Dirac neutrinos from flavor symmetry

We present a model where Majorana neutrino mass terms are forbidden by the flavor symmetry group $\mathrm{\Delta }(27)$. Neutrinos are Dirac fermions and their masses arise in the same way as those of the charged fermions, due to very small Yukawa couplings. The model fits current neutrino oscillation data and correlates the octant of the atmospheric angle ${\theta }_{23}$ with the magnitude of the lightest neutrino mass, with maximal mixing excluded for any neutrino mass hierarchy.

Figure 1

Correlation between the atmospheric angle and the lightest neutrino mass for the NH case. The horizontal dotted lines represent the best fit values; the (dark) blue and (light) gray horizontal bands are the $1\sigma$ and $2\sigma$ allowed ranges, respectively. The blue (light gray), red (gray), and black points are model expectations corresponding to vev deviations of 10%, 20%, and 30%, respectively (see text for more details). The vertical dot-dashed line indicates KATRIN’s sensitivity [36].

Figure 2

Same as Fig. 1 for the IH case. Note that in this case a 30% vev deviation is not enough to reach the best fit value of ${\theta }_{23}$.