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Register a new userFermion masses and flavor mixings and strong CP problem
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Authors
Y. H. Ahn
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For all the success of the Standard Model (SM), it is on the verge of being surpassed. In this regard we argue, by showing a minimal flavor-structured model based on the non-Abelian discrete $SL_2(F_3)$ symmetry, that $U(1)$ mixed-gravitational anomaly cancellation could be of central importance in constraining the fermion contents of a new chiral gauge theory. Such anomaly-free condition together with the SM flavor structure demands a condition $k_1,X_1/2=k_2,X_2$ with $X_i$ being a charge of $U(1)_{X_i}$ and $k_i$ being an integer, both of which are flavor dependent. We show that axionic domain-wall condition $N_{rm DW}$ with the anomaly free-condition depends on both $U(1)_X$ charged quark and lepton flavors; the seesaw scale congruent to the scale of Peccei-Quinn symmetry breakdown can be constrained through constraints coming from astrophysics and particle physics. Then the model extended by $SL_2(F_3)times U(1)_X$ symmetry can well be flavor-structured in a unique way that $N_{rm DW}=1$ with the $U(1)_X$ mixed-gravitational anomaly-free condition demands additional Majorana fermion and the flavor puzzles of SM are well delineated by new expansion parameters expressed in terms of $U(1)_X$ charges and $U(1)_X$-$[SU(3)_C]^2$ anomaly coefficients. And the model provides remarkable results on neutrino (hierarchical mass spectra and unmeasurable neutrinoless-double-beta decay rate together with the predictions on atmospheric mixing angle and leptonic Dirac CP phase favored by the recent long-baseline neutrino experiments), QCD axion, and flavored-axion.
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CP violation, fermion masses and mixing angles including that of neutrinos are studied in an SUSY SO(10)$times Delta (48)times$ U(1) model. The nonabelian SU(3) discrete family symmetry $Delta(48)$ associated with a simple scheme of U(1) charge assignment on various fields concerned in superpotential leads to unique Yukawa coupling matrices with zero textures. Thirteen parameters involving masses and mixing angles in the quark and charged lepton sector are successfully predicted by only four parameters. The masses and mixing angles for the neutrino sector could also be predicted by constructing an appropriate heavy Majorana neutrino mass matrix without involving new parameters. It is found that the atmospheric neutrino deficit, the mass limit put by hot dark matter and the LSND $bar{ u}_{mu} to bar{ u}_{e}$ events may simultaneously be explained, but solar neutrino puzzle can be solved only by introducing a sterile neutrino. An additional parameter is added to obtain the mass and mixing of the sterile neutrino. The hadronic parameters $B_{K}$ and $f_{B}sqrt{B}$ are extracted from the observed $K^{0}$-$bar{K}^{0}$ and $B^{0}$-$bar{B}^{0}$ mixings respectively. The direct CP violation ($epsilon/epsilon$) in kaon decays and the three angles $alpha$, $beta$ and $gamma$ of the unitarity triangle in the CKM matrix are also presented. More precise measurements of $alpha_{s}(M_{Z})$, $|V_{cb}|$, $|V_{ub}/V_{cb}|$, $m_{t}$, as well as various CP violation and neutrino oscillation experiments will provide an important test for the present model and guide us to a more fundamental theory.
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