S4 Flavor Symmetry and Fermion Masses: Towards a Grand Unified theory of Flavor

摘要

Pursuing a bottom-up approach to explore which flavor symmetry could serve asan explanation of the observed fermion masses and mixings, we discuss anextension of the standard model (SM) where the flavor structure for both quarksand leptons is determined by a spontaneously broken S4 and the requirement thatits particle content is embeddable simultaneously into the conventional SO(10)grand unified theory (GUT) and a continuous flavor symmetry G_f like SO(3)_f orSU(3)_f. We explicitly provide the Yukawa and the Higgs sector of the model andshow its viability in two numerical examples which arise as small deviationsfrom rank one matrices. In the first case, the corresponding mass matrix isdemocratic and in the second one only its 2-3 block is non-vanishing. Wedemonstrate that the Higgs potential allows for the appropriate vacuumexpectation value (VEV) configurations in both cases, if CP is conserved. Forthe first case, the chosen Yukawa couplings can be made natural by invoking anauxiliary Z2 symmetry. The numerical study we perform shows that the best-fitvalues for the lepton mixing angles theta_12 and theta_23 can be accommodatedfor normal neutrino mass hierarchy. The results for the quark mixing anglesturn out to be too small. Furthermore the CP-violating phase delta can only bereproduced correctly in one of the examples. The small mixing angle values arelikely to be brought into the experimentally allowed ranges by includingradiative corrections. Interestingly, due to the S4 symmetry the mass matrix ofthe right-handed neutrinos is proportional to the unit matrix.