Neutrino masses and mixing in $A_5$ with flavour antisymmetry

Abstract

We discuss consequences of assuming that the (Majorana) neutrino mass matrix $M_{\nu }$ and the charged lepton mass matrix $M_l$ satisfy, $S_{\nu }^T{M}_{\nu }{S}_{\nu }=-M_{\nu },T_l^{†}{M}_l{M}_l^{†}{T}_l=M_l{M}_l^{†}$ with respect to some discrete groups $S_{\nu },T_l$ contained in $A_5$. These assumptions lead to a neutrino mass spectrum with two degenerate and one massless neutrino and also constrain mixing among them. We derive possible mixing patterns following from the choices $S_{\nu }=Z_2,Z_2\times Z_2$ and $T_l=Z_2,Z_2\times Z_2,Z_3,Z_5$ as subgroups of $A_5$. One predicts the maximal atmospheric neutrino mixing angle ${\theta }_{23}$ and $\mu$-$\tau$ reflection symmetry in large number of cases but it is also possible to obtain non-maximal values for ${\theta }_{23}$. Only the third column of the neutrino mixing matrix can be obtained at the leading order due to degeneracy in masses of two of the neutrinos. We take up a specific example within $A_5$ group and identify Higgs vacuum expectations values which realize the above assumptions. Non-leading terms present in this example are shown to lead to splitting among degenerate pairs and a consistent description of both neutrino masses and mixing angles.

Comments: 18 pages