Third Family Corrections to Tri-bimaximal Lepton Mixing and a New Sum Rule
arXiv:0711.4727 · doi:10.1016/j.physletb.2008.12.013
Abstract
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 = r cos 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.
arXiv comment4 pages, 1 figure; v2:references added, minor clarifications
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