Fermion Mass Hierarchy in the Grand Unified Theory on $S_1/(Z_2\times Z_2^{\prime })$ Orbifold

Abstract

We suggest a simple grand unified theory where the fifth dimensional coordinate is compactified on an $S_1/(Z_2\times Z_2^{\prime })$ orbifold. This model is based on the supersymmetric flipped $SU(5)\times U(1)$ grand unified theory, which can realize not only the triplet-doublet splitting but also the natural fermion mass hierarchies. The triplet-doublet splitting is realized by $S_1/(Z_2\times Z_2^{\prime })$ orbifolding, which also reduces the gauge group as $SU(5)\times U(1)\to SU(3{)}_c\times SU(2{)}_L\times U(1{)}_Z\times U(1{)}_X$. The suitable fermion mass hierarchies are generated by integrating out extra three sets of vector-like heavy fields which can propagate in five dimensions. The radiative corrections to the large Yukawa coupling of right-handed neutrinos can reduce the gauge group to $SU(3{)}_c\times SU(2{)}_L\times U(1{)}_Y$.

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