Deviations from $\mu$-$\tau$ symmetry using $\Delta$(27) group on neutrino masses and mixings

Abstract

Implication of neutrino mass model based on $\Delta$(27) discrete flavor symmetry, on parameters of neutrino oscillations, CP violation and effective neutrino masses is studied using type-I seesaw mechanism. The Standard Model particle content is extended by adding two additional Higgs doublets, three right-handed neutrinos and two scalar triplets under $\Delta$(27) symmetry predicting diagonal charged lepton mass matrix. This can generate the desired deviation from $\mu - \tau$ symmetry. The resulting neutrino oscillation parameters are well agreed with the latest global fit oscillation data. The sum of the three absolute neutrino mass eigenvalues, $\sum\limits_{i}|m_{i}|$ (i=1,2,3) is found to be consistent with that of the value given by latest Planck cosmological data, $\sum\limits_{i}|m_{i}|<$0.12 eV. The model further predicts effective neutrino masses for neutrinoless double beta decay, 4.15 meV $\leq m_{ee}\leq$ 30.6 meV, tritium beta decay, 8.4 meV $\leq m_{\beta}\leq$ 30.5 meV, Jarlskog invariant, $J_{CP}=\pm 0.022$ for CP violation, baryon asymmetry $Y_{B}=1.15 \times 10^{-10}$ for normal hierarchical case; and also 49.5 meV $\leq m_{ee}\leq$ 51.7 meV, 49.5 meV $\leq m_{\beta}\leq$ 51.4 meV, $J_{CP}=\pm 0.022$, $Y_{B}=1.12\times 10^{-10}$ for inverted hierarchical case respectively.