Back Propagation Learning Using a Super Stable Motion

Mass Hierarchy from SU(1,1) Horizontal Symmetry

“…2) 3) This model is a vector-like 4) generalization 5) of the minimal supersymmetric standard model(MSSM) 6) , and the three chiral generations and the hierarchical Yukawa coupling structure are realized through the mechanism called "spontaneous generation of generations". 2) In the model, a MSSM chiral superfield(f ) is extended to a chiral superfield(F ) which belongs to an infinite dimensional unitary representation of the horizontal gauge symmetry SU (1,1). For example, the three generations of quark doublets q is extended to a SU(1, 1) multiplet; Q α = {q α , q α+1 , q α+2 , q α+3 , · · ·}, (1 .…”

“…2). Let us assume that we have g massless modes {q (0) , q (1) , q (2) , · · · , q (g−1) } and write…”

Model of Generations of Quarks and Leptons

“…We realize that the parity (P), charge conjugation (C) and time reversal (T) are the symmetries of the model at the fundamental level, which are realized ahtomatically under the condition of leftright symmetry. Any non-conservations of these symmetries are due to the spontaneous breakdown of SU (1,1). Especially the CP-violating phase in the Kobayashi-Maskawa matrix ll) comes solely from relative phase of (1/t) and ('I>).…”

“…1 ) I will make an attempt at an understanding of chiral structure of generations of quarks and leptons and the hierarchical structure of their Yukawa interactions with Higgs scalars based on the gauge group of standard SU (3) x SU (2) x U(1) times horizontal symmetry 2 ) G H, on supersymmetry 3 ) and on the additional scenario of "spontaneous generation of generations" . 1 ) Nowadays the standard understanding of chiral generations of quarks and leptons is that it is related to the topology of the compactified space of the string vacuum. 4 ) For the further and deeper understanding of the chiral generations, clearly we need the understanding of the interrelation between different string vacua, that is, the connection among vacua with different number of generations.…”

Chasing after flavor symmetries of quarks from the bottom up

“…We reacknowledge that a flavorsymmetric part of Yukawa coupling matrix can be realized by a rank-one matrix and a democratic-type one occupies a special position, based on Dirac's naturalness. * E-mail: haru@azusa.shinshu-u.ac.jp 1 The flavor structure of quarks and leptons has been studied intensively, based on various flavor symmetries [6,7,8,9,10,11,12,13].…”