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We propose a generalized $\mu-\tau$ reflection symmetry to constrain thelepton flavor mixing parameters. We obtain a new correlation between theatmospheric mixing angle $\theta_{23}$ and the "Dirac" CP violation phase$\delta_{\rm CP}$. Only in a specific limit our proposed CP transformationreduces to standard $\mu-\tau$ reflection, for which $\theta_{23}$ and$\delta_{CP}$ are both maximal. The "Majorana" phases are predicted to lie attheir CP-conserving values with important implications for the neutrinolessdouble beta decay rates. We also study the phenomenological implications of ourscheme for present and future neutrino oscillation experiments including T2K,NO$\nu$A and DUNE.

Generalized $\mu-\tau$ reflection symmetry and leptonic CP violation