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Neutrino Mass Sum-rules in Flavor Symmetry Models
High Energy Physics - Phenomenology · Submitted 29 Jul 2010
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The sum-rules could be used to distinguish some of the many models in the literature, which all lead to the same neutrino oscillation results.
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The abstract, sentence by sentence
Four different neutrino mass sum-rules have been analyzed: these frequently arise in flavor symmetry models based on the groups A_4, S_4 or T', which are often constructed to generate tri-bimaximal mixing. In general, neutrino mass can be probed in three different ways, using beta decay, neutrino-less double beta decay and cosmology. The general relations between the corresponding three neutrino mass observables are well known. The sum-rules lead to relations between the observables that are different from the general case and therefore only certain regions in parameter space are allowed. Plots of the neutrino mass observables are given for the sum-rules, and analytical expressions for the observables are provided. The case of deviations from the exact sum-rules is also discussed, which can introduce new features. The sum-rules could be used to distinguish some of the many models in the literature, which all lead to the same neutrino oscillation results.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Four different neutrino mass sum-rules have been analyzed: these frequently arise in flavor symmetry models based on the groups A_4, S_4 or T', which are often constructed to generate tri-bimaximal mixing. | contribution 0.52 | 0.24 | 0.05 | asserted 0.94 |
| s1 | In general, neutrino mass can be probed in three different ways, using beta decay, neutrino-less double beta decay and cosmology. | background 1.00 | 0.05 | 0.02 | asserted 0.77 |
| s2 | The general relations between the corresponding three neutrino mass observables are well known. | background 1.00 | 0.05 | 0.03 | asserted 1.00 |
| s3 | The sum-rules lead to relations between the observables that are different from the general case and therefore only certain regions in parameter space are allowed. | result 0.64 | 0.41 | 0.32 | asserted 1.00 |
| s4 | Plots of the neutrino mass observables are given for the sum-rules, and analytical expressions for the observables are provided. | contribution 0.80 | 0.90 | 0.10 | asserted 1.00 |
| s5 | The case of deviations from the exact sum-rules is also discussed, which can introduce new features. | contribution 0.90 | 0.55 | 0.06 | hedged possibility 0.60 |
| s6 | The sum-rules could be used to distinguish some of the many models in the literature, which all lead to the same neutrino oscillation results. | interpretation 0.95 | 0.22 | 0.46 | hedged possibility 1.00 |
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The paper
Original abstract
Four different neutrino mass sum-rules have been analyzed: these frequently arise in flavor symmetry models based on the groups A_4, S_4 or T', which are often constructed to generate tri-bimaximal mixing. In general, neutrino mass can be probed in three different ways, using beta decay, neutrino-less double beta decay and cosmology. The general relations between the corresponding three neutrino mass observables are well known. The sum-rules lead to relations between the observables that are different from the general case and therefore only certain regions in parameter space are allowed. Plots of the neutrino mass observables are given for the sum-rules, and analytical expressions for the observables are provided. The case of deviations from the exact sum-rules is also discussed, which can introduce new features. The sum-rules could be used to distinguish some of the many models in the literature, which all lead to the same neutrino oscillation results.
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References
How the literature uses it
38 arXiv papers cite this in 63 sentences
Papers citing it · 39 sentences without a confident label
Contests it 1 paper
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The only attempt to investigate approximate sum rules that we are aware of had been presented in Ref. [ref] , however, it had been pointed out [ref] that the approach in that reference is likely to be insufficient because the corrections have been attributed to one particular mass eigenvalue only, namely $m_3$.
Predictivity of Neutrino Mass Sum Rules · Introduction · contest 0.80
Builds on it 1 paper
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In [ref] this type of deviation from the sum rule was parametrized as [equation] This means that the results in [ref] can be directly translated to our case through the equality $ε=3|ϵ|/|m^0_heaviest|$.
Reactor mixing angle from hybrid neutrino masses · Sum-rules and constraints on neutrino observables · 0.88
Uses its data or values 1 paper
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We showcase the results in Fig. [ref], wherein the upper left (right) panel reflects the behaviour of $⟨m_ee ⟩$ [ref] w.r.t. sum of neutrino mass ($∑m_ν_i$) (lightest neutrino mass $m_min)$ [ref] abiding the KamLAND-Zen bound [ref] and the bottom panel shows the correlation between Majorana phases i.e., ($α_21$ and $α_31$).
Type III seesaw under $A_4$ modular symmetry with leptogenesis · Numerical Analysis · 0.80
Compares with it 4 papers
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The presence of a non-zero $θ_13$ modifies the predicted values of observable compared to the models in [ref] .
Minimal extension of tri-bimaximal mixing and generalized Z_2 X Z_2 symmetries · Phenomenology · 0.92
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Note here that the light neutrino mass matrix in Eq. ([ref]) contains 5 physical parameters ($m_0, y_2,y_3,κ̃,ϕ$), leading to a neutrino mass sum-rule [The flavor symmetry models giving an exact TMB mixing pattern have neutrino mass sum-rules [ref] , which are different from our model due to in general $y_2,3≠1$.] $1/m_ν_1-1/m_ν_3=2/m_ν_2$ in the limit $y_2,3→1$, while the neutrino mass matrix in Eq.([ref]) has 7 physical parameters.
Flavored Peccei-Quinn symmetry · Lepton sector · 0.86
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Note that this sum rule is different from previous neutrino mass sum rules obtained in the context of Majorana neutrinos [ref] .
Dirac Neutrinos with $S_4$ Flavor Symmetry in Warped Extra Dimensions · The model · 0.97
Cites it as background 16 papers
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[ref], where $C_i,χ_i$ and $d$ are constants predicted in the underlying model [ref] .
The Future of Lepton Flavor · Neutrino mass sum rules · 0.92
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As has been discussed at length in [ref] , neutrino mass sum-rules add further constraints on neutrino observables: the lightest neutrino mass ($m_light$), the sum of absolute neutrino masses ($∑m_ν_i$), the kinematic electron neutrino mass in $β$ decay ($m_β$) and the effective mass for $0νββ$ ($⟨m_ee⟩$).
Reactor mixing angle from hybrid neutrino masses · Sum-rules and constraints on neutrino observables · 0.93
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One example of these model-independent predictions is the sum rule that imposes a relation among absolute neutrino masses [ref] or neutrino mixing parameters [ref] .
Radiative Corrections to the Solar Lepton Mixing Sum Rule · Introduction · 0.84
What it cites · 21 sentences without a confident label
Builds on 3 papers
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For instance, the $A_4$ model from Ref. [ref] can be modified [ref] by adding right-handed neutrinos transforming as $3$, leading to an “inverted” sum-rule [equation] Again, by replacing the singlet $1$ by two singlets $1'$, $1”$ and assuming the same tuning between their VEVs and couplings as above, the sum-rule [ref] [equation] is found.
Deviations from tribimaximal mixing due to the vacuum expectation value misalignment in A_4 models · Sum-rules in flavor symmetry models · 0.97
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For instance, the $A_4$ model from Ref. [ref] can be modified [ref] by adding right-handed neutrinos transforming as $3$, leading to an “inverted” sum-rule [equation] Again, by replacing the singlet $1$ by two singlets $1'$, $1”$ and assuming the same tuning between their VEVs and couplings as above, the sum-rule [ref] [equation] is found.
Tri-Bimaximal Neutrino Mixing from Discrete Symmetry in Extra Dimensions · Sum-rules in flavor symmetry models · 0.97
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For instance, the $A_4$ model from Ref. [ref] can be modified [ref] by adding right-handed neutrinos transforming as $3$, leading to an “inverted” sum-rule [equation] Again, by replacing the singlet $1$ by two singlets $1'$, $1”$ and assuming the same tuning between their VEVs and couplings as above, the sum-rule [ref] [equation] is found.
Tri-Bimaximal Neutrino Mixing, A4 and the Modular Symmetry · Sum-rules in flavor symmetry models · 0.97
Uses data or values from 3 papers
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However, this would conflict with the upper bound from cosmology [ref] , so that points above $≈1.3$ eV ($≈0.5$ eV) are not shown.
Neutrino and axion hot dark matter bounds after WMAP-7 · Perturbed sum-rules · 0.92
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The best-fit values of the oscillation parameters, and their $3σ$ ranges (taken from Ref. [ref] , see Table [ref]) have been used.
Observables sensitive to absolute neutrino masses. II · General case · 1.00
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The upper limit on $$ from the Mainz and Troitsk experiments is 2.3 eV [ref] ; improvement by one order of magnitude is envisaged by the KATRIN experiment.
Final Results from phase II of the Mainz Neutrino Mass Search in Tritium $\beta$ Decay · General case · 1.00
Cites as support 1 paper
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This can be seen for instance in Ref. [ref] , where the above sum-rule is obtained with $S_4$.
Fermion Masses and Mixings in a S4 Based Model · Sum-rules in flavor symmetry models · 0.98
Cites as background 4 papers
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In most cases, a model is constructed in order to reproduce the so-called TBM pattern [ref] , defined by the following leptonic, or PMNS, mixing matrix [equation] Here $s_ij = sinθ_ij$, $c_ij = cosθ_ij$, and $P = diag(1,e^i α/2,e^i (β/2 + δ))$ contains the Majorana phases $α$ and $β$.
Symmetries and Generalisations of Tri-Bimaximal Neutrino Mixing · Introduction · 0.96
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The non-Abelian symmetries $A_4$ and $S_4$ have been widely used in the literature (see the reviews in Ref. [ref] ).
Discrete Flavor Symmetries and Models of Neutrino Mixing · Sum-rules in flavor symmetry models · 1.00
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The non-Abelian symmetries $A_4$ and $S_4$ have been widely used in the literature (see the reviews in Ref. [ref] ).
Non-Abelian Discrete Symmetries in Particle Physics · Sum-rules in flavor symmetry models · 1.00
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