II. THE STANDARD MODEL The Standard Model (SM) is defined as follows: It is spontaneously broken by the vacuum expectation values (VEV) of a single Higgs scalar, φ (1 , 2)$_{1}$$_{/}$$_{2}$ ( 〈 φ $^{0}$〉 = $_{v/}$√$_{2):}$ The Standard Model Lagrangian, L $_{SM}$, is the most general renormalizable Lagrangian that is consistent with the gauge symmetry (2.1), the particle content (2.3) and the pattern of spontaneous symmetry breaking (2.2). It can be divided to three parts: The source of all flavor physics is in the Yukawa interactions: (where ˜ φ = iτ$_{2}$φ $^{†}$). This part of the Lagrangian is, in general, flavor-dependent (that is, Y f ̸∝ 1 ) and CP violating. In the absence of the Yukawa matrices Y $^{d}$, Y u and Y $^{e}$, the SM has a large U (3) 5 global symmetry: The non-Abelian part of this symmetry is particularly relevant to flavor physics: The point that is important for our purposes is that L $_{kinetic+gauge}$+ L Higgs respect the non-Abelian flavor symmetry S (3) 3 q × SU (3) 2 $_{ℓ}$, under which (i) The gauge symmetry is (ii) There are three fermion generations, each consisting of five representations of G$_{SM}$ : G$_{SM}$ = SU (3)$_{C}$ × SU (2)$_{L}$ × U (1)$_{Y}$ . (2.1) G$_{SM}$ → SU (3)$_{C}$ × U (1)$_{EM}$ . (2.2) Q$_{Li}$ (3 , 2)$_{+1}$$_{/}$$_{6}$ , U$_{Ri}$ (3 , 1)$_{+2}$$_{/}$$_{3}$ , D$_{Ri}$ (3 , 1)$_{−}$$_{1}$$_{/}$$_{3}$ , L$_{Li}$ (1 , 2)$_{−}$$_{1}$$_{/}$$_{2}$ , E$_{Ri}$ (1 , 1)$_{−}$$_{1}$ . (2.3) L SM = L kinetic+gauge + L Higgs + L $_{Yukawa}$. (2.4) −L Yukawa = Y d ij Q$_{Li}$φD$_{Rj}$ + Y u ij Q$_{Li}$ ˜ φU$_{Rj}$ + Y e ij L$_{Li}$φE$_{Rj}$ + h . c .. (2.5) G$_{global}$ ( Y u,d,e = 0) = SU (3) 3 q × SU (3) 2 ℓ × U (1) $^{5}$. (2.6) SU (3) 3 q = SU (3)$_{Q}$ × SU (3)$_{U}$ × SU (3)$_{D}$ , SU (3) 2 ℓ = SU (3)$_{L}$ × SU (3)$_{E}$ . (2.7) Q$_{L}$ → V$_{Q}$Q$_{L}$, U$_{R}$ → V$_{U}$U$_{R}$, D$_{R}$ → V$_{D}$D$_{R}$, L$_{L}$ → V$_{L}$L$_{L}$, E$_{R}$ → V$_{E}$E$_{R}$, (2.8) 3