SO(10) unification with horizontal symmetry

We extend the nonsupersymmetric SO(10) grand unification theories by adding a horizontal symmetry, which connects the three generations of fermions. Without committing to any specific symmetry group, we investigate the 1-loop renormalization group evolutions of the gauge couplings with one and two intermediate breaking scales. We find that depending on the SO(10) breaking chains, gauge coupling unification is compatible with only a handful of choices of representations of the Higgs bosons under the horizontal symmetry.Comment: 21 pages, 6 tables. v2: Further clarifications added primarily in Discussions Section, References updated, to be published in PR

Partial Yukawa unification and a supersymmetric origin of flavor mixing

In a large class of supersymmetric SO(10) and left-right models, requiring that the effective theory below the scale of $SU(2)_R$ breaking be the MSSM implies partial Yukawa unification with $Y_u=Y_d$ and $Y_e=Y_{\nu^D}$. The same result also emerges in models with a horizontal $SU(3)_H$ symmetry. As a result, at the tree level, these models lead to vanishing quark mixing angles. We show that the correct mixing pattern can be generated in these models at the loop level from the flavor structure associated with the supersymmetry breaking terms. We generalize the constraints on supersymmetric parameters from flavor changing neutral current (FCNC) processes to include several squark mass insertions and confirm the consistency of the scheme. The expectations of this scheme for CP violating observables in the $B$ meson system are quiet different from the KM model, so it can be tested at the B factories

The Paths of Unification In The GUST With The G x G Gauge Groups of E(8) x E(8)

In the framework of the four dimensional heterotic superstring with free fermions we discuss the rank eight and/or sixteen Grand Unified String Theories (GUST) which contain the SU(3)_H - gauge family symmetry. We explicitly investigate the paths of the unification in the GUST with gauge symmetry G x G = [SU(5) x U(1) x (SU(3) x U(1))_H]^2. We show that the GUSTs with the G x G gauge group allow to make the scale of unification to be consistent with the string scale M_SU = g_{string} * 5 * 10^17 GeV.Comment: 18 pages, 2 Postscript figures, uses epsf.st

Horizontal symmetry in Higgs sector of GUT with U(1)_A symmetry

In a series of papers, we pointed out that an anomalous $U(1)_A$ gauge symmetry naturally solves various problems in grand unified theories (GUTs) and that a horizontal gauge symmetry, $SU(2)_H$ or $SU(3)_H$, not only realizes the unification of three generation quarks and leptons in fewer multiplets but also solves the supersymmetric flavor problem. In this paper, we examine the possibility that the Higgs sectors of the GUT symmetry and of the horizontal symmetry are unified, that is, there are some Higgs fields whose vacuum expectation values (VEVs) break both the GUT gauge symmetry and the horizontal symmetry at the same time. Although the scale of the VEVs become too large to suppress the flavor changing neutral current processes sufficiently, the unification is possible. In addition, for the $SU(3)_H$ models, the $SU(3)_H$ gauge anomaly is cancelled in the unified models without introducing additional fields in contrast with the previous models in which the Higgs sectors are not unified.Comment: 35 page

Hierarchical Mass Matrices in a Minimal SO(10) Grand Unification I

We consider a minimal SO(10) unified model with horizontal Peccei-Quinn symmetry. The hierarchical structure of quark-lepton mass matrices is naturally implemented by the remnants of certain irrelevant terms. Georgi-Jarlskog relations are also realized due to the horizontal symmetry.Comment: phyzzx and tables, 15 pages, KUNS 125

Fermion masses and mixings in gauge theories

The recent evidence for neutrino oscillations stimulate us to discuss again the problem of fermion masses and mixings in gauge theories. In the standard model, several forms for quark mass matrices are equivalent. They become ansatze within most extensions of the standard model, where also relations between quark and lepton sectors may hold. In a seesaw framework, these relations can constrain the scale of heavy neutrino mass, which is often related to the scale of intermediate or unification gauge symmetry. As a consequence, two main scenarios arise. Hierarchies of masses and mixings may be explained by broken horizontal symmetries.Comment: 25 pages, RevTex, no figures. Few misprints corrected and two references adde