In the context of Calabi-Yau string models we explore the origin of characteristic pattern of quark-lepton masses and the CKM matrix. The discrete $R$-symmetry $Z_K \times Z_2$ is introduced and the $Z_2$ is assigned to the $R$-parity. The gauge symmetry at the string scale, $SU(6) \times SU(2)_R$, is broken into the standard model gauge group at a very large intermediate energy scale. At energies below the intermediate scale down-type quarks and also leptons are mixed with unobserved heavy states, respectively. On the other hand, there are no such mixings for up-type quarks. Due to the large mixings between light states and heavy ones we can derive phenomenologically viable fermion mass hierarchies and the CKM matrix. Mass spectra for intermediate-scale matter beyond the MSSM are also determined. Within this framework proton lifetime is long enough to be consistent with experimental data. As for the string scale unification of gauge couplings, however, consistent solutions are not yet found.Comment: 49 pages, 1 figure, Latex Revised version includes discussion on FCNC problems. Final version to appear in Prog. Theor. Phys. Vol.96 No.

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In the four-dimensional effective theory from string compactification discrete flavor symmetries arise from symmetric structure of the compactified space and generally contain both the R symmetry and non-R symmetry. We point out that a new type of non-Abelian flavor symmetry can also appear if the compact space is non-commutative. Introducing the dihedral group D 4 as such a new type of flavor symmetry together with the R symmetry and non-R symmetry in SU (6) × SU (2) R model, we explain not only fermion mass hierarchies but also hierarchical energy scales including the breaking scale of the GUT-type gauge symmetry, intermediate Majorana masses of R-handed neutrinos and the scale of µ-term.

There are experimental indications of large flavor mixing between ν µ and ν τ . In the unification models, in which the massless sector includes extra particles beyond the standard model, there possibly appear the mixings between quarks (leptons) and the extra particles. When large mixings occur, lepton flavor mixings can be quite different from quark flavor mixings. By taking the string inspired SU (6) × SU (2) R model with global flavor symmetries, we obtain the neutrino flavor mixing sin θ 23 ≃ λ = sin θ C around the unification scale. It can be expected that due to large Yukawa couplings of neutrinos, the renormalization effect increases sin 2θ 23 naturally up to ∼ 1 at the electroweak scale. Fermion mass spectra and the CKM matrix of quarks obtained in this paper are also phenomenologically viable.

In Calabi-Yau superstring models it is found that two large intermediate energy scales of symmetry breaking can be induced for special types of the nonrenormalizable interactions. In the models one set of SO(10)-singlet, righthanded neutrino and their mirror chiral superfields is needed. Through the study of the minimization of the scalarpotential, the conditions for the presence of two large intermediate scales are obtained. In this scheme a Majorana-mass possibly amounts to O(10 9∼10 GeV). This large Majorana-mass solves the solar neutrino problem and also is compatible with the cosmological bound for stable light neutrinos.