Model of flavor with quaternion symmetry

We present a renormalizable fermion mass model based on the symmetry $Q_4$ that accommodates all fermion masses and mixing angles in both the quark and lepton sectors. It requires the presence of only four $SU(2)$ doublet scalar fields transforming nontrivially under the flavor symmetry and the assumption of an alignment between first and second generation Yukawa couplings. No right-handed neutrinos are present in the model and neutrino masses are generated radiatively through the introduction of two additional $SU(2)$ singlet fields charged under both hypercharge and lepton number.

Figure 1

Angles that reproduce the experimental mass differences ratio for the neutrino sector. Note that ${\theta }_{13}>0$ throughout the range.

Figure 2

left: Allowed range for the $0\nu \beta \beta$-decay in the $Q_4$ model. right: The light blue band corresponds to the allowed range for $|m_{\beta \beta }|$ from oscillation data at $3\sigma$ [27], the dashed line represents the lower limit from direct observation in ${}^{76}\mathrm{Ge}$ ($|m_{\beta \beta }|<0.20$ [25]), and the small dark blue spot is the allowed range in the left figure obtained from our model.

Figure 3

One loop diagram giving rise to neutrino Majorana mass.