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The approach unifying all the internal degrees of freedom--proposed by one of us--is offering a new way of understanding families of quarks and leptons: A part of the starting Lagrange density in d(=1+13), which includes two kinds of spin connection fields--the gauge fields of two types of Clifford algebra objects--transforms the right handed quarks and leptons into the left handed ones manifesting in d=1+3 the Yukawa couplings of the Standard model. We study the influence of the way of breaking symmetries on the Yukawa couplings and estimate properties of the fourth family--the quark masses and the mixing matrix, investigating the possibility that the fourth family of quarks and leptons appears at low enough energies to be observable with the new generation of accelerators.
To include the quark sector, the $A_{5}equiv I$ (icosahedron) four generation lepton model is extended to a binary icosahedral symmetry $I$ flavor model. We find the masses of fermions, including the heavy sectors, can be accommodated. At leading ord
In Phys. Rev. A 62, 062314 (2000), D{u}r, Vidal and Cirac indicated that there are infinitely many SLOCC classes for four qubits. Verstraete, Dehaene, and Verschelde in Phys. Rev. A 65, 052112 (2002) proposed nine families of states corresponding to
We exploit a recent advance in the study of topological superconductors to propose a solution to the family puzzle of particle physics in the context of SO(18) (or more correctly, Spin(18)) grand unification. We argue that Yukawa couplings of interme
The tremendous phenomenological success of the Standard Model (SM) suggests that its flavor structure and gauge interactions may not be arbitrary but should have a fundamental first-principle explanation. In this work, we explore how the basic distin
The non-Abelian discrete symmetry D(7) of the heptagon is successfully applied to both quark and lepton mass matrices, including CP violation.