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A new S3 flavor model based on $\mathrm{SU}(3)_C \otimes \mathrm{SU}(3)_L\otimes \mathrm{U}(1)_X$ gauge symmetry responsible for fermion masses andmixings different from our previous work is constructed.  The new feature is a two - dimensional representation of a Higgs anti-sextetunder $S_3$ which responsible for neutrino masses and mixings. The neutrinosacquire small masses from only an anti-sextet of $\mathrm{SU(3)}$ which is in adoublet under $S_3$. If the difference of components of the anti-sextet isregarded as a small perturbation, S3 is equivalently broken into identity, thecorresponding neutrino mass mixing matrix acquires the most general form andthe model can fit the latest data on neutrino oscillation. This way of thesymmetry breaking helps us to reduce a content in the Higgs sector, only one ananti-sextet instead of two as in our previous work. Our results show that theneutrino masses are naturally small and a small deviation from thetri-bimaximal neutrino mixing form can be realized. The Higgs potential of themodel as well as the minimization conditions and gauge boson masses and mixingsis also considered.

Neutrino mass and mixing in the 3-3-1 model and S3 flavor symmetry with minimal Higgs content