In this work we propose an extension to the Standard Model in which we consider a type-III two-Higgs-doublet model (2HDM) plus massive neutrinos and the horizontal flavor symmetry $S_3$ ($\nu 2\mathrm{HDM}\otimes S_3$). In the above framework and with the explicit breaking of flavor symmetry $S_3$, the Yukawa matrices in the flavor-adapted basis are represented by means of a matrix with two texture zeros. Also, the active neutrinos are considered as Majorana particles and their masses are generated through the type-I seesaw mechanism. The unitary matrices that diagonalize the mass matrices, as well as the flavor-mixing matrices, are expressed in terms of fermion mass ratios. Consequently, in the mass basis the entries of the Yukawa matrices naturally acquire the form of the so-called Cheng-Sher ansatz. For the leptonic sector of $\nu 2\mathrm{HDM}\otimes S_3$, we compare, through a ${\chi }^2$ likelihood test, the theoretical expressions of the flavor-mixing angles with the masses and flavor-mixing leptons current experimental data. The results obtained in this ${\chi }^2$ analysis are in very good agreement with the current experimental data. We also obtain allowed value ranges for the “Dirac-like” phase factor, as well as for the two Majorana phase factors. Furthermore, we study the phenomenological implications of these numerical values of the $CP$-violation phases on the neutrinoless double-beta decay, and for long baseline neutrino oscillation experiments such as T2K, $\mathrm{NO}\nu \mathrm{A}$, and DUNE.

• Received 20 April 2017

DOI:https://doi.org/10.1103/PhysRevD.97.035003

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Published by the American Physical Society