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

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 $$\\delta $$