Charged lepton corrections to neutrino mixing angles and CP phases revisited

We re-analyze charged lepton corrections to neutrino mixing angles and CP phases, carefully including CP phases from the charged lepton sector. We present simple analytical formulae for including the charged lepton corrections and derive compact new results for small neutrino and charged lepton mixings θ13ν and θ13e. We find a generic relation θ12+12θ12ecos(δ−π)≈θ12ν, which relates the prediction from the neutrino sector θ12ν to the charged lepton mixing θ12e and to the MNS neutrino oscillation phase δ. We apply our formula to the examples of bimaximal or tri-bimaximal neutrino mixing. One implication is that the so-called quark-lepton complementarity relation θ12+θC=45° can only hold for δ=π and it gets modified in the presence of leptonic CP violation. On the other hand, the lepton mixing θ13 generated from the charged lepton correction θ12e is independent of CP phases and given by θ13=12θ12e. Combining these results leads to a model-independent sum rule: θ12+θ13cos(δ−π)≈θ12ν where θ12ν=(35.26°)45° in the case of (tri-)bimaximal neutrino mixing, for example.