Model of Geometric Neutrino Mixing

Current neutrino oscillation data from solar, atmospheric, and reactor experiments are consistent with the neutrino mixing matrix elements taking values sin θ12 = 1/3, sin θ23 = 1/2, and sin 2 θ13 = 0. We present a class of renormalizable gauge models which realize such a geometric mixing pattern naturally. These models, which are based on the non–Abelian discrete symmetry A4, place significant restrictions on the neutrino mass spectrum, which we analyze. It is shown that baryogenesis via leptogenesis occurs quite naturally, with a single phase (determined from neutrino oscillation data) appearing in leptonic asymmetry and in neutrinoless double beta decay. Such predicted correlations would provide further tests of this class of models. Introduction Our understanding of the fundamental properties of neutrinos has improved dramatically over the last few years. Atmospheric and solar neutrino experiments have by now firmly established occurrences of neutrino flavor oscillations [1]. In order for neutrinos to oscillate, they must have non–degenerate masses. In addition, different neutrino flavor states must mix with one another. When positive evidence for oscillations from solar and atmospheric neutrinos are combined with results from reactor data [2, 3], one obtains the following neutrino mass and mixing pattern (with 2σ error bars) [3]: ∆m⊙ = m 2 2 −m1 = 7.92× 10−5(1± 0.09) eV, (1) ∆matm = m 2 3 −m2 = ±2.4× 10−3(1+0.21 −0.61) eV, (2) sin θ12 = 0.314(1 +0.18 −0.15) , sin 2 θ23 = 0.44(1 +0.41 −0.22) , sin 2 θ13 = 0.9 +0.23 −0.9 × 10−2 . (3) Here mi are the (positive) neutrino mass eigenvalues, and θij are the neutrino mixing angles. m2 −m1 > 0 in Eq. (1) is necessary for MSW resonance to occur inside the Sun. The sign of ∆matm, which is physical, is currently unknown. A remarkable feature of the oscillation data is that they are all consistent with a “geometric” neutrino mixing pattern defined by the parameters sin θ12 = 1/3, sin 2 θ23 = 1/2, and sin θ13 = 0. In fact, these geometric mixing angles are very close to the central values of Eq. (3). We observe that unlike the quark mixing angles, which are related to the quark mass ratios in many models (eg: θC ≃ √ md/ms), the neutrino mixing angles seem to be unrelated to the neutrino mass ratios. The purpose of this Letter is to provide a derivation of such a geometric neutrino mixing based on renormalizable gauge theories. The neutrino mixing matrix (the MNS matrix) that we will derive has the form [4, 5, 6, 7] UMNS = 