Model-Independent Analysis of Tri-bimaximal Mixing – a Softly-Broken Hidden or an Accidental Symmetry?
نویسندگان
چکیده
To address the issue of whether tri-bimaximal mixing (TBM) is a softly-broken hidden or an accidental symmetry, we adopt a model-independent analysis in which we perturb a neutrino mass matrix leading to TBM in the most general way but leave the three texture zeros of the diagonal charged lepton mass matrix unperturbed. We compare predictions for the perturbed neutrino TBM parameters with those obtained from typical SO(10) grand unified theories with a variety of flavor symmetries. Whereas SO(10) GUTs almost always predict a normal mass hierarchy for the light neutrinos, TBM has a priori no preference for neutrino masses. We find, in particular for the latter, that the value of |Ue3| is very sensitive to the neutrino mass scale and ordering. Observation of |Ue3| within the next few years would be incompatible with TBM and a normal mass hierarchy and suggest the apparent TBM symmetry is accidental in nature. No such conclusions can be drawn for the inverted and quasi-degenerate hierarchy spectra. email: [email protected] email: [email protected] Neutrino oscillations seem to point towards a lepton flavor structure completely different from that of the quark sector. In particular, the PMNS lepton mixing matrix has a very different structure from that of the CKM quark mixing matrix. Nevertheless, this seemingly incompatible feature can be reconciled in Grand Unified Theories (GUTs), where quarks and leptons belong to the same multiplets. In particular, GUTs based on SO(10), which allow for a seesaw mechanism [1] without adding singlets by hand, have been frequently studied in the past ten years; see e.g. [2]. The models often specify in addition a particular flavor symmetry with charges assigned to the fermion and Higgs SO(10) multiplets, although so-called “minimal” Higgs models may rely on no flavor symmetry at all. Another more recent approach for explaining the neutrino mixing scheme has involved the introduction of lepton flavor symmetries. The goal of such models has been to reproduce the approximate tri-bimaximal mixing (TBM) form observed by Harrison, Perkins and Scott among others [3]:
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