Abstract
We study a supersymmetric SO(10) gauge theory in six dimensions compactified on an orbifold. Three sequential quark–lepton families are localized at the three fixpoints where SO(10) is broken to its three GUT subgroups. Split bulk multiplets yield the Higgs doublets of the standard model and as additional states lepton doublets and down-quark singlets. The physical quarks and leptons are mixtures of brane and bulk states. The model naturally explains small quark mixings together with large lepton mixings in the charged current. A small hierarchy of neutrino masses is obtained due to the different down-quark and up-quark mass hierarchies. None of the usual GUT relations between fermion masses holds exactly.
Highlights
Φc ψαWhere we choose M∗ > 1/R5,6 ∼ ΛGUT to be the cutoff of the 6d theory, and the bulk fields have been properly normalized
We study a supersymmetric SO(10) gauge theory in six dimensions compactified on an orbifold
The explanation of the masses and mixings of quarks and leptons remains a challenge for theories which go beyond the standard model [1, 2]
Summary
Where we choose M∗ > 1/R5,6 ∼ ΛGUT to be the cutoff of the 6d theory, and the bulk fields have been properly normalized. The three ‘families’ are separated by distances large compared to the cutoff scale M∗ They can only have diagonal Yukawa couplings with the bulk Higgs fields. The brane fields can mix with the bulk zero modes for which we expect no suppression. These mixings take place only among left-handed leptons and right-handed down-quarks. The corresponding Yukawa couplings have to be hierarchical in order to obtain a realistic spectrum of quark and lepton masses. For our discussion of mass eigenvalues and mixing angles we shall need the two matrices mmT and mT m, which in the basis ei are both hierarchical, mmT μ21(1 + β2 + γ2) μ1μ2(1 + αβ) μ1μ2(1 + αβ) μ22(1 + α2).
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