Pursuing a bottom-up approach to explore which flavor symmetry could serve as
an explanation of the observed fermion masses and mixings, we discuss an
extension of the standard model (SM) where the flavor structure for both quarks
and leptons is determined by a spontaneously broken S4 and the requirement that
its 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 or
SU(3)_f. We explicitly provide the Yukawa and the Higgs sector of the model and
show its viability in two numerical examples which arise as small deviations
from rank one matrices. In the first case, the corresponding mass matrix is
democratic and in the second one only its 2-3 block is non-vanishing. We
demonstrate that the Higgs potential allows for the appropriate vacuum
expectation value (VEV) configurations in both cases, if CP is conserved. For
the first case, the chosen Yukawa couplings can be made natural by invoking an
auxiliary Z2 symmetry. The numerical study we perform shows that the best-fit
values for the lepton mixing angles theta_12 and theta_23 can be accommodated
for normal neutrino mass hierarchy. The results for the quark mixing angles
turn out to be too small. Furthermore the CP-violating phase delta can only be
reproduced correctly in one of the examples. The small mixing angle values are
likely to be brought into the experimentally allowed ranges by including
radiative corrections. Interestingly, due to the S4 symmetry the mass matrix of
the right-handed neutrinos is proportional to the unit matrix.Comment: 27 pages, published version with minor change
