Fermion Mass Hierarchy in the Grand Unified Theory on $S_1/(Z_2 \times Z_2')$ Orbifold

The grand unification of flavor(GUF) in extra dimensions is discussed. After reviewing the old GUF, I present a GUF model SU(7) in 5D with the recently popular field theoretic orbifold compactification.

We consider the 5D gauge unification of $SU(2)_L\times U(1)_Y$ into $SU(3)_W$ at a TeV scale. Compactification of the extra dimension on an orbifold $S^1/(Z_2\times Z'_2)$ allows fixed points where $SU(2)_L\times U(1)_Y$ representations can be assigned. We explain the long proton lifetime and the top-bottom mass hierarchy and etc. geometrically. We also show that local gauge anomalies on the orbifold can be exactly cancelled by a 5D Chern-Simons term with a jumping coefficien...

The generation of the fermion mass hierarchy in the standard model of particle physics is a long-standing puzzle. The recent discoveries from neutrino physics suggests that the mixing in the lepton sector is large compared to the quark mixings. To understand this asymmetry between the quark and lepton mixings is an important aim for particle physics. In this regard, two promising approaches from the theoretical side are grand unified theories and family symmetries. In this no...

We discuss a possibility whether a model of grand gauge-Higgs unification incorporating family unification in higher dimensions can be constructed. We first extend a five dimensional $SU(6)$ grand gauge-Higgs unification model to a five dimensional $SU(7)$ grand gauge-Higgs unification model compactified on an orbifold $S^1/Z_2$ to obtain three generations of quarks and leptons after symmetrybreaking of the larger family unified gauge group. A prescription of constructing a s...

We study the phenomenology of a 5D $SU(3)_W$ model on a $S_1/(Z_2\times Z'_2)$ orbifold in which the minimal scalar sector plays an essential role of radiatively generating neutrino Majorana masses without the benefits of right-handed singlets. We carefully examine how do the exotic scalars affect the renormalization group (RG) equations for the gauge couplings and the 5D $SU(3)_W$ unification. We found that the compactification scale of extra dimension is in the range of $1/...

Based on the generalized gauge theory on $M^4\times Z_2\times Z_3$, we reconstructed the realistic SU(5) Grand Unified model by a suitable assignment of fermion fields. The action of group elements $Z_2$ on fermion fields is the charge conjugation while the action of $Z_3$ elements represent generation translation. We find that to fit the spontaneous symmetry breaking and gauge hierarchy of SU(5) model a linear term of curvature has to be introduced. A new mass relation is ob...

We propose a supersymmetric SU(5) orbifold GUT in 5 dimensions in which supersymmetry breaking at the boundaries give rise to split supersymmetry spectrum. The extra dimension is compactified on a $S^1/Z_2 \times Z_2^\prime$ orbifold having two fixed points. The standard model fermions are localized in the standard model brane, where supersymmetry is broken by the nonvanishing of the F-term of a superfield X at some intermediate scale. All scalar superpartners acquires mass a...

We investigate gauge coupling unification in higher dimensional GUT models with split supersymmetry. We focus on 5d and 6d orbifold GUTs, which permit a simple solution to several problems of 4D GUTs as well as control over GUT scale threshold corrections. In orbifold GUTs, calculable threshold corrections can raise or lower the prediction for $\alpha_s(M_Z)$ in a way that depends on the location of Higgs fields. On the other hand, split supersymmetry lowers the prediction fo...

We propose a new mechanism towards the solution to the doublet-triplet Higgs mass splitting problem in the supersymmetric grand unified theory. Our model is based on the gauge group $SU(5)_H \times SU(5)_{GUT}$, where $SU(5)_H$ and $SU(5)_{GUT}$ are a new strong gauge interaction and the ordinary grand unified gauge group, respectively. The doublet-triplet Higgs mass splitting is realized through the quantum deformation of moduli space caused by the strong $SU(5)_H$ gauge dyn...

We construct a five dimensional supersymmetric SO(10)$\times$D$_3$ grand unified model with an $S^1/(Z_2 \times Z^\prime_2)$ orbifold as the extra dimension. The orbifold breaks half of the supersymmetry and breaks the SO(10) gauge symmetry down to ${\rm SU(4)}_C \times {\rm SU(2)}_L \times {\rm SU(2)}_R$. The Higgs mechanism is used to break the remaining gauge symmetry the rest of the way to the Standard Model. We place matter fields variously in the bulk and on the orbifol...