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 theta(nu)(13) and theta(e)(13). We find a generic relation theta(12) + theta(12) cos(8 - pi) approximate to theta(nu)(12), which relates the prediction from the neutrino sector theta(nu)(12) to the charged lepton mixing Bit and to the MNS neutrino oscillation phase delta. 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 theta(12) + theta(C) = 45 degrees can only hold for delta = pi and it gets modified in the presence of leptonic CP violation. On the other hand, the lepton mixing theta(13) generated from the charged lepton correction theta(12) is independent of CP phases and given by theta(13) = 1/root 2 theta(e)(12) . Combining these results leads to a model-independent sum rule: theta(12) + theta(13) cos(delta - pi) approximate to theta(nu)(12) where theta(12) = (35.26 degrees) 45 degrees in the case of (tri-)bimaximal neutrino mixing, for example. (c) 2005 Elsevier B.V. All rights reserved.