Predicting neutrino parameters from SO(3) family symmetry and quark-lepton unification

S.F.King

REVIEW

Predicting neutrino parameters from SO(3) family symmetry and quark-lepton unification

S.F.King

High Energy Physics - Phenomenology · Submitted 28 Jun 2005 · 26 references

Pith's verdict: CSD is the durable contribution; the 3.06° reactor-angle number is the part that didn't survive, and the paper never quantifies its own subleading corrections to θ13^ν.

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arXiv IDhep-ph/0506297 (version 3)

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CitationS.F.King. "Predicting neutrino parameters from SO(3) family symmetry and quark-lepton unification." arXiv:hep-ph/0506297 (2005). https://pith.science/paper/FN6C2IMR

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Editor's note

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Two things here are worth your time, and one number is not. The durable piece is constrained sequential dominance: Eqs. 20–22 give a short, checkable list of conditions on Yukawa magnitudes and phases that force tri-bimaximal mixing out of the see-saw, independent of any particular family symmetry. That is a genuinely reusable result, and it is why people still cite this paper. The second piece is the complementarity relation, θ12 + (1/√2)(θ_C/3)cos(δ−π) ≈ 35.26°, which ties the solar-angle deviation to the MNS phase. The phase bookkeeping in Sec. 4 is careful, and the observation that the phase entering the charged-lepton correction to θ12 is exactly δ−π is real work, not an accident. On the reader's main worry: the 1/3 in θ_e12 ≈ θ_C/3 is not a free choice. It falls out of the Σ adjoint coupling, where the hypercharge of e^c versus d^c (Y=1 vs 1/3) supplies the Georgi-Jarlskog factor — Eq. 48 with Eqs. 50–51. I would push back on scoring that as arbitrary. The model has many parameters, but they are fixed in the charged-fermion sector; nothing is tuned to neutrino data, which was the whole point. The real soft spot is the one the stress test flags, and it sits in the paper's own text. θ13 ≈ 3.06° needs θ13^ν = 0, which CSD enforces by e*b + f*c = 0 exactly. But the sentence after Eq. 52 says subleading operators with φ23/M² ~ ε̄ ≈ 0.15 correct the Yukawa entries, breaking a=b=c and e=−f at that order. Nobody propagates this into Eq. 15. With M1/M2 only bounded by Eq. 55, θ13^ν could plausibly be a degree — a third of the prediction, and larger than the −0.5° RG shift the paper does quote. The honest prediction is a range of roughly 2–4°, and the abstract's sharp 3.06° overstates it. For what it is worth, the measured θ13 is about 8.8°, so the specific number is dead. That does not retroactively kill the framework — CSD and the complementarity template are what later model builders picked up — but the testability claim has now been settled against the paper. Worth a serious referee. Send it out, and have the referee press on whether the CSD conditions are truly sufficient rather than merely consistent.

Referee report

Significance

The paper's strengths are real and should be named. The CSD conditions in Eqs. 20–22 are a clean, family-symmetry-independent characterization of tri-bimaximal mixing from sequential dominance, and the derivation of the charged-lepton corrections in Eqs. 73–82 is careful about phases. The δ–θ12 relation in Eq. 111 is a genuinely novel and falsifiable prediction linking a low-energy neutrino observable to the phase structure of the unified model. The construction is worked out in enough detail (Table 1, Eqs. 33–54, Appendix B) to be credible as a model-building paper, and the predictions are stated with ranges where the model leaves a phase undetermined (Eqs. 105–108). The paper is a useful contribution to the quark-lepton complementarity literature.

Major objections (2)

[§4, Eqs. 15, 22, 81, 99] The sharpness of the headline prediction θ13 ≈ 3.06° rests on θ13^ν = 0, which holds only at leading order in CSD. Eq. 15 gives θ13^ν ∝ |a|(e*b + f*c)/[|e|²+|f|²]^{3/2} × Y/X, and CSD (Eq. 22) sets e*b + f*c = 0 exactly. However, the text immediately after Eq. 52 states that subleading operators with φ23/M² ∼ ε̄ ∼ 0.15 correct the Yukawa entries, which breaks e*b + f*c = 0 at order ε̄. The paper does not estimate the resulting θ13^ν. Since Y/X is only constrained to be ≪ 1 by Eq. 55, a correction of order ε̄ × (Y/X) could be a non-negligible fraction of 3.06°, comparable to the paper's own quoted RG error of −0.5° in Eq. 113. The authors acknowledge 'subleading operator corrections' generically after Eq. 114, but do not propagate them to θ13. An explicit estimate of this correction, or a symmetry argument showing it is suppressed, is needed to support the claim that θ13 ≈ 3.06° is a sharp testable prediction.
[§4, Eqs. 96–99 and 42–48] The factor of 1/3 in θEL12 ≈ θC/3 is not a free choice: within the model it follows from the Σ adjoint coupling, whose hypercharge Y(e)=1 versus Y(d)=1/3 supplies the Georgi-Jarlskog factor (Eq. 48; Eq. 51 versus Eq. 50). That is a strength of the construction and answers the concern that the 1/3 is arbitrary. However, the derivation relies on the messenger-scale assumption M_e ≈ M_d (Eq. 42) and on the specific expansion parameters in Eqs. 43–48, which are chosen to fit the charged fermion masses. The paper does not quantify how sensitive the 3.06° prediction is to these assumptions. A brief estimate of the tolerance on M_e/M_d and on ε̄ would strengthen the claim that the prediction is a consequence of the unification rather than of the parameter choices.

Minor objections (5)

[§3, first paragraph; §2 after Eq. 20; Appendix A] There are several typographical errors: 'famly' in the Section 3 introduction, 'automaticaly' after Eq. 20, 'analagous' in Appendix A, and 'Froggat-Nielsen' after Eq. 41 (should be Froggatt-Nielsen). The spelling of 'seesaw' and 'see-saw' is inconsistent throughout.
[Footnote 1 and reference [15]] The bi-maximal complementarity comparison in footnote 1 cites Bjorken's work as unpublished. Since the footnote uses this comparison to motivate the tri-bimaximal relation, a published reference for the bi-maximal complementarity claim would help the reader.
[Eq. 42] The relation M_d ≈ (1/3)M_u is asserted without explanation. A sentence on its origin, or a reference to where it is derived, would help the reader assess how much of the subsequent prediction depends on this numerical choice.
[§4, Eqs. 65, 83–85] The paper claims consistency with all quark and lepton masses and mixings, but the mass ratios in Eqs. 65, 83, and 84 are order-of-magnitude relations with O(1) Yukawa couplings. A more explicit statement of the accuracy of these fits, and of the factors of 2 and 3 in Eqs. 49–52, would make the 'realistic model' claim easier to assess.
[Eq. 4] It would help to state explicitly that the matrix in Eq. 4 is the tri-bimaximal form and to connect its entries directly to the CSD conditions in Eqs. 20–22, so that the reader can see at a glance which condition fixes which entry.

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The paper

The paper claims

The paper argues that tri-bimaximal neutrino mixing, corrected by charged-lepton mixing tied to quark mixing via Pati-Salam unification, predicts a reactor angle near 3.06 degrees and a CP phase fixed by the solar angle.

The reading

The paper asks whether the neutrino mixing angles and the neutrino CP phase can be predicted by starting from tri-bimaximal neutrino mixing and then correcting it with charged-lepton mixing that is tied to quark mixing through Pati-Salam unification. The motivation is that quark mixing angles are measured much better than neutrino parameters, so a unified relation would turn future neutrino measurements into tests of high-energy unification. The author shows that constrained sequential dominance can produce tri-bimaximal neutrino mixing from the see-saw mechanism, builds an $SO(3)$ family-symmetry model that realizes it, and uses Georgi-Jarlskog relations to relate the charged-lepton mixing angle to the Cabibbo angle. The resulting relations predict a reactor angle near $3.06^circ$, an atmospheric angle within $2.4^circ$ of maximal, and a CP phase fixed by the solar angle. If borne out, high-precision neutrino experiments would be probing the structure of quark-lepton unification.

What carries the argument

The load-bearing mechanism is tri-bimaximal complementarity: the physical MNS matrix is $V_{eL}V_{nu L}^dagger$, with $V_{nu L}$ tri-bimaximal from constrained sequential dominance (CSD) and $V_{eL}$ a small charged-lepton mixing matrix related to quark mixing. CSD imposes $|a|=|b|=|c|$, $|e|=|f|$, $d=0$, and phases $phi'_b=0$, $phi'_c=pi$ on the neutrino Yukawa matrix, which yields $tan theta^nu_{23}=1$, $tan theta^nu_{12}=1/sqrt{2}$, and $theta^nu_{13}=0$ independently of neutrino masses. The Georgi-Jarlskog relations, especially $theta_{e12} approx theta_C/3$, then convert the charged-lepton correction into the reactor-angle prediction and the solar-angle/CP-phase relation. The $SO(3)$ family symmetry and Pati-Salam messenger sector are the model-building machinery that produces these Yukawa textures and vacuum alignments.

Extended reading notes

Core claim

The central claim is that starting from tri-bimaximal neutrino mixing and applying charged-lepton corrections whose size is fixed by quark-lepton unification gives a small set of relations among measurable neutrino parameters. In the model, constrained sequential dominance makes the neutrino mixing matrix tri-bimaximal, while the Georgi-Jarlskog relations make the charged-lepton 1-2 mixing angle one third of the Cabibbo angle, $theta_{e12} approx theta_C/3$, and make $theta_{e23}$ and $theta_{e13}$ track the corresponding CKM angles. The resulting MNS matrix predicts $theta_{13} approx theta_C/(3sqrt{2}) approx 3.06^circ$, or $sin^2 2theta_{13} approx 1.1times 10^{-2}$; $theta_{23} approx 45^circ pm 2.4^circ$, with the correction controlled by a quark-sector phase; and the tri-bimaximal complementarity relation $theta_{12}+(theta_C/(3sqrt{2}))cos(delta-pi) approx 35.26^circ$. Equivalently, a measured solar angle fixes the neutrino CP phase through $cos(delta-pi) approx (35.26^circ-theta_{12})/3.06^circ$. The author presents an explicit $SO(3)$ family-symmetry model with Pati-Salam unification that realizes these ingredients, so the predictions are meant as tests of that unified structure rather than as general theorems.

Load-bearing premise

The prediction of a small reactor angle depends on the Georgi-Jarlskog relation $theta_{e12} approx theta_C/3$, a modeling choice motivated by $m_mu/m_s=3$ at the unification scale rather than derived from first principles; a different Clebsch factor would change $theta_{13}$ substantially.

Editorial extensions

If this is right

The reactor angle is predicted at $theta_{13} approx 3.06^circ$, equivalently $sin^2 2theta_{13} approx 1.1times 10^{-2}$, a target for next-generation reactor and superbeam experiments.
The atmospheric angle is maximal to within the CKM angle: $theta_{23}=45^circ pm 2.4^circ$, with the sign and size of the correction controlled by a quark-sector phase.
A precise solar-angle measurement determines the neutrino CP phase through $cos(delta-pi) approx (35.26^circ-theta_{12})/3.06^circ$, so a neutrino factory could test the relation.
The scheme ties low-energy neutrino parameters to Pati-Salam unification and the Georgi-Jarlskog relations, so precision neutrino data would probe the high-energy quark-lepton structure.
If constrained sequential dominance holds, tri-bimaximal neutrino mixing follows independently of the neutrino masses, with charged-lepton corrections producing the observable deviations.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If next-generation experiments find $theta_{13}$ near $3^circ$, that would support the Georgi-Jarlskog $1/3$ factor and weaken the alternative Clebsch-$3/2$ route that gives $theta_{13} approx theta_C$.
The CP-phase relation makes the model overdetermined: a precise $theta_{12}$ plus an independent $delta$ measurement could reveal whether any discrepancy comes from renormalization-group running or from the family-symmetry sector.
Because the atmospheric-angle correction carries an undetermined quark phase, $theta_{23}$ alone is a weak test; the sharper test is the correlated pattern of $theta_{13}$, $theta_{12}$, and $delta$.
The same CSD conditions could be embedded in discrete family symmetries; if those embeddings reproduce the same $theta_{13}$ and $delta$ relations, the predictions would be less tied to $SO(3)$ and more tied to the CSD-plus-GJ structure.

Original abstract

We show how the neutrino mixing angles and oscillation phase can be predicted from tri-bimaximal neutrino mixing, corrected by charged lepton mixing angles which are related to quark mixing angles via quark-lepton unification. The tri-bimaximal neutrino mixing can naturally originate from the see-saw mechanism via constrained sequential dominance (CSD), where CSD can result from the vacuum alignment of a non-Abelian family symmetry such as SO(3). We construct a realistic model of quark and lepton masses and mixings based on SO(3) family symmetry with quark-lepton unification based on the Pati-Salam gauge group. The atmospheric angle is predicted to be approximately maximal $\theta_{23}= 45^\circ$, corrected by the quark mixing angle $\theta_{23}^{\mathrm{CKM}}\approx 2.4^\circ$, with the correction controlled by an undetermined phase in the quark sector. The solar angle is predicted by the tri-bimaximal complementarity relation: $\theta_{12}+ \frac{1}{\sqrt{2}}\frac{\theta_{\mathrm{C}}}{3} \cos (\delta - \pi) \approx 35.26^\circ $, where $\theta_{\mathrm{C}}$ is the Cabibbo angle and $\delta$ is the neutrino oscillation phase. The reactor angle is predicted to be $\theta_{13} \approx \frac{1}{\sqrt{2}}\frac{\theta_{\mathrm{C}}}{3}\approx 3.06^\circ$. The MNS neutrino oscillation phase $\delta$ is predicted in terms of the solar angle to be $\cos (\delta - \pi) \approx (35.26^\circ - \theta_{12}^\circ)/3.06^\circ $. These predictions can all be tested by future high precision neutrino oscillation experiments, thereby probing the nature of high energy quark-lepton unification.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 6,829 input tokens, $0.0003 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.74 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.98 · compares with prior results 0.14 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; show every role.

We show how the neutrino mixing angles and oscillation phase can be predicted from tri-bimaximal neutrino mixing, corrected by charged lepton mixing angles which are related to quark mixing angles via quark-lepton unification. The tri-bimaximal neutrino mixing can naturally originate from the see-saw mechanism via constrained sequential dominance (CSD), where CSD can result from the vacuum alignment of a non-Abelian family symmetry such as SO(3). We construct a realistic model of quark and lepton masses and mixings based on SO(3) family symmetry with quark-lepton unification based on the Pati-Salam gauge group. The atmospheric angle is predicted to be approximately maximal $\theta_{23}= 45^\circ$, corrected by the quark mixing angle $\theta_{23}^{\mathrm{CKM}}\approx 2.4^\circ$, with the correction controlled by an undetermined phase in the quark sector. The solar angle is predicted by the tri-bimaximal complementarity relation: $\theta_{12}+ \frac{1}{\sqrt{2}}\frac{\theta_{\mathrm{C}}}{3} \cos (\delta - \pi) \approx 35.26^\circ $, where $\theta_{\mathrm{C}}$ is the Cabibbo angle and $\delta$ is the neutrino oscillation phase. The reactor angle is predicted to be $\theta_{13} \approx \frac{1}{\sqrt{2}}\frac{\theta_{\mathrm{C}}}{3}\approx 3.06^\circ$. The MNS neutrino oscillation phase $\delta$ is predicted in terms of the solar angle to be $\cos (\delta - \pi) \approx (35.26^\circ - \theta_{12}^\circ)/3.06^\circ $. These predictions can all be tested by future high precision neutrino oscillation experiments, thereby probing the nature of high energy quark-lepton unification.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We show how the neutrino mixing angles and oscillation phase can be predicted from tri-bimaximal neutrino mixing, corrected by charged lepton mixing angles which are related to quark mixing angles via quark-lepton unification.	contribution 0.92	0.88	0.72	asserted 1.00
s1	The tri-bimaximal neutrino mixing can naturally originate from the see-saw mechanism via constrained sequential dominance (CSD), where CSD can result from the vacuum alignment of a non-Abelian family symmetry such as SO(3).	background 0.81	0.16	0.07	hedged possibility 0.76
s2	We construct a realistic model of quark and lepton masses and mixings based on SO(3) family symmetry with quark-lepton unification based on the Pati-Salam gauge group.	contribution 0.81	0.93	0.11	asserted 1.00
s3	The atmospheric angle is predicted to be approximately maximal $\theta_{23}= 45^\circ$, corrected by the quark mixing angle $\theta_{23}^{\mathrm{CKM}}\approx 2.4^\circ$, with the correction controlled by an undetermined phase in the quark sector.	result 1.00	0.86	0.19	asserted 0.98
s4	The solar angle is predicted by the tri-bimaximal complementarity relation: $\theta_{12}+ \frac{1}{\sqrt{2}}\frac{\theta_{\mathrm{C}}}{3} \cos (\delta - \pi) \approx 35.26^\circ $, where $\theta_{\mathrm{C}}$ is the Cabibbo angle and $\delta$ is the neutrino oscillation phase.	result 0.99	0.78	0.16	asserted 0.99
s5	The reactor angle is predicted to be $\theta_{13} \approx \frac{1}{\sqrt{2}}\frac{\theta_{\mathrm{C}}}{3}\approx 3.06^\circ$.	result 1.00	0.85	0.11	asserted 1.00
s6	The MNS neutrino oscillation phase $\delta$ is predicted in terms of the solar angle to be $\cos (\delta - \pi) \approx (35.26^\circ - \theta_{12}^\circ)/3.06^\circ $.	result 1.00	0.85	0.14	asserted 1.00
s7	These predictions can all be tested by future high precision neutrino oscillation experiments, thereby probing the nature of high energy quark-lepton unification.	interpretation 0.54	0.20	0.32	hedged possibility 0.82

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.95.

What was examined, and what was not

sources read

arXiv listing abstract v3

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

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S sections
T body sentences
C citations
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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

References

Works cited (26)

[1]

M. Maltoni, T. Schwetz, M. A. Tortola and J. W. F. Valle, Ne w J. Phys. 6 (2004) 122 [arXiv:hep-ph/0405172]

View on Pith Pith review arXiv 2004
[2]

F.J.Gilman et al, in Review of Particle Physics (2004), p.130

View on Pith 2004
[3]

For a review see e.g. S. F. King, Rept. Prog. Phys. 67 (2004) 107 [arXiv:hep-ph/0310204]

View on Pith Pith review arXiv 2004
[4]

H. Minakata, “Quark-Lepton Complementarity: a Review, ” arXiv:hep-ph/0505262

View on Pith Pith review arXiv
[5]

M. Raidal, Phys. Rev. Lett. 93 (2004) 161801, hep-ph/0404046

View on Pith Pith review arXiv 2004
[6]

H. Minakata and A. Y. Smirnov, Phys. Rev. D 70, 073009 (2004), hep-ph/0405088

View on Pith Pith review arXiv 2004
[7]

P. H. Frampton and R. N. Mohapatra, JHEP 0501, 025 (2005), hep-ph/0407139. 23

View on Pith Pith review arXiv 2005
[8]

J. Ferrandis and S. Pakvasa, Phys. Rev. D 71 (2005) 033004, hep-ph/0412038; S. K. Kang, C. S. Kim and J. Lee, arXiv:hep-ph/0501029; N. Li a nd B. Q. Ma, hep-ph/0501226; K. Cheung, S. K. Kang, C. S. Kim and J. Lee, he p-ph/0503122; Z. z. Xing, hep-ph/0503200; A. Datta, L. Everett and P. Ramon d, arXiv: hep-ph/0503222; T. Ohlsson, arXiv:hep-ph/0506094

View on Pith Pith review arXiv 2005
[9]

S. Antusch, S. F. King and R. N. Mohapatra, arXiv:hep-ph/ 0504007

View on Pith
[10]

M. Lindner, M. A. Schmidt and A. Y. Smirnov, arXiv:hep-p h/0505067

View on Pith
[11]

S. F. King and N. N. Singh, Nucl. Phys. B 596 (2001) 81 [arXiv:hep-ph/0007243]

View on Pith Pith review arXiv 2001
[12]

S. F. King, JHEP 0209 (2002) 011 [arXiv:hep-ph/0204360]; S. F. King, Phys. Rev. D 67 (2003) 113010 [arXiv:hep-ph/0211228]

View on Pith Pith review arXiv 2002
[13]

H. Georgi and C. Jarlskog, Phys. Lett. B 86 (1979) 297

View on Pith 1979
[14]

P. F. Harrison, D. H. Perkins and W. G. Scott, Phys. Lett. B 530 (2002) 167 [arXiv:hep-ph/0202074]; P. F. Harrison and W. G. Scott, Phy s. Lett. B 535 (2002) 163 [arXiv:hep-ph/0203209]; P. F. Harrison and W. G. Scott, Phys. Lett. B 557 (2003) 76 [arXiv:hep-ph/0302025]; C.I.Low and R.R.Volkas , hep-ph/0305243; see also: L. Wolfenstein, Phys. Rev. D 18 (1978) 958

View on Pith Pith review arXiv 2002
[15]

J. D. Bjorken(unpublished); J. Ferrandis and S. Pakvas a, Phys. Lett. B 603 (2004) 184 [arXiv:hep-ph/0409204]

View on Pith Pith review arXiv 2004
[16]

G. G. Ross, Proceedings of Seesaw 25, Int. Conf. on the Se esaw mechanism, 10- 11 June 2004, Paris; S. F. King and G. G. Ross, Phys. Lett. B 574 (2003) 239 [arXiv:hep-ph/0307190]; S. F. King and G. G. Ross, Phys. Let t. B 520 (2001) 243 [arXiv:hep-ph/0108112]

View on Pith Pith review arXiv 2003
[17]

G. Altarelli and F. Feruglio, arXiv:hep-ph/0504165; E . Ma, arXiv:hep-ph/0505209; E. Ma, Phys. Rev. D 70 (2004) 031901

View on Pith Pith review arXiv 2004
[18]

S. F. King, Phys. Lett. B 439 (1998) 350 [arXiv:hep-ph/9806440]; S. F. King, Nucl. Phys. B 562 (1999) 57 [arXiv:hep-ph/9904210]; S. F. King, Nucl. Phys. B 576 (2000) 85 [arXiv:hep-ph/9912492]

View on Pith Pith review arXiv 1998
[19]

S. Antusch and S. F. King, Nucl. Phys. B 705 (2005) 239 [arXiv:hep-ph/0402121]

View on Pith Pith review arXiv 2005
[20]

T. Hambye and G. Senjanovic, Phys. Lett. B 582 (2004) 73 [arXiv:hep-ph/0307237]; S. Antusch and S. F. King, Phys. Lett. B 597 (2004) 199 [arXiv:hep-ph/0405093]

View on Pith Pith review arXiv 2004
[21]

R. Barbieri, L. J. Hall, G. L. Kane and G. G. Ross, arXiv:h ep-ph/9901228. 24

View on Pith
[22]

R. G. Roberts, A. Romanino, G. G. Ross, and L. Velasco-Se villa, Nucl. Phys. B615 (2001), 358–384, hep-ph/0104088; B. C. Allanach and S. F. Ki ng, Nucl. Phys. B 456 (1995) 57 [arXiv:hep-ph/9502219]; B. C. Allanach and S. F. K ing, Nucl. Phys. B 459 (1996) 75 [arXiv:hep-ph/9509205]; B. C. Allanach, S. F. Kin g, G. K. Leontaris and S. Lola, Phys. Lett. B 40...

View on Pith Pith review arXiv 2001
[23]

J. C. Pati and A. Salam, Phys. Rev. D 10 , 270 (1974)

View on Pith 1974
[24]

S. F. King, Phys. Lett. B 325 (1994) 129 [Erratum-ibid. B 325 (1994) 538]

View on Pith 1994
[25]

S. F. King and Q. Shaﬁ, Phys. Lett. B 422 (1998) 135 [arXiv:hep-ph/9711288]

View on Pith Pith review arXiv 1998
[26]

S. Antusch, J. Kersten, M. Lindner, M. Ratz and M. A. Schm idt, JHEP 0503 (2005) 024 [arXiv:hep-ph/0501272]. 25

View on Pith Pith review arXiv 2005

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hep-ph 2011-03 conditional novelty 5.0 of 10

Two explicit SU(5) models with A4 or S4 family symmetry and Z2/Z4 shaping symmetries predict a right-angled CKM unitarity triangle alongside tri-bimaximal lepton mixing.
Revisiting Bimaximal Neutrino Mixing in a Model with S4 Discrete Symmetry
hep-ph 2009-03 conditional novelty 5.0 of 10

An S4 x Z4 x U(1) flavour model reproduces bimaximal neutrino mixing at leading order and shifts only the solar and reactor angles by Cabibbo-sized charged-lepton corrections, leaving the atmospheric angle maximal at ...
A4 See-Saw Models and Form Dominance
hep-ph 2009-03 conditional novelty 5.0 of 10

Form Dominance, a generalization of Constrained Sequential Dominance, links each right-handed neutrino to one light neutrino mass eigenstate and is shown to hold in two minimal A4 see-saw models, producing testable ma...
The Future of Lepton Flavor
hep-ph 2026-06 unverdicted novelty 4.0 of 10

Upcoming neutrino experiments are projected to substantially reduce the number of viable leptonic flavor models in five popular classes by measuring mass ordering, theta_23 octant, delta_CP, and absolute mass scale.
Interpreting the KM3-230213A PeV Neutrino Event via Vector Dark Matter Decay and Its Multi-Messenger Signatures
hep-ph 2025-07 conditional novelty 4.0 of 10

A U(1)_X vector dark matter model explains the KM3-230213A PeV neutrino via DM decay and predicts a cosmic string gravitational wave background consistent with PTA observations, but with several parameters fitted to the data.
Discrete Flavour Groups, \theta_13 and Lepton Flavour Violation
hep-ph 2012-05 conditional novelty 4.0 of 10

Among discrete flavour models, Lin-type A4 best reproduces the measured mixing angles, and in the CMSSM the MEG muon-to-electron-gamma bound excludes the parameter region needed for the muon g-2 anomaly.
The minimal seesaw and leptogenesis models
hep-ph 2020-08 accept novelty 3.0 of 10

A comprehensive review of the two-right-handed-neutrino seesaw and its leptogenesis, organizing parametrizations, texture zeros, flavor symmetries and CP-violation predictions against current neutrino oscillation data.
Models of Neutrino Mass, Mixing and CP Violation
hep-ph 2015-10 conditional novelty 3.0 of 10

Neutrino mixing data, especially the large reactor angle, is argued to favour models with a non-Abelian discrete family symmetry and constrained sequential dominance, which tie lepton mixing angles to a single CP-viol...
Pieces of the Flavour Puzzle
hep-ph 2015-03 accept novelty 3.0 of 10

The review argues that fermion masses and mixing angles can be organized by a single map with order-one inputs, realizable in many frameworks including SU(5) and SO(10) unification, but that no compelling symmetry pri...
Neutrino Mass and Mixing: from Theory to Experiment
hep-ph 2014-02 accept novelty 3.0 of 10

A structured review of discrete non-Abelian family symmetries in neutrino physics, covering finite-group theory, model-building strategies (flavons vs multi-Higgs, direct vs indirect), and the mixing and mass sum rule...
Neutrino Mass and Mixing with Discrete Symmetry
hep-ph 2013-01 conditional novelty 3.0 of 10

Discrete family symmetry remains a viable framework for neutrino flavour after Daya Bay and RENO, but only if models include controlled corrections, new flavon alignments, or larger groups that generate a non-zero rea...
Repressing Anarchy in Neutrino Mass Textures
hep-ph 2012-07 conditional novelty 3.0 of 10

Against 2012 neutrino data, a hierarchical U(1) charge pattern (no seesaw) and a pseudo mu-tau anarchy pattern (seesaw) reproduce mixing and mass ratios far more often than pure Anarchy, at equal parameter count.
Neutrino Mass and Mixing with Modular Symmetry
hep-ph 2023-11 accept novelty 2.0 of 10

Modular symmetry can organize neutrino masses and lepton mixing through a single modulus and modular forms, but the reviewed models still fit several parameters to data.
Unified Models of Neutrinos, Flavour and CP Violation
hep-ph 2017-01 accept novelty 2.0 of 10

A review argues that viable neutrino flavour models should be predictive, minimal, symmetry-based, and unified, and presents the Littlest Seesaw as the leading candidate.
Neutrinos
hep-ex 2013-10 accept novelty 2.0 of 10

The 2013 Snowmass neutrino working group report surveys three-flavor oscillation, mass ordering, CP violation, absolute mass, double-beta decay, scattering, and sterile-neutrino anomalies, and recommends a staged long...
Right-handed neutrinos: seesaw models and signatures
hep-ph 2025-02 conditional novelty 1.0 of 10

A pedagogical review that explains how adding right-handed neutrinos can generate small neutrino masses through seesaw mechanisms and what experimental signatures such models predict.
Discrete Flavor Symmetries and Models of Neutrino Mixing
hep-ph 2010-02 accept novelty 1.0 of 10

A review of how A4, S4, and related discrete flavor groups can produce tri-bimaximal neutrino mixing at leading order, with small calculable corrections and testable predictions for theta13 and lepton flavor violation.
A review of mu-tau flavor symmetry in neutrino physics
hep-ph 2015-12 accept

An approximate mu-tau symmetry of the neutrino mass matrix can organize the observed lepton mixing pattern, and its soft breaking can account for the small reactor angle and CP violation.

How later papers used it

88 later papers cite it

Evidence: substantial. 54 of the citing papers share no author with it, and 6 of those carry a confident label from Pith's citation classifier.

Pith read 21 of the 200 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

1 paper by the same authors is listed below: 1 used its method or tool.

Uses its method or tool 1 paper · 1 by the same authors

By the same authors

Used the idea of constrained sequential dominance to derive the tri-bimaximal form of the neutrino mass matrix from the see-saw mechanism.

Neutrino Mass Models: a road map (2008) (same authors) · 0.85 · paraphrased: the licence does not allow quoting

How the literature uses it

82 arXiv papers cite this in 191 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 140 sentences without a confident label

Uses its method or tool 1 paper

It is possible to derive the TB form of the neutrino mass matrix in Eq.[ref] from the see-saw mechanism in a very elegant way using the idea of constrained sequential dominance (CSD) [ref] as follows.

Neutrino Mass Models: a road map · Family Symmetry? · 0.85

Uses its data or values 1 paper

The experiments have measured the two mass-squared differences (solar and atmospheric) associated with neutrino oscillations, and the ratio of the solar-to-atmospheric mass-squared difference ($r$) is found to be [ref] [equation] This may be an indication of the involvement of two different mass scales that might originate from entirely separate mechanisms[Within the framework of type-I seesaw mechanism, the hierarchy of the atmospheric and solar neutrino mass scales can also be explained through the mechanisms of sequential dominance [ref] and constrained sequential dominance [ref] where one of the right-handed neutrinos is considered to dominantly contribute the light neutrino masses.].

Phenomenology of the flavor symmetric scoto-seesaw model with dark matter and TM$_1$ mixing · Introduction · 0.82

Compares with it 7 papers

It is remarkable that Eq.([ref]) belongs to a set of well-known leptonic mixing sum rules [ref] , and the same results have been obtained in Ref. [ref] .

Adjoint SUSY $SU(5)$ Grand Unified Model with $S_4$ Flavor Symmetry · Down type quarks and charged leptons sector · 0.91
The result obtained on the trimaximal condition later is also different from the constrained sequential dominance [ref] .

Conditions of naturalness and fine-tunings for type-I seesaw mechanism with four-zero texture · Reasons for conditions · 0.99
It is interesting to compare FD for TBM defined above to Constrained Sequential Dominance (CSD) defined in [ref] .

A4 See-Saw Models and Form Dominance · Form Dominance · 0.97

Cites it as background 35 papers

A very predictive minimal seesaw model with one texture zero is the so-called CSD($n$) model [ref] , where the parameter $n$ was usually assumed to be a positive integer.

A New Littlest Seesaw Model · Introduction · 0.87
Tri-bimaximal neutrino mixing [ref] corresponds to the choice [ref] : [equation] This is called constrained sequential dominance (CSD) [ref] .

Lepton Flavour Violation in the Constrained MSSM with Constrained Sequential Dominance · CSD and tri-bimaximal neutrino mixing · 0.84
A very predictive minimal seesaw model with two right-handed neutrinos and one texture zero is the so-called constrained sequential dominance (CSD) model [ref] .

Littlest Modular Seesaw · Introduction · 0.83

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

[1] [1]

M. Maltoni, T. Schwetz, M. A. Tortola and J. W. F. Valle, Ne w J. Phys. 6 (2004) 122 [arXiv:hep-ph/0405172]

View on Pith Pith review arXiv 2004

[2] [2]

F.J.Gilman et al, in Review of Particle Physics (2004), p.130

View on Pith 2004

[3] [3]

For a review see e.g. S. F. King, Rept. Prog. Phys. 67 (2004) 107 [arXiv:hep-ph/0310204]

View on Pith Pith review arXiv 2004

[4] [4]

H. Minakata, “Quark-Lepton Complementarity: a Review, ” arXiv:hep-ph/0505262

View on Pith Pith review arXiv

[5] [5]

M. Raidal, Phys. Rev. Lett. 93 (2004) 161801, hep-ph/0404046

View on Pith Pith review arXiv 2004

[6] [6]

H. Minakata and A. Y. Smirnov, Phys. Rev. D 70, 073009 (2004), hep-ph/0405088

View on Pith Pith review arXiv 2004

[7] [7]

P. H. Frampton and R. N. Mohapatra, JHEP 0501, 025 (2005), hep-ph/0407139. 23

View on Pith Pith review arXiv 2005

[8] [8]

J. Ferrandis and S. Pakvasa, Phys. Rev. D 71 (2005) 033004, hep-ph/0412038; S. K. Kang, C. S. Kim and J. Lee, arXiv:hep-ph/0501029; N. Li a nd B. Q. Ma, hep-ph/0501226; K. Cheung, S. K. Kang, C. S. Kim and J. Lee, he p-ph/0503122; Z. z. Xing, hep-ph/0503200; A. Datta, L. Everett and P. Ramon d, arXiv: hep-ph/0503222; T. Ohlsson, arXiv:hep-ph/0506094

View on Pith Pith review arXiv 2005

[9] [9]

S. Antusch, S. F. King and R. N. Mohapatra, arXiv:hep-ph/ 0504007

View on Pith

[10] [10]

M. Lindner, M. A. Schmidt and A. Y. Smirnov, arXiv:hep-p h/0505067

View on Pith

[11] [11]

S. F. King and N. N. Singh, Nucl. Phys. B 596 (2001) 81 [arXiv:hep-ph/0007243]

View on Pith Pith review arXiv 2001

[12] [12]

S. F. King, JHEP 0209 (2002) 011 [arXiv:hep-ph/0204360]; S. F. King, Phys. Rev. D 67 (2003) 113010 [arXiv:hep-ph/0211228]

View on Pith Pith review arXiv 2002

[13] [13]

H. Georgi and C. Jarlskog, Phys. Lett. B 86 (1979) 297

View on Pith 1979

[14] [14]

P. F. Harrison, D. H. Perkins and W. G. Scott, Phys. Lett. B 530 (2002) 167 [arXiv:hep-ph/0202074]; P. F. Harrison and W. G. Scott, Phy s. Lett. B 535 (2002) 163 [arXiv:hep-ph/0203209]; P. F. Harrison and W. G. Scott, Phys. Lett. B 557 (2003) 76 [arXiv:hep-ph/0302025]; C.I.Low and R.R.Volkas , hep-ph/0305243; see also: L. Wolfenstein, Phys. Rev. D 18 (1978) 958

View on Pith Pith review arXiv 2002

[15] [15]

J. D. Bjorken(unpublished); J. Ferrandis and S. Pakvas a, Phys. Lett. B 603 (2004) 184 [arXiv:hep-ph/0409204]

View on Pith Pith review arXiv 2004

[16] [16]

G. G. Ross, Proceedings of Seesaw 25, Int. Conf. on the Se esaw mechanism, 10- 11 June 2004, Paris; S. F. King and G. G. Ross, Phys. Lett. B 574 (2003) 239 [arXiv:hep-ph/0307190]; S. F. King and G. G. Ross, Phys. Let t. B 520 (2001) 243 [arXiv:hep-ph/0108112]

View on Pith Pith review arXiv 2003

[17] [17]

G. Altarelli and F. Feruglio, arXiv:hep-ph/0504165; E . Ma, arXiv:hep-ph/0505209; E. Ma, Phys. Rev. D 70 (2004) 031901

View on Pith Pith review arXiv 2004

[18] [18]

S. F. King, Phys. Lett. B 439 (1998) 350 [arXiv:hep-ph/9806440]; S. F. King, Nucl. Phys. B 562 (1999) 57 [arXiv:hep-ph/9904210]; S. F. King, Nucl. Phys. B 576 (2000) 85 [arXiv:hep-ph/9912492]

View on Pith Pith review arXiv 1998

[19] [19]

S. Antusch and S. F. King, Nucl. Phys. B 705 (2005) 239 [arXiv:hep-ph/0402121]

View on Pith Pith review arXiv 2005

[20] [20]

T. Hambye and G. Senjanovic, Phys. Lett. B 582 (2004) 73 [arXiv:hep-ph/0307237]; S. Antusch and S. F. King, Phys. Lett. B 597 (2004) 199 [arXiv:hep-ph/0405093]

View on Pith Pith review arXiv 2004

[21] [21]

R. Barbieri, L. J. Hall, G. L. Kane and G. G. Ross, arXiv:h ep-ph/9901228. 24

View on Pith

[22] [22]

R. G. Roberts, A. Romanino, G. G. Ross, and L. Velasco-Se villa, Nucl. Phys. B615 (2001), 358–384, hep-ph/0104088; B. C. Allanach and S. F. Ki ng, Nucl. Phys. B 456 (1995) 57 [arXiv:hep-ph/9502219]; B. C. Allanach and S. F. K ing, Nucl. Phys. B 459 (1996) 75 [arXiv:hep-ph/9509205]; B. C. Allanach, S. F. Kin g, G. K. Leontaris and S. Lola, Phys. Lett. B 40...

View on Pith Pith review arXiv 2001

[23] [23]

J. C. Pati and A. Salam, Phys. Rev. D 10 , 270 (1974)

View on Pith 1974

[24] [24]

S. F. King, Phys. Lett. B 325 (1994) 129 [Erratum-ibid. B 325 (1994) 538]

View on Pith 1994

[25] [25]

S. F. King and Q. Shaﬁ, Phys. Lett. B 422 (1998) 135 [arXiv:hep-ph/9711288]

View on Pith Pith review arXiv 1998

[26] [26]

S. Antusch, J. Kersten, M. Lindner, M. Ratz and M. A. Schm idt, JHEP 0503 (2005) 024 [arXiv:hep-ph/0501272]. 25

View on Pith Pith review arXiv 2005