Golden ratio prediction for solar neutrino mixing

Abstract

It has recently been speculated that the solar neutrino mixing angle is connected to the golden ratio ϕ. Two such proposals have been made, cot θ 12 = ϕ and cos θ 12 = ϕ/2. We compare these Ansätze and discuss a model leading to cos θ 12 = ϕ/2 based on the dihedral group D 10 . This symmetry is a natural candidate because the angle in the expression cos θ 12 = ϕ/2 is simply π/5, or 36 degrees. This is the exterior angle of a decagon and D 10 is its rotational symmetry group. We also estimate radiative corrections to the golden ratio predictions. * 1 Actually, prediction (A) would lie very slightly outside the 2σ range of Ref. [3], which is sin 2 θ 12 = 0.278 ÷ 0.352.

Viability of exact tri-bimaximal, golden-ratio and bimaximal mixing patterns and renormalization-group running effects

“…We then see that only a fair χ 2 fit is reached for TBM in the NH case, and θ 12 and θ 23 indeed have large pulls, confirming our previous analytical findings. As shown in table 3, it is not difficult to achieve the observed value of θ 13 . We next present the allowed parameter space for the free parameters in figure 1, where for each yellow point their predictions on three mixing angles and two mass-squared differences are within the 3σ ranges from ref.…”

“…This can be seen by inspecting the RGE of θ 13 . According to [60][61][62][63], we have dθ 13 dt ∝ m 1 cos(…”

“…1 For quite a long time, these constant mixing patterns had been regarded as good candidates for the leptonic flavor mixing matrix, as they all agreed with the experimental data fairly well. Motivated by the simplicity of these mixing patterns and the excellent agreement with 1 There exists an alternative mixing pattern involving the golden ratio [12,13], which assumes …”

The golden ratio prediction for the solar angle from a natural model with A 5 flavour symmetry

“…Consequently we have sin 2 θ 12 = 1 4 (3 − φ) ≈ 0.345, about two standard deviations above the experimental value. In [10] this prediction was deduced from the symmetry of the dihedral group D 10 . m ν leading to this mixing pattern.…”

SUSY SU(5)×S 4 GUT flavor model for fermion masses and mixings with adjoint, large θ 13 PMNS

“…The two nonzero leptonic mixing angles θ ν 12 and θ ν 23 are predicted to be rather large by contrast with the quark mixing angles, which are known to be very small [23]. Besides the Tri-Bimaximal mixing pattern ansatz, similar simple mixing patterns with vanishing θ ν 13 were proposed, such as Bimaximal (BM) [24][25][26], Golden-Ratio (GR) [27][28][29][30][31] and Democratic [32][33][34] mixing patterns. The simple patterns suggest some kind of underlying non-Abelian discrete flavor symmetry G f would exist in the lepton sector at least.…”