From Hierarchical Radiative Quark Mass Matrices and Mixing to FCNC in SU(2)L⊗U(1)Y ⊗U(1)H

We present an extension of the Standard Model (SM) without supersymmetry, which we use to calculate order of magnitude values for the elements of the quark mass matrices in the SM. Our model have the following characteristics a) give only tree level mass to top quark, b) generates approximately , using the top quark as seed, the RRR-textures correspondent to the solution wich have three texture zeroes in Mu and two texture zeroes in Md, c) fixes one horizontal scale of O(10TeV). The specific model described here is one horizontal extension of the standard model SU(3)× SU(2)L × U(1)Y × Z11 with Z11 a subset of an abelian extension already presented [2]. e-mail: [email protected] 1 Hierarchical Radiative Quark and Lepton Mass Matrices In an early reference [5] a model was constructed based in an extension Z8×Z5 of the Standard Model that generated radiative mass for all quarks and leptons using the top quark as seed. The Z8 assignaments for quarks and leptons was puted by hand to obtain properly mass matrices. The Z5 is included to prevent conflict with experimental results. The assignaments of quarks and scalars under Z8 that generated quark masses are shown in Table 1. Table 1 Z8 Quarks Scalars −3 bR, sR, dR −2 (c, s)L ζ 4 (bs)R −1 tR, cR, uR 0 (t, b)L φ2, ζ −1/3 1 (dc, us, bt)L +1 φ1(t̄RtL) +2 (u, d)L ψ(sb, ct)L, ζ −4/3 3 (ct)R ζ 2/3 5 +3 +4 ζ −1/3 2 (cb, cs, cd, tb, su)R, (sc)L The scalars bosons φ1, φ2 are doublets under SU(2) and singlets under SU(3), whereas the ζ ’s are color triplets and SU(2) singlets, and ψ is a color triplet as well as an SU(2) triplet. The upper indices in them denote their charges and the pairs in parentesis that the follow denotes the couplings between quarks that permit they. So the L sector of quarks, asummed to transform under Z8 as shown in Table 1, fixes the acquisition of radiative masses: in the line coresponding to Z8 = 0 appear that d will obtain its mass from cL (this mass will be write as zm1), u will obtain its mass from sL, b will obtain their mass from tL (m5) all they trough ζ1; s will obtain one mass from c (m2) trough ζ2; and other from b (m4) trough ψ; c from t trough ψ, all according with comment in [3]: “An interesting feature of the cascade mechanism[1] is that it couples the up quarks to the strange and bottom quarks and couples the down quarks to the charm and top quarks trough the higher order corrections, thus providing a natural explanation, for the 1 observation mu < md”. On the other hand the R sector fixes the mixing between quarks: in the line Z8 = +4 we can see that c will mix with bR, sR, dR trough ζ2, this will conduct to non-diagonal entries diferent from zero in the first and second lines of Md; the single couplings b with sR trough ζ4, c with tR trough ζ3, t with bR trough ζ2 and s with uR trough ζ2 imply no mixing and therefore the third line of Md will have only M33 6= 0 and Mu will be diagonal. In this assignament, Z8 = 0 for the third doublet of quarks and to put the same Z8 for all the down right sector and the same Z8 for all the up right sector (see Table 1), minimizes the numbers of scalars. When we put all join, we obtain the following cascade : 0 loop : mt tL tR 1 loop : mc, m5 ζ1 ζ2 bL tL tR bR , ψ ζ3 cL tL tR cR 2 loop : m1, m2 +m4, m3 ζ2 ζ2 sL cL cR dR , ζ2 ζ2 sL cL cR sR + ψ ζ4 sL bL bR sR , ζ2 ζ2 sL cL cR bR 2 loop : zm1, zm2, zm3 ζ1 ζ2 dL cL cR dR , ζ1 ζ2 dL cL cR sR , ζ1 ζ2 dL cL cR bR 3 looop : mu ζ1 ζ2 uL sL sR uR (1) that define the following mass matrices Md = 