Exploring Partial $\mu$-$\tau$ Reflection Symmetry at DUNE and Hyper-Kamiokande

We study origin, consequences and testability of a hypothesis of `partial $\mu$-$\tau$' reflection symmetry. This symmetry predicts $|U_{\mu i}|=|U_{\tau i}|~(i=1,2,3)$ 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 $\theta_{23}$ and $\delta_{CP}$ 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 $\mu$-$\tau$ reflection symmetry. We show how the predictions of this symmetry compare with the allowed area in the $\sin^2\theta_{23} - \delta_{CP}$ 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 $\theta_{23}$ and $\delta_{CP}$ predicted by the symmetries. We find that when simulated data of DUNE and HK is fitted with the symmetry predictions, the $\theta_{23}-\delta_{CP}$ parameter space gets largely restricted near the CP conserving values of $\delta_{CP}$. Finally, we illustrate the capability of these experiments to distinguish between the two cases leading to partial $\mu-\tau$ symmetry namely $|U_{\mu1}| = |U_{\tau 1}|$ and $|U_{\mu 2}| = |U_{\tau 2}|$.