The Role of the Anomalous U(1)_A for the Solution of the Doublet-Triplet Splitting Problem

Abstract

The anomalous U(1)_A symmetry provides a generic method of getting accidental symmetries. Therefore, it can play a crucial role in solving the doublet-triplet splitting and the μ-problems via the `pseudo-Goldstone' mechanism: U(1)_A can naturally uncorrelate the two grand unified Higgs sectors in the superpotential and simultaneously induce the desired expectation values through the Fayet-Iliopoulos D-term. The zero modes of the resulting compact vacuum degeneracy can be identified with the massless electroweak Higgs doublets. This automatically solves the doublet-triplet splitting and the μ-problems to all orders in M_P^{-1}. No additional discrete or global symmetries are needed. U(1)_A can also play the role of the `matter parity' and suppress the baryon number violating operators. We present the simplest SU(6) gauge model with a minimal Higgs sector and no doublet-triplet splitting problem. This model also relates the fermion mass hierarchy to the hierarchy of scales and predicts, for the generic non-minimal Kahler potential, approximately universal values for the tree-level electroweak Higgs mass parameters.