High Energy Physics - Phenomenology · arXiv:1011.6167 v2 · submitted 29 Nov 2010
Vacuum misalignment corrections to tri-bimaximal mixing and form dominance
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“The analytic results show that the corrections to tri-bimaximal mixing and form dominance depend on the pattern of the vacuum misalignment, with the two effects being uncorrelated.”
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Abstract
Tri-bimaximal neutrino mixing may arise from see-saw models based on family symmetry which is spontaneously broken by flavons with particular vacuum alignments. However recent analyses hint that tri-bimaximal mixing may be insensitive to the precise form of vacuum alignment. In this paper we derive approximate analytic results which express the deviations from tri-bimaximal neutrino mixing due to vacuum misalignment. We also relate vacuum misalignment to departures from form dominance, corresponding to deviations from the real orthogonal R matrix, where such corrections are necessary to allow for successful leptogenesis. The analytic results show that the corrections to tri-bimaximal mixing and form dominance depend on the pattern of the vacuum misalignment, with the two effects being uncorrelated.
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abstract compiled · 2026-09-23 · no language-model review
How the main claim is stated: asserted 1.00
What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.26 · human participants 0.01 · controlled comparison 0.15 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.51 · mentions code or data availability 0.01
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This table labels the abstract only (arXiv listing abstract v2). The number is the probability the classifier gave the label.
| Sentence | Role | The authors' own work | States the main conclusion | Strength |
|---|---|---|---|---|
| Tri-bimaximal neutrino mixing may arise from see-saw models based on family symmetry which is spontaneously broken by flavons with particular vacuum alignments. | background 1.00 | 0.05 | 0.03 | hedged possibility 1.00 |
| However recent analyses hint that tri-bimaximal mixing may be insensitive to the precise form of vacuum alignment. | background 0.87 | 0.04 | 0.03 | hedged possibility 1.00 |
| In this paper we derive approximate analytic results which express the deviations from tri-bimaximal neutrino mixing due to vacuum misalignment. | contribution 0.96 | 0.96 | 0.11 | asserted 1.00 |
| We also relate vacuum misalignment to departures from form dominance, corresponding to deviations from the real orthogonal $R$ matrix, where such corrections are necessary to allow for successful leptogenesis. | contribution 0.96 | 0.72 | 0.11 | asserted 0.99 |
| The analytic results show that the corrections to tri-bimaximal mixing and form dominance depend on the pattern of the vacuum misalignment, with the two effects being uncorrelated. | result 1.00 | 0.94 | 0.83 | asserted 1.00 |
What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00
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- arXiv listing abstract v2
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,300 input tokens, $0.0002 reported.
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Cited by 5 Pith papers
Reviewed papers on Pith that cite this one. The full citation record
- Leptogenesis in the two right-handed neutrino model revisited hep-ph · Jul 2011
- Trimaximal neutrino mixing from vacuum alignment in A4 and S4 models hep-ph · Jul 2011
- Phenomenology of Lepton Masses and Mixing with Discrete Flavor Symmetries hep-ph · Oct 2023
- Neutrino Mass and Mixing with Discrete Symmetry hep-ph · Jan 2013
- Right-handed neutrinos: seesaw models and signatures hep-ph · Feb 2025
How the literature uses it
10 arXiv papers cite this in 16 sentences
Papers citing it · 13 sentences without a confident label
Uses its method or tool 1 paper
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Following [ref] , we parameterise $ΔΦ_i$ in the basis of these TB column vectors $Φ_i^TB$, ΔΦ_i = ∑_j α_ij Φ^TB_j .
Trimaximal neutrino mixing from vacuum alignment in A4 and S4 models · Perturbative diagonalisation of $M_R$ · 0.91
Cites it as background 2 papers
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Yet another avenue is to introduce perturbations in the flavon sector that modify their vacuum alignments and hence the form of the lepton mass matrices [ref] .
Nonzero $\theta_{13}$ in $SO(3) \rightarrow A_4$ lepton models · Introduction · 0.92
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This scenario is referred to as form dominance in the literature [ref] .
Lepton Mixing Predictions from $S_4$ in the Tri-Direct CP approach to Two Right-handed Neutrino Models · Mixing patterns derived from $S_4$ with NO neutrino masses · 0.88
What it cites · 86 sentences without a confident label
Uses the method or tool of 2 papers
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To first order in $r,s,a$ the lepton mixing matrix $U$ (where as usual $U_MNS=U.P_Maj$) can be written as [ref] , [Other related proposals to parametrize the lepton mixing matrix have been considered in [ref] .] [equation] from which the deviations of the columns of $U= (Φ_1,Φ_2,Φ_3)$ in Eq.[ref], namely $ΔΦ_i$, may be read off as follows, [equation]
Parametrizing the lepton mixing matrix in terms of deviations from tri-bimaximal mixing · Deviations from tri-bimaximal mixing · 0.91
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To first order in $r,s,a$ the lepton mixing matrix $U$ (where as usual $U_MNS=U.P_Maj$) can be written as [ref] , [Other related proposals to parametrize the lepton mixing matrix have been considered in [ref] .] [equation] from which the deviations of the columns of $U= (Φ_1,Φ_2,Φ_3)$ in Eq.[ref], namely $ΔΦ_i$, may be read off as follows, [equation]
Nearly Tri-Bimaximal Neutrino Mixing and CP Violation · Deviations from tri-bimaximal mixing · 0.91
Uses data or values from 1 paper
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The global fits of the conventional mixing angles [ref] can be translated into the $1σ$ ranges: [equation]
Updated global fit to three neutrino mixing: status of the hints of theta13 > 0 · Deviations from tri-bimaximal mixing · 0.99
Compares with 2 papers
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We also note that the results in this paper are complementary and more general than the analytic results in [ref] which were confined to sequential dominance (SD) [ref] , and were derived in a completely different way based on a perturbative diagonalization of the neutrino mass matrix in powers of small neutrino mass ratios assuming a hierarchical mass spectrum.
Neutrino Mixing Angles in Sequential Dominance to NLO and NNLO · Introduction · 0.97
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We also note that the results in this paper are complementary and more general than the analytic results in [ref] which were confined to sequential dominance (SD) [ref] , and were derived in a completely different way based on a perturbative diagonalization of the neutrino mass matrix in powers of small neutrino mass ratios assuming a hierarchical mass spectrum.
Atmospheric and Solar Neutrinos with a Heavy Singlet · Introduction · 0.97
Cites as support 2 papers
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On the contrary, the analyses [ref] seem to motivate indirect family symmetry models with the accidental emergence of the Klein symmetry, and indicate that tri-bimaximal mixing may be insensitive to relatively large vacuum misalignment.
Tri-bimaximal Neutrino Mixing and $\theta_{13}$ · Example: deviations due to the reactor angle · 0.99
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On the contrary, the analyses [ref] seem to motivate indirect family symmetry models with the accidental emergence of the Klein symmetry, and indicate that tri-bimaximal mixing may be insensitive to relatively large vacuum misalignment.
Is the tri-bimaximal mixing accidental? · Example: deviations due to the reactor angle · 0.99
Cites as background 21 papers
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To set the notation, recall that, in the type I see-saw mechanism [ref] , the starting point is a heavy right-handed Majorana neutrino mass matrix $M_RR$ and a Dirac neutrino mass matrix (in the left-right convention) $M_D$, with the light effective left-handed Majorana neutrino mass matrix $M^ν$ given by the type I see-saw formula [ref] , [equation] In a basis in which $M_RR$ is diagonal with real and positive eigenvalues $M_i$, we may write, [equation] and $M_D$ may be written in terms of three general column vectors $m_D1,m_D2,m_D3$, [equation] The see-saw formula then gives, [equation] As first observed in [ref] $M^ν_TB$ may be achieved if the columns of the Dirac mass matrix are aligned along the columns of the TB mixing matrix, $U^TB=(Φ_1^TB, Φ_2^TB, Φ_3^TB)$, [equation] where $a_i$ are three complex constants.
A4 See-Saw Models and Form Dominance · Form Dominance · 0.94
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To set the notation, recall that, in the type I see-saw mechanism [ref] , the starting point is a heavy right-handed Majorana neutrino mass matrix $M_RR$ and a Dirac neutrino mass matrix (in the left-right convention) $M_D$, with the light effective left-handed Majorana neutrino mass matrix $M^ν$ given by the type I see-saw formula [ref] , [equation] In a basis in which $M_RR$ is diagonal with real and positive eigenvalues $M_i$, we may write, [equation] and $M_D$ may be written in terms of three general column vectors $m_D1,m_D2,m_D3$, [equation] The see-saw formula then gives, [equation] As first observed in [ref] $M^ν_TB$ may be achieved if the columns of the Dirac mass matrix are aligned along the columns of the TB mixing matrix, $U^TB=(Φ_1^TB, Φ_2^TB, Φ_3^TB)$, [equation] where $a_i$ are three complex constants.
Predicting neutrino parameters from SO(3) family symmetry and quark-lepton unification · Form Dominance · 0.94
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In the indirect models the underlying family symmetry of the Lagrangian $G_f$ is completely broken, and the flavour symmetry of the neutrino mass matrix $Z_2^S ×Z_2^U$ emerges entirely as an accidental symmetry, due to the quadratic appearance of such flavons in effective Majorana Lagrangian which results in a neutrino mass matrix of the desired form in Eq.[ref] [ref] .
On the origin of neutrino flavour symmetry · Direct vs Indirect Models · 0.90
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