Third family corrections to tri-bimaximal lepton mixing and a new sum rule

We investigate the theoretical stability of the predictions of tri-bimaximal neutrino mixing with respect to third family wave-function corrections. Such third family wave-function corrections can arise from either the canonical normalisation of the kinetic terms or renormalisation group running effects. At leading order both sorts of corrections can be subsumed into a single universal parameter. For hierarchical neutrinos. this leads to a new testable lepton mixing Sum rule s = rcos delta + 2/3 a (where s, r, a describe the deviations of solar, reactor and atmospheric mixing angles from their tri-bimaximal values, and delta is the observable Dirac CP phase) which is stable under all leading order third family wave-function corrections, as well as Cabibbo-like charged lepton mixing effects. (C) 2008 Elsevier B.N. All rights reserved.