanism. The crucial role is played by the anomalous U(1)A gauge symmetry and no additional discrete or global symmetries are needed. Remarkably, such models can be realized even if the 75-plet Higgs is replaced by the standard 24-plet. The same U(1)A symmetry can also guarantee an exact or approximate conservation of R parity, by suppressing the B and L violating operators to the needed level. The neutrino masses and the proton decay via d = 5 operators are also examined. We also extend the model by incorporating U(1)A as a horizontal symmetry for explaining the fermion mass and mixing hierarchy. Interestingly, in this scheme the necessary mild violation of the troublesome SU(5) degeneracy between the down quark and the charged lepton masses can be induced by certain R-parity violating operatiors.