Exploring Partial $μ$-$τ$ Reflection Symmetry at DUNE and Hyper-Kamiokande
We study origin, consequences and testability of a hypothesis of `partial $μ$-$τ$' reflection symmetry. This symmetry predicts $ |U_{μi}|=|U_{τi}|~(i=1,2,3) $ for a single column of the leptonic mixing matrix $U$. Depending on whether this symmetry holds for the first or second column of $U$ different correlations between $θ_{23}$ and $ δ_{CP} $ can be obtained. This symmetry can be obtained using discrete flavour symmetries. In particular, all the subgroups of SU(3) with 3-dimensional irreducible representation which are classified as class C or D can lead to partial $μ$-$τ$ reflection symmetry. We show how the predictions of this symmetry compare with the allowed area in the $\sin^2θ_{23} - δ_{CP}$ plane as obtained from the global analysis of neutrino oscillation data. Furthermore, we study the possibility of testing these symmetries at the proposed DUNE and Hyper-Kamiokande (HK) experiments (T2HK, T2HKK), by incorporating the correlations between $θ_{23}$ and $ δ_{CP}$ predicted by the symmetries. We find that when simulated data of DUNE and HK is fitted with the symmetry predictions, the $θ_{23}-δ_{CP}$ parameter space gets largely restricted near the CP conserving values of $ δ_{CP} $. Finally, we illustrate the capability of these experiments to distinguish between the two cases leading to partial $μ-τ$ symmetry namely $|U_{\mu1}| = |U_{τ1}|$ and $|U_{μ2}| = |U_{τ2}|$.