Gauge Coupling Unification with Anomalous U(1)_A Gauge Symmetry

Abstract

Recently we proposed a natural scenario of grand unified theories with anomalous U(1)_A gauge symmetry, in which doublet-triplet splitting is realized in SO(10) unification using Dimopoulos-Wilczek mechanism and realistic quark and lepton mass matrices can be obtained in a simple way. The scenario has an additional remarkable feature that the symmetry breaking scale and the mass spectrum of super heavy particles are determined essentially by anomalous U(1)_A charges. Therefore once all the anomalous U(1)_A charges are fixed, the gauge coupling flows can be calculated. We examine several models in which the gauge coupling unification is realized. Examining the conditions for the coupling unification, we show that when all the fields except those of the minimal SUSY standard model become super-heavy, the unification scale generically becomes just below the usual GUT scale Λ_G\sim 2\times 10^{16} GeV and the cutoff scale becomes around Λ_G. Since the lower GUT scale leads to shorter life time of nucleon, the proton decay via dimension six operator p\to e^+π^0 can be seen in future experiment. On the other hand, the lower cutoff scale than the Planck scale may imply the existence of extra dimension in which only gravity modes can propagate.