Almost general analysis of μ − τ reflection symmetry perturbed by charged leptons and its testability by DUNE and T2HK

In this paper, we generally analyze the $\mu -\tau$ reflection symmetry modified by small mixings of charged leptons and how will future experiments verify deviations from the predictions of the symmetry. As an approximation, the left-handed diagonalization $U_e$ of charged leptons is assumed to have a similar magnitude as the CKM matrix. In other words, the 1-3 mixing is neglected and the 1-2 and 2-3 mixing are to be approximately $O\left(0.1\right)$. The Dirac CP phase δ of the MNS matrix is evaluated in such parameter regions. As a result, deviations from the predictions $\sin {\theta }_{23}=\pi /4$ and $\delta =\pm \pi /2$ depend on relative CP phases between $U_e$ and diagonalization of neutrinos $U_{\nu }$. While phases of the second and third generations cause only about $\pm {10}^{\circ }$ deviations for the Dirac phase δ, the phase of the first generation can cause up to $\pm {30}^{\circ }$. This flavor dependence is distinguished to some extent by the next-generation experiments. On the other hand, if δ is not observed, such a scenario is excluded by about 5 years of observation.