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Register a new userNon-Anomalous Flavor Symmetries and $SU(6) times SU(2)_R$ Model
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We introduce the flavor symmetry ${bf Z}_M times {bf Z}_N times D_4$ into the $SU(6) times SU(2)_R$ string-inspired model. The cyclic group ${bf Z}_M$ and the dihedral group $D_4$ are R symmetries, while ${bf Z}_N$ is a non-R symmetry. By imposing the anomaly-free conditions on the model, we obtain a viable solution under many phenomenological constraints coming from the particle spectra. For neutrino sector, we find a LMA-MSW solution but not SMA-MSW ones. The solution includes phenomenologically acceptable results concerning fermion masses and mixings and also concerning hierarchical energy scales including the GUT scale, the $mu$ scale and the Majorana mass scale of R-handed neutrinos.
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The lepton masses and mixings are studied on the basis of string inspired $SU(6)times SU(2)_R$ model with global flavor symmetries. Provided that sizable mixings between lepton doublets $L$ and Higgsino-like fields $H_d$ with even R-parity occur and that seesaw mechanism is at work in the neutrino sector, the model can yield a large mixing angle solution with $tan theta_{12}, tan theta_{23} = O(sqrt{l})$ $({l}= 0.22)$, which is consistent with the recent experimental data on atmospheric and solar neutrinos. In the solution Dirac mass hierarchies in the neutrino sector cancel out with the heavy Majorana sector in large part due to seesaw mechanism. Hierarchical pattern of charged lepton masses can be also explained.
In the $SU(6) times SU(2)_R$ string-inspired model, we evolve the couplings and the masses down from the string scale $M_S$ using the renormalization group equations and minimize the effective potential. This model has the flavor symmetry including the binary dihedral group $tilde{D}_4$. We show that the scalar mass squared of the gauge non-singlet matter field possibly goes negative slightly below the string scale. As a consequence, the precocious radiative breaking of the gauge symmetry down to the standard model gauge group can occur. In the present model, the large Yukawa coupling which plays an important role in the symmetry breaking is identical with the colored Higgs coupling related to the longevity of the proton.
We study the path from the string scale physics to the low-energy physics in the $SU(6) times SU(2)_R$ string-inspired model with the flavor symmetry ${bf Z}_M times {bf Z}_N times tilde{D}_4$. The flavor symmetry controls the mass spectra of heavy particles as well as those of quarks and leptons in the intermediate energy region ranging from the string scale ($sim 10^{18} {rm GeV}$) to the electroweak scale. In this paper we examine the mass spectra of heavy particles in detail in our model. The renormalization group evolution of the gauge couplings is studied up to two-loop order. A consistent solution of the gauge unification around the string scale is found by adjusting the spectra of the anti-generation matter fields.
The quark mixing matrix $V_{CKM}$ is studied in depth on the basis of superstring inspired $SU(6)times SU(2)_R$ model with global flavor symmetries. The sizable mixings between right-handed down-type quark $D^c$ and colored Higgs field $g^c$ potentially occur but no such mixings in up-type quark sector. In the model the hierarchical pattern of $V_{CKM}$ is understood systematically. It is shown that due to large $D^c$-$g^c$ mixings $V_{ub}$ is naturally suppressed compared to $V_{td}$. It is pointed out that the observed suppression of $V_{ub}$ is in favor of the presence of $SU(2)_R$ gauge symmetry but not in accord with generic SU(5) GUT.
We discuss proton decay in a recently proposed model of supersymmetric hybrid inflation based on the gauge symmetry $SU(4)_c times SU(2)_L times SU(2)_R$. A $U(1), R$ symmetry plays an essential role in realizing inflation as well as in eliminating some undesirable baryon number violating operators. Proton decay is primarily mediated by a variety of color triplets from chiral superfields, and it lies in the observable range for a range of intermediate scale masses for the triplets. The decay modes include $p rightarrow e^{+}(mu^+) + pi^0$, $p rightarrow bar{ u} + pi^{+}$, $p rightarrow K^0 + e^+(mu^{+})$, and $p rightarrow K^+ + bar{ u}$, with a lifetime estimate of order $10^{34}-10^{36}$ yrs and accessible at Hyper-Kamiokande and future upgrades. The unification at the Grand Unified Theory (GUT) scale $M_{rm GUT}$ ($sim 10^{16}$ GeV) of the Minimal Supersymmetric Standard Model (MSSM) gauge couplings is briefly discussed.
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