Strong Incompatability of Tribimaximal Mixing with Quark-Lepton Complementarity

Although tribimaximal mixing (TBM) and quark-lepton complementarity (QLC) are both compatible with experimental data within one standard deviation (1σ), the TBM and QLC assumptions are mutually exclusive by 56σ. [email protected] [email protected] Two popular assumptions in particle phenomenology model building are tribimaximal mixing (TBM) and quark-lepton complementarity(QLC). In this article we wish to point out that because both TBM and QLC involve exact angles it is dangerous to attempt to combine TBM with QLC. To illustrate our point, it suffices to write down some relationships involving experimentally determined values of mixing angles and exact angles predicted on the basis of different theoretical assumptions. In TBM the assumption [1] is that the neutrino mixing angle θ12 satisfies tan θ12 = 1 √ 2 (1) corresponding to θ12 = 35.26... . The experimental value [2] (θ12) Experiment = 33.9 ± 2.3 (2) agrees within one standard deviation (1σ). In QLC the assumption is [3,4] that θ12 and the quark mixing angle Θ12 satisfy exactly θ12 +Θ12 = 45.00... o (3) and the experimental value [2] (Θ12) Experiment = 13.14± 0.06. (4) together with Eq.(2) agrees within 1σ. If, however, we assume both TBM and QLC we predict exactly (Θ12) TBM+QLC = 9.74... (5) which disagrees with experiment, Eq.(4), by an astonishing 56σ. Thus, any model which assumes simultaneously TBM and QLC has vanishing probability of being correct. Another theoretical assumption introduces a further exact angle. From the viewpoint of T ′ flavor symmetry where T ′ is the binary tetrahedral group, Eq.(3) is replaced by a different relationship between θ12 and Θ12 involving a third exact angle [5] (θ12 +Θ12) T ′ = (