An $$A_4$$ model to accommodate maximal $$\theta _{23}$$ and maximal $$\delta $$ consistent with $$\mu $$–$$\tau $$ reflection symmetry

Abstract

Abstract In this work, we construct an $$A_4$$ A 4 -based flavor symmetry model within the framework of the type-I seesaw mechanism to realize a light neutrino mass matrix consistent with $$\mu $$ μ – $$\tau $$ τ reflection symmetry. The entire framework is based on the Standard Model gauge symmetry extended by the discrete group $$A_4 \times Z_2 \times Z_4$$ A 4 × Z 2 × Z 4 . In general, the elements of the light Majorana neutrino mass matrix are complex. The $$\mu $$ μ – $$\tau $$ τ reflection symmetric texture of the mass matrix can be realized in a generalized CP symmetry limit. In this symmetry limit, the model predicts a maximal atmospheric mixing angle $$\theta _{23} = \pi /4$$ θ 23 = π / 4 and a maximal Dirac CP phase $$\delta = (\pi /2) / (3\pi /2)$$ δ = ( π / 2 ) / ( 3 π / 2 ) . These features are consistent with current experimental observations, including a near-maximal value of $$\theta _{23}$$ θ 23 , a non-zero $$\theta _{13}$$ θ 13 , and a preference for $$\delta $$ δ close to $$270^\circ $$ 270 ∘ , as indicated by the T2K and NO $$\nu $$ ν A experiments. Non-maximal values of $$\theta _{23}$$ θ 23 and $$\delta $$ δ can be accommodated when one does not restrict to the CP symmetry limit. The model predictions for the mixing angles and the Dirac CP phase $$\delta $$