Deviations from Tri-bimaximal Mixing: Charged Lepton Corrections and Renormalization Group Running

We analyze the effects of charged lepton corrections and renormalization group (RG) running on the low energy predictions of theories which accurately predict tri-bimaximal neutrino mixing at the high energy scale. In particular we focus on GUT inspired see-saw models with accurate tri-bimaximal neutrino mixing at the GUT scale, in which the charged lepton corrections are Cabibbo-like and give rise to sum rules valid at the GUT scale. We study numerically the RG corrections to a variety of such neutrino mixing sum rules in order to assess their accuracy and reliability when comparing them to future low energy neutrino oscillation experiments. Our results indicate that the RG corrections to neutrino mixing sum rules are typically small (less than one degree), at least in the examples studied with hierarchical neutrinos.