New fermion mass textures from anomalous U(1) symmetries with baryon and lepton number conservation

In this paper, we present solutions to the fermion mass hierarchy problem in the context of the minimal supersymmetric standard theory augmented by an anomalous family-dependent U(1)_X symmetry. The latter is spontaneously broken by non-zero vevs of a pair of singlet fields whose magnitude is determined through the D- and F-flatness conditions of the superpotential. We derive the general solutions to the anomaly cancellation conditions and show that they allow numerous choices for the U(1)_X fermion charges which give several fermion mass textures in agreement with the observed fermion mass hierarchy and mixing. Solutions with U(1)_X fermion charge assignments are found which forbid or substantially suppress the dangerous baryon and lepton number violating operators and the lepton-higgs mixing coupling while a higgs mixing mass classification of the fermion mass textures with respect to the sum of the doublet-higgs U(1)_X-charges and show that suppression of dimension-five operators naturally occurs for various charge assignments. We work out cases which retain a quartic term providing the left-handed neutrinos with Majorana masses in the absence of right-handed neutrino components and consistent with the experimental bounds. Although there exist solutions which naturally combine all the above features with rather natural U(1)_X charges, the suppression of the \mu-term occurs for particular assignments.