Quark mass hierarchy and mixing via geometry of extra dimension with point interactions

Abstract

We propose a new model which can naturally explain origins of fermion generations, quark mass hierarchy, and Cabibbo-Kobayashi-Maskawa matrix simultaneously from geometry of an extra dimension. We take the extra dimension to be an interval with point interactions, which are additional boundary points in the bulk space of the interval. Because of the Dirichlet boundary condition for fermion at the positions of point interactions, profiles of chiral fermion zero modes are split and localized, and then we can realize three generations from each five-dimensional Dirac fermion. Our model allows fermion flavor mixing but the form of non-diagonal elements of fermion mass matrices is found to be severely restricted due to geometry of the extra dimension. The Robin boundary condition for a scalar leads to an extra coordinate-dependent vacuum expectation value, which can naturally explain the fermion mass hierarchy.

34 pages, 13 figures, 1 table (v1); 40 pages, 17 figures, 2 tables, Appendix B is added, Eq. (119) and Fig. 13 are corrected (v2); 40 pages, 17 figures, 2 tables, published version in PTEP, some typos are fixed (v3)

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• Comprehensive Analysis of Yukawa Hierarchies on $T^2/Z_N$ with Magnetic Fluxes
• Shifted orbifold models with magnetic flux
• $CP$ phase from twisted Higgs vacuum expectation value in extra dimension
• Non-minimal Universal Extra Dimensions with Brane Local Terms: The Top Quark Sector
• Realization of lepton masses and mixing angles from point interactions in an extra dimension
• Dynamical generation of fermion mass hierarchy in an extra dimension
• Majorana neutrinos with point interactions
• 6d Dirac fermion on a rectangle; scrutinizing boundary conditions, mode functions and spectrum
• Index theorem on $T^2/{\mathbb{Z}}_N$ orbifolds
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• Family Unification in Special Grand Unification
• Large Star/Rose Extra Dimension with Small Leaves/Petals
• Active Dirac Neutrinos via $SU(2{)}_L$ Doublets in 5d
• Dynamical generation of quark/lepton mass hierarchy in an extra dimension
• 5d Dirac fermion on quantum graph
• Instantons and Berry's connections on quantum graph
• Family Unification in $SO(16)$ Grand Unification
• Correspondence of topological classification between quantum graph extra dimension and topological matter