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.

18 pages

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• Consequences of minimal seesaw with complex $\mu \tau$ antisymmetry of neutrinos
• Analysis of four-zero textures in $3+1$ framework
• CP transformed mixed $\mu \tau$ antisymmetry for neutrinos and its consequences
• $\mu -\tau$ Reflection Symmetry and Its Explicit Breaking for Leptogenesis in a Minimal Seesaw Model
• Consequences of $\mu$-$\tau$ reflection symmetry for $3+1$ neutrino mixing
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• On the textures of neutrino mass matrix for maximal atmospheric mixing angle and Dirac CP phase
• Obtaining nonvanishing ${\theta }_{13}$ with constrained neutrino Yukawa matrix and implications for flavor model buildings