Golden ratio prediction for solar neutrino mixing

We formulate a consistent model predicting, in the leading order approximation, maximal atmospheric mixing angle, vanishing reactor angle and tan θ 12 = 1/φ where φ = (1 + √ 5)/2 is the Golden Ratio. The model is based on the flavour symmetry A 5 ×Z 5 ×Z 3 , spontaneously broken by a set of flavon fields. By minimizing the scalar potential of the theory up to the next-to-leading order in the symmetry breaking parameter, we demonstrate that this mixing pattern is naturally achieved in a finite portion of the parameter space, through the vacuum alignment of the flavon fields. The leading order approximation is stable against higher-order corrections. We also compare our construction to other models based on discrete symmetry groups.

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Feruglio

Paris

2011

“…We have θ 23 = 45 • and θ 13 = 0 for all three mixing patterns in question, while θ 12 = arctan(1/ √ 2) ≈ 35.3 • for TBM [2][3][4][5], θ 12 = 45 • for BM [6][7][8] and θ 12 = arctan[2/(1 + √ 5)] ≈ 31.7 • for GR [9][10][11]. 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.…”

Section: Introductionmentioning

confidence: 99%

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

Zhang

Zhou

2016

In light of the latest neutrino oscillation data, we examine whether the leptonic flavor mixing matrix can take on an exact form of tri-bimaximal (TBM), golden-ratio (GR) or bimaximal (BM) mixing pattern at a superhigh-energy scale, where such a mixing pattern could be realized by a flavor symmetry, and become compatible with experimental data at the low-energy scale. Within the framework of the Minimal Supersymmetric Standard Model (MSSM), the only hope for realizing such a possibility is to count on the corrections from the renomalization-group (RG) running. In this work we focus on these radiative corrections, and fully explore the allowed parameter space for each of these mixing patterns. We find that when the upper bound on the sum of neutrino masses Σ ν ≡ m 1 + m 2 + m 3 < 0.23 eV at the 95% confidence level from Planck 2015 is taken into account, none of these mixing patterns can be identified as the leptonic mixing matrix below the seesaw threshold. If this cosmological upper bound on the sum of neutrino masses were relaxed, the TBM and GR mixing patterns would still be compatible with the latest neutrino oscillation data at the 3σ level, but not at the 1σ level. Even in this case, no such a possibility exists for the BM mixing.

“…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.…”

Section: Jhep06(2016)032mentioning

confidence: 99%

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

Zhao¹,

Zhang²

2016

Abstract:We propose an S 4 flavor model based on supersymmetric (SUSY) SU(5) GUT. The first and third generations of 10 dimensional representations in SU(5) are all assigned to be 1 1 of S 4 . The second generation of 10 is to be 1 2 of S 4 . Right-handed neutrinos of singlet 1 and three generations of5 are all assigned to be 3 1 of S 4 . The VEVs of two sets of flavon fields are allowed a moderate hierarchy, that is Φ ν ∼ λ c Φ e . Tri-Bimaximal (TBM) mixing can be produced at both leading order (LO) and next to next to leading order (NNLO) in neutrino sector. All the masses of up-type quarks are obtained at LO. We also get the bottom-tau unification m τ = m b and the popular Georgi-Jarlskog relation m µ = 3m s as well as a new mass relation m e = 8 27 m d in which the novel Clebsch-Gordan (CG) factor arises from the adjoint field H 24 . The GUT relation leads to a sizable mixing angle θ e 12 ∼ θ c and the correct quark mixing matrix V CKM can also be realised in the model. The resulting CKM-like mixing matrix of charged leptons modifies the vanishing θ ν 13 in TBM mixing to a large θ PMNS 13 θ c / √ 2, in excellent agreement with experimental results. A Dirac CP violation phase φ 12 ±π/2 is required to make the deviation from θ ν 12 small. We also present some phenomenological numerical results predicted by the model.