Discrete flavor symmetry and minimal seesaw mechanism

This work proposes a neutrino mass model that is derived using the minimal seesaw mechanism, which contains only two right-handed neutrinos, under the non-Abelian discrete flavor symmetry ${\mathbb{S}}_4\otimes {\mathbb{Z}}_2$. Two standard model doublets, $L_{\mu }$ and $L_{\tau }$, are assigned simultaneously to a $\mathbf{2}$ representation of ${\mathbb{S}}_4$. When the scalar fields introduced in this model, in addition to the standard model Higgs, and the leptons are coupled within the symmetry, the seesaw mechanism results in the tribimaximal neutrino mixing. This study examined the possible deviations from tribimaximal mixing related to the experimental data.

Figure 1

Unshaded regions exhibit the allowed ranges in the elements of PMNS matrix at the 90% C.L. The curve (a) $|U_{e2}|$ is obtained at $t=0$ in Eq. (17), and its intersections with the bounds are at $u/w=0.82$ and at $u/w=1.07$. The curve (b) $|U_{e3}|$ is obtained at $u/w=1$, and its intersection with the bound is at $t/w=0.35$, whereas the curve (c) $|U_{\mu 3}|$ has an intersection with the bound at $t/w=0.46$.

Figure 2

Unshaded regions exhibit the allowed ranges in the elements of the PMNS matrix at the 90% C.L. The curve (a) $|U_{e2}|$ is obtained at $t=0$ in Eq. (18), and its intersections with the bounds are at $v/w=0.135$ and at $v/w=0.165$. The curve (b) $|U_{e3}|$ is obtained at $v/w=0.15$, and its intersection with the bound is at $g_1/g_2=3.8$, whereas the curve (c) $|U_{\mu 3}|$ has an intersection with the bound at $g_1/g_2=4.6$.