Patterns of quark mass matrices in a class of Calabi-Yau models

Abstract

We study a class of superstring models compactified in the 3-generation Calabi-Yau manifold of Tian and Yau. Our analysis includes the complete $E_6$-singlet sector, which has been recently evaluated using techniques of spectral and exact sequences. We use the discrete symmetries of the models to find flat directions of symmetry breaking that leave unbroken a low energy matter parity and make all leptoquarks heavy while preserving light Higgs fields. Then we classify the patterns of ordinary quark mass matrices and show that (without invoking effects due to nonrenormalizable terms) only one structure can accommodate the observed value of fermion masses and mixing angles, with preference for a heavy {\it top} quark ( $m_t\ge 170$ GeV for $V_{13}\le 0.013$ ). The model, which unifies perturbatively and predicts a realistic structure of quark mass matrices with texture zeroes, is one of the many possible string vacua. However, in contrast with what is often assumed in the search for realistic unified scenarios, it is highly nonminimal near the unification scale and the predicted mass matrices have no simple symmetry properties.