A Flavor Symmetry for quasi-degenerate Neutrinos: L_mu-L_tau

Sandhya Choubey; Werner Rodejohann

REVIEW

A Flavor Symmetry for quasi-degenerate Neutrinos: L_mu-L_tau

Sandhya Choubey, Werner Rodejohann

High Energy Physics - Phenomenology · Submitted 15 Nov 2004 · 36 references

Pith's verdict: A clean, honest treatment of L_mu−L_tau as the quasi-degenerate corner of the Abelian flavor-symmetry triangle; the scaling relations are one-parameter correlations, not first-principles predictions, and the abstract should say so.

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CitationSandhya Choubey, Werner Rodejohann. "A Flavor Symmetry for quasi-degenerate Neutrinos: L_mu-L_tau." arXiv:hep-ph/0411190 (2004). https://pith.science/paper/RXWFVZPN

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Editor's note

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The thing worth knowing: this is the quasi-degenerate leg of a three-way classification the authors make explicit in Table 1 — L_e for normal hierarchy, L_e−L_mu−L_tau for inverted, L_mu−L_tau for quasi-degenerate. That framing is the paper's real contribution, and it's a good one. The zeroth-order algebra is trivial and correct: (c,0,0; 0,0,s; 0,s,0) is diagonalized by a maximal 23 rotation independent of θ, giving masses c m0 and ±s m0. Maximal θ23, zero θ12, zero θ13, quasi-degeneracy — all of it falls out immediately, and the authors don't dress it up as more than it is. What's genuinely new is the breaking analysis: democratic perturbation plus radiative corrections, cross-checked against exact numerical scans; the anarchical perturbation as a contrast case; and the see-saw model in §4 with three right-handed neutrinos and small soft breaking in M_R. That model is minimal and clean, and it's a real improvement over the type-II construction in [18], which needed two doublets and three triplets. Now the soft spots. The stress-test's main point is half right. Eq. (23) comes from plugging the observed Δm_A² into Eq. (19), so ε is forced to track 1/m0². But that isn't circular in the damaging sense: ε does double duty for Δm_A² and Ue3, and that shared parameter is exactly what makes Ue3 a function of m0 alone. It's a one-parameter correlation, a legitimate kind of prediction. What's off is the abstract stating it as a bald scaling without the conditional. The authors do write 'plugged in' in the text, so this is an abstract-level overstatement, not a mathematical error. The secondary point about the sin²2θ23 ≥ 0.95 cut doesn't land: that cut allows sin²θ23 within roughly 0.5 ± 0.11, far looser than the ≲0.01 deviation being reported. The cut isn't imposing the result. The real weakness is the one the authors flag themselves: θ ≈ 3π/4 requires m_ee ≈ m_μτ, which needs another symmetry, and tan β ≈ 35–65 is a stiff price. They're honest about it, and Table 1 puts it in plain view. One post-hoc check worth noting: measured |Ue3| ≈ 0.15 now sits above what this branch gives for m0 ≳ 0.1 eV, pushing the viable window to the low end of quasi-degeneracy. Who should read it: anyone working on Abelian flavor symmetries or quasi-degenerate spectra. It deserves a referee.

Referee report

Significance

If the construction holds, L_mu - L_tau is a viable organizing principle for quasi-degenerate neutrinos, and the paper's correlations tie the common mass scale probed by cosmology and KATRIN to Ue3, theta23, and the 0nubb effective mass, which makes the scenario falsifiable. The linear algebra of Eqs. (4)-(5) is correct and elementary, and the analytic approximations of Section 3.1 are cross-checked against exact numerical scans in Figs. 1 and 2, which is the right methodology. I checked the concern that the scan cut sin^2 2theta23 >= 0.95 in Eq. (27) pre-determines the reported deviation from maximal mixing, and it does not: that cut permits |1/2 - sin^2 theta23| up to about 0.11, whereas the envelope in Fig. 1 is at or below 0.01, so the correlation is genuinely tighter than the prior. The see-saw model is minimal and renormalizable, and the paper is candid about the extra symmetry required (Table 1). The main weaknesses are a misprinted analytic formula, an unquantified tuning of the zeroth-order angle, and an imprecise statement of the logical status of the 1/m0^4 relation.

Major objections (3)

[Section 3.1, Eq. (21)] Eq. (21) states tan^2 theta12 ≃ 2|epsilon delta_tau|. With the values used elsewhere in the paper (epsilon about 0.07 and delta_tau about -0.07), the right-hand side is about 0.01, far below the observed tan^2 theta12 = 0.34-0.44 that the scan in Eq. (27) requires. Combining Eqs. (22) and (24) instead gives the ratio form tan^2 theta12 ≃ 2|epsilon/delta_tau|, which is presumably what was intended. Because Eq. (21) is presented as one of the simple analytic correlations of the scheme, it should be corrected and its consistency with Eq. (24) checked explicitly; the numerical results in Fig. 1 are independent of this slip, but a reader following the analytic chain will be misled.
[Section 3.1, text following Eq. (16) and Table 1] The paper correctly acknowledges that an additional symmetry is needed to explain why the ee and mu-tau entries of Eq. (4) should be nearly equal, and Table 1 lists this as an extra requirement. What is never quantified is how close theta must be to 3pi/4. From Eq. (19) and the requirement that the zeroth-order splitting m0^2 cos 2theta be small compared with Delta m_A^2 ≃ 2 sqrt(2) epsilon m0^2, one needs |cos 2theta| of order epsilon or smaller, i.e., theta within a few degrees of 3pi/4 for epsilon about 0.07. Since this tuning is of the same order as the symmetry-breaking parameter itself, the reader cannot judge from the paper whether the symmetry or the tuned zeroth-order point is doing the work. A short quantitative statement of the allowed range of theta, alongside the acknowledged extra symmetry, would make the accounting transparent.
[Abstract and Section 3.1, Eqs. (23)-(25)] The 1/m0^4 scaling of Ue3^2 and |1/2 - sin^2 theta23| is a genuine correlation among three observables once Delta m_A^2 is fixed to its measured value, but the paper presents it as a prediction of the m0 dependence without saying that Delta m_A^2 is an input. Eq. (23) follows by substituting the observed Delta m_A^2 into Ue3 ≃ epsilon via Eq. (19), and Eq. (24) then follows from Eq. (22). This is legitimate and testable, since measuring m0 and Ue3 checks the relation, but the logical status should be stated explicitly in Section 3.1 and in the abstract so that the scaling is not read as a parameter-free prediction of m0 itself. The same applies to Eq. (25), which is an algebraic rearrangement of Eqs. (20) and (22) rather than an independent cross-check.

Minor objections (8)

[Section 3.2, text around Eq. (28)] The statement that 'there is also no upper limit on epsilon any more' contradicts the preceding sentence, which states that epsilon is again bounded from above by 1/sqrt(10) in the scan. Clarify whether the bound is a scan artifact or a physical requirement of the anarchical case.
[Section 3.1, Eq. (25)] Expanding Eq. (20) gives m0 = sqrt(2) <m>/(1 - sqrt(2) epsilon), hence Sigma ≃ 3 sqrt(2) <m> (1 + sqrt(2) Ue3) to first order, whereas Eq. (25) is printed with a minus sign. Please check the sign.
[Section 4, Eq. (32)] The model reproduces Eq. (4) with c = a^2/X and s = bd/Y, both free ratios, so the model does not by itself prefer the near-equality of the ee and mu-tau entries that Section 3.1 requires. The paper acknowledges that a further symmetry is needed, but it would help to say explicitly that the model inherits the tuning of Major Comment 2 rather than resolving it.
[Section 3.1, inverted ordering] The analytic expressions for the inverted case are given only at theta = 7pi/4, while the text states that values slightly below 7pi/4 are preferred and that this makes a precise analytic calculation difficult. Either state the size of the shift or present the inverted case as numerical only, so the reader knows which statements are analytic and which are fit output.
[Figure 1] The panels showing sin^2 theta23 against m0 and against tan(beta) span only 0.496-0.51 on the vertical axis, which makes the dark-side/light-side separation hard to read. A horizontal reference line at theta23 = pi/4 would help.
[Table 1] The entry 'a ≃ -b (↔ R < 1)' in the L_mu - L_tau row is too compressed to be self-explanatory; spell out what a and b denote and why the sign condition corresponds to R < 1.
[References] Reference [9] (Maltoni et al., hep-ph/0405172) appears in the bibliography but I could not find it cited in the text; either cite it where the oscillation data are quoted or remove it.
[Throughout] The symbol for the symmetry-breaking parameter is typeset inconsistently as epsilon and as the variant epsilon glyph; please unify the notation.

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The paper

The paper claims

A muon-minus-tauon flavor symmetry can organize neutrino masses into a quasi-degenerate trio and, once softly broken, reproduce the observed mixing pattern.

The reading

The paper asks whether a simple rule assigning opposite charges to muon and tau neutrinos and zero charge to the electron neutrino, a flavor symmetry called $L_Âµ-L_Ï„$, can be the organizing principle behind neutrino mass and mixing. If the rule is exact, the neutrino mass matrix has a special form that gives three nearly equal masses, maximal atmospheric mixing, and zero solar and reactor mixing; the last two are in conflict with data, so the authors treat the symmetry as approximate. They show that adding a small flavor-blind perturbation and standard radiative corrections can shift the angles and mass splittings into the observed range, for both normal and inverted mass ordering. The payoff is a compact scheme with sharp correlations: the reactor angle and the deviation from maximal atmospheric mixing shrink as the fourth power of the common neutrino mass scale, and neutrinoless double beta decay should be within reach of next-generation experiments.

What carries the argument

The load-bearing object is the $L_Âµ-L_Ï„$-conserving mass matrix with entries $m_{ee}=m_0Â·cosÂ¸$, $m_{ÂµÏ„}=m_0Â·sinÂ¸$, and zeros elsewhere. Its diagonalization is independent of $Â¸$, which is why maximal atmospheric mixing and zero $Â¸_{13}$ come for free. The symmetry's exact prediction of a single nonzero $Â·Delta m^2$ is both the appeal and the problem: breaking it by a small flavor-blind perturbation $Âµ$ times the all-ones matrix, with radiative corrections from charged-lepton Yukawa couplings $Â·delta_Â±$, generates $Â¸_{12}$ and the atmospheric splitting. In the see-saw model the same texture arises from Dirac couplings $a,b,d$ and a heavy Majorana matrix with charges 0, 1, and -1; soft breaking in that heavy matrix feeds down to the light neutrino matrix.

Extended reading notes

Core claim

The central claim is that the most general neutrino mass matrix conserving the lepton-number difference $L_Âµ-L_Ï„$ has a special form, with entries $m_{ee}=m_0Â·cosÂ¸$ and $m_{ÂµÏ„}=m_0Â·sinÂ¸$ and zeros elsewhere, and that this form predicts quasi-degenerate neutrino masses with one maximal mixing angle and two zero mixing angles. The matrix is diagonalized by a maximal 23 rotation independent of $Â¸$, giving masses $m_0Â·cosÂ¸$ and $Â±m_0Â·sinÂ¸$; for $Â¸$ away from 0 or $Ï€/2$ the three masses are of the same order. Exact symmetry leaves only one nonzero mass-squared difference, $m_0^2Â·cos 2Â¸$, so the observed atmospheric splitting and the solar angle must come from soft breaking. The authors show that a small democratic perturbation plus radiative corrections, or a random order-one perturbation, can reproduce the oscillation data for both normal and inverted ordering; in the democratic case $|U_{e3}|^2$ and $|1/2-Â·sin^2Â¸_{23}|$ scale as $1/m_0^4$. They also build a see-saw model with one Higgs doublet and three heavy right-handed neutrinos whose heavy Majorana mass matrix is softly broken, generating the required approximate $L_Âµ-L_Ï„$ texture.

Load-bearing premise

The load-bearing premise is that the zeroth-order angle $Â¸$ is close to $3Ï€/4$ (or $7Ï€/4$), so the $ee$ and $ÂµÏ„$ entries of the mass matrix have nearly equal magnitude; the paper itself notes that an additional symmetry is needed to explain why this alignment should hold.

Editorial extensions

If this is right

If the symmetry is approximately realized, the three neutrino masses are nearly equal, so cosmology's $Â·SigmaÂ·simeq 3m_0$ and KATRIN's absolute-mass reach become direct tests.
Neutrinoless double beta decay is predicted with an effective mass around 0.05 to 0.35 eV in the democratic-breaking scan, within reach of next-generation experiments and with only moderate cancellation.
In the democratic-breaking case, larger $m_0$ pushes $|U_{e3}|^2$ and $|1/2-Â·sin^2Â¸_{23}|$ toward zero as $1/m_0^4$, linking reactor and atmospheric mixing precision to the absolute mass scale.
For the democratic perturbation, normal ordering places atmospheric mixing on the dark side, $Â¸_{23}>Ï€/4$, while inverted ordering places it on the light side, $Â¸_{23}<Ï€/4$; the random perturbation can put it on either side.
The see-saw realization needs only one Higgs doublet and three heavy right-handed neutrinos, with small soft $L_Âµ-L_Ï„$ breaking in the heavy Majorana sector.

Reading between the lines

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

A future absolute-mass measurement plus precision $Â¸_{23}$ and $|U_{e3}|$ can test the democratic-breaking correlation without needing a full oscillation fit, because the same $m_0$ controls all three observables.
The need for an additional symmetry to align the $ee$ and $ÂµÏ„$ entries suggests embedding this scheme in a discrete family symmetry or a UV completion where that alignment is natural; the paper's A4 comparison is one nearby example.
Because the radiative-correction version requires large $Â·tanÂ·beta$, lepton-flavor-violating searches such as $ÂµÂ·to eÂ·gamma$ become a correlated probe that could distinguish this scheme from A4-based versions, which the paper notes prefer $Â·tanÂ·beta<8$.
If the $L_Âµ-L_Ï„$ symmetry is gauged, as the paper notes is anomaly-free, a light gauge boson or precision-lepton test could provide a non-neutrino handle on the same charge assignment.

Original abstract

We consider the flavor symmetry L_mu - L_tau for the neutrino mass matrix. The most general neutrino mass matrix conserving L_mu - L_tau predicts quasi-degenerate neutrino masses with one maximal and two zero mixing angles. The presence of L_mu - L_tau can also be motivated by the near-bimaximal form of the neutrino mixing matrix. Furthermore, it is a special case of mu-tau symmetric mass matrices. Breaking the flavor symmetry by adding a small flavor-blind term to the neutrino mass matrix and/or by applying radiative corrections is shown to reproduce the observed neutrino oscillation phenomenology. Both the normal and inverted mass ordering can be accommodated within this scheme. Moderate cancellation for neutrinoless double beta decay is expected. The observables U_{e3}^2 and |1/2 - \sin^2\theta_{23}| are proportional to the inverse of the fourth power of the common neutrino mass scale. We comment on whether the atmospheric neutrino mixing is expected to lie above or below pi/4. We finally present a model based on the see-saw mechanism which generates a light neutrino mass matrix with an (approximate) L_mu - L_tau flavor symmetry. This is a minimal model with just one standard Higgs doublet and three heavy right-handed neutrinos. It needs only small values for the soft L_mu - L_tau breaking terms to reproduce the phenomenological viable mass textures analyzed.

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, 8,794 input tokens, $0.0004 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.27 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.47 · compares with prior results 0.19 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

We consider the flavor symmetry L_mu - L_tau for the neutrino mass matrix. The most general neutrino mass matrix conserving L_mu - L_tau predicts quasi-degenerate neutrino masses with one maximal and two zero mixing angles. The presence of L_mu - L_tau can also be motivated by the near-bimaximal form of the neutrino mixing matrix. Furthermore, it is a special case of mu-tau symmetric mass matrices. Breaking the flavor symmetry by adding a small flavor-blind term to the neutrino mass matrix and/or by applying radiative corrections is shown to reproduce the observed neutrino oscillation phenomenology. Both the normal and inverted mass ordering can be accommodated within this scheme. Moderate cancellation for neutrinoless double beta decay is expected. The observables U_{e3}^2 and |1/2 - \sin^2\theta_{23}| are proportional to the inverse of the fourth power of the common neutrino mass scale. We comment on whether the atmospheric neutrino mixing is expected to lie above or below pi/4. We finally present a model based on the see-saw mechanism which generates a light neutrino mass matrix with an (approximate) L_mu - L_tau flavor symmetry. This is a minimal model with just one standard Higgs doublet and three heavy right-handed neutrinos. It needs only small values for the soft L_mu - L_tau breaking terms to reproduce the phenomenological viable mass textures analyzed.

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 consider the flavor symmetry L_mu - L_tau for the neutrino mass matrix.	contribution 0.86	0.75	0.05	asserted 0.60
s1	The most general neutrino mass matrix conserving L_mu - L_tau predicts quasi-degenerate neutrino masses with one maximal and two zero mixing angles.	result 0.93	0.64	0.46	asserted 1.00
s2	The presence of L_mu - L_tau can also be motivated by the near-bimaximal form of the neutrino mixing matrix.	interpretation 0.49	0.21	0.06	hedged possibility 0.92
s3	Furthermore, it is a special case of mu-tau symmetric mass matrices.	background 0.89	0.20	0.05	asserted 1.00
s4	Breaking the flavor symmetry by adding a small flavor-blind term to the neutrino mass matrix and/or by applying radiative corrections is shown to reproduce the observed neutrino oscillation phenomenology.	result 0.54	0.80	0.39	asserted 1.00
s5	Both the normal and inverted mass ordering can be accommodated within this scheme.	result 0.96	0.72	0.09	asserted 0.53
s6	Moderate cancellation for neutrinoless double beta decay is expected.	result 0.81	0.67	0.06	hedged possibility 0.79
s7	The observables U_{e3}^2 and \|1/2 - \sin^2\theta_{23}\| are proportional to the inverse of the fourth power of the common neutrino mass scale.	result 0.98	0.78	0.11	asserted 1.00
s8	We comment on whether the atmospheric neutrino mixing is expected to lie above or below pi/4.	interpretation 0.59	0.45	0.04	unclear 0.62
s9	We finally present a model based on the see-saw mechanism which generates a light neutrino mass matrix with an (approximate) L_mu - L_tau flavor symmetry.	contribution 0.78	0.91	0.16	asserted 1.00
s10	This is a minimal model with just one standard Higgs doublet and three heavy right-handed neutrinos.	method 0.71	0.71	0.05	asserted 1.00
s11	It needs only small values for the soft L_mu - L_tau breaking terms to reproduce the phenomenological viable mass textures analyzed.	result 0.55	0.73	0.10	asserted 0.96

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.93.

What was examined, and what was not

sources read

arXiv listing abstract v2

not examined

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

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

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

Figures

**Figure 1.** Scatter plots of some of the correlations of the paramet

**Figure 2.** Scatter plots of some of the correlations of the paramet

Figures reproduced from arXiv:hep-ph/0411190 by the authors.

References

Works cited (36)

[18]

N. F. Bell and R. R. Volkas, Phys. Rev. D 63, 013006 (2001)

View on Pith 2001
[1]

B. Pontecorvo, Zh. Eksp. Teor. Fiz. 33, 549 (1957) and 34, 247 (1958); Z. Maki, M. Nakagawa and S. Sakata, Prog. Theor. Phys. 28, 870 (1962)

View on Pith 1957
[2]

M. Apollonio et al. [CHOOZ Collaboration], Eur. Phys. J. C 27, 331 (2003); F. Boehm et al. , Phys. Rev. D 64, 112001 (2001). 15

View on Pith 2003
[3]

E. Kearns, talk given at “Neutrino 2004” June 14-19, 2004, Par is, France, http://neutrino2004.in2p3.fr

View on Pith 2004
[4]

T. Nakaya et al. , talk given at “Neutrino 2004”, June 14-19, 2004, Paris, France, http://neutrino2004.in2p3.fr; M.H. Ahn et al., Phys.Rev.Lett. 90 (2003) 041801; hep-ex/0411038

View on Pith Pith review arXiv 2003
[5]

B. T. Cleveland et al. , Astrophys. J. 496, 505 (1998); C. Cattadori, Talk at “Neutrino 2004”, Paris, France, June 14-19, 2004 http://neutrino2004.in2p3.fr; S. Fukuda et al. [Super-Kamiokande Collaboration], Phys. Lett. B 539, 179 (2002); S. N. Ahmed et al. [SNO Collaboration], Phys. Rev. Lett. 92, 181301 (2004)

View on Pith 1998
[6]

T. Araki et al. , [KamLAND Collaboration], hep-ex/0406035

View on Pith Pith review arXiv
[7]

G. L. Fogli et al. , hep-ph/0408045

View on Pith Pith review arXiv
[8]

See, e.g., A. Bandyopadhyay, et al. , hep-ph/0406328; J. N. Bahcall, M. C. Gonzalez- Garcia and C. Pena-Garay, JHEP 0408, 016 (2004)

View on Pith Pith review arXiv 2004
[9]

M. Maltoni et al. , hep-ph/0405172

View on Pith Pith review arXiv
[10]

F. Vissani, hep-ph/9708483; V. D. Barger, S. Pakvasa, T. J. Weiler and K. Whisnant, Phys. Lett. B 437, 107 (1998); A. J. Baltz, A. S. Goldhaber and M. Goldhaber, Phys. Rev. Lett. 81, 5730 (1998); H. Georgi and S. L. Glashow, Phys. Rev. D 61, 097301 (2000); I. Stancu and D. V. Ahluwalia, Phys. Lett. B 460, 431 (1999)

View on Pith Pith review arXiv 1998
[11]

M. Jezabek and Y. Sumino, Phys. Lett. B 457, 139 (1999) Z. z. Xing, Phys. Rev. D 64, 093013 (2001); C. Giunti and M. Tanimoto, Phys. Rev. D 66, 053013 (2002); Phys. Rev. D 66, 113006 (2002); G. Altarelli, F. Feruglio and I. Masina, Nucl. Phys. B 689, 157 (2004); A. Romanino, Phys. Rev. D 70, 013003 (2004); W. Rodejohann, hep-ph/0403236 (to appear in Phys....

View on Pith Pith review arXiv 1999
[12]

P. H. Frampton, S. T. Petcov and W. Rodejohann, Nucl. Phys. B 687, 31 (2004)

View on Pith 2004
[13]

S. T. Petcov, W. Rodejohann, hep-ph/0409135

View on Pith Pith review arXiv
[14]

F. Vissani, JHEP 9811, 025 (1998)

View on Pith 1998
[15]

S. T. Petcov, Phys. Lett. B 110, 245 (1982); for more recent studies see, e.g., R. Bar- bieri et al. , JHEP 9812, 017 (1998); A. S. Joshipura and S. D. Rindani, Eur. Phys. J. C 14, 85 (2000); R. N. Mohapatra, A. Perez-Lorenzana and C. A. de S ousa Pires, Phys. Lett. B 474, 355 (2000); Q. Shaﬁ and Z. Tavartkiladze, Phys. Lett. B 482, 145 (2000). L. Lavoura...

View on Pith 1982
[16]

L. Lavoura and W. Grimus, JHEP 0009, 007 (2000); hep-ph/0410279

View on Pith Pith review arXiv 2000
[17]

P. Binetruy et al. , Nucl. Phys. B 496, 3 (1997)

View on Pith 1997
[19]

K. S. Babu, E. Ma and J. W. F. Valle, Phys. Lett. B 552, 207 (2003); M. Hirsch et al., Phys. Rev. D 69, 093006 (2004)

View on Pith 2003
[20]

X. G. He et al. , Phys. Rev. D 43, 22 (1991); Phys. Rev. D 44, 2118 (1991); see also E. Ma, D. P. Roy and S. Roy, Phys. Lett. B 525, 101 (2002)

View on Pith 1991
[21]

See e.g., C. S. Lam, Phys. Lett. B 507, 214 (2001); T. Kitabayashi and M. Yasue, Phys. Rev. D 67, 015006 (2003); W. Grimus and L. Lavoura, Phys. Lett. B 572, 189 (2003); E. Ma, Phys. Rev. D 66, 117301 (2002); Y. Koide, Phys. Rev. D 69, 093001 (2004); W. Grimus, et al. , hep-ph/0408123; R. N. Mohapatra, JHEP 0410, 027 (2004)

View on Pith Pith review arXiv 2001
[22]

S. Hannestad, JCAP 0305, 004 (2003); hep-ph/0409108

View on Pith Pith review arXiv 2003
[23]

U. Seljak et al. , astro-ph/0407372

View on Pith Pith review arXiv
[24]

See, e.g., S. R. Elliott and J. Engel, J. Phys. G 30, R183 (2004) and references therein

View on Pith 2004
[25]

W. Rodejohann, Nucl. Phys. B 597, 110 (2001); Z. z. Xing, Phys. Rev. D 68, 053002 (2003); more realistic recent analyzes are V. Barger et al. , Phys. Lett. B 540, 247 (2002); S. Pascoli, S. T. Petcov and W. Rodejohann, Phys. L ett. B 549, 177 (2002); F. Deppisch, H. Pas and J. Suhonen; hep-ph/0409306; A . Joniec, M. Zralek, hep-ph/0411070

View on Pith Pith review arXiv 2001
[26]

W. Rodejohann, Phys. Rev. D 69, 033005 (2004)

View on Pith 2004
[27]

M. Raidal, Phys. Rev. Lett. 93, 161801 (2004); H. Minakata and A. Y. Smirnov, hep-ph/0405088; P. H. Frampton and R. N. Mohapatra, hep-ph/ 0407139; see also J. Ferrandis and S. Pakvasa, hep-ph/0409204

View on Pith Pith review arXiv 2004
[28]

See, e.g., J.A. Casas, et al. , Nucl. Phys. B 573, 652 (2000); P.H. Chankowski, S. Pokorski, Int. J. Mod. Phys. A 17 (2002) 575; S. Antusch, et al. , Nucl. Phys. B 674, 401 (2003)

View on Pith 2000
[29]

S. Antusch et al. , hep-ph/0404268; H. Minakata, M. Sonoyama and H. Sugiyama, hep-ph/0406073; M. C. Gonzalez-Garcia, M. Maltoni and A. Y. Smir nov, hep-ph/0408170; S. Choubey and P. Roy, Phys. Rev. Lett. 93, 021803 (2004). 17

View on Pith Pith review arXiv 2004
[30]

J. Bernabeu, S. Palomares Ruiz and S. T. Petcov, Nucl. Phys. B 669, 255 (2003); O. L. G. Peres and A. Y. Smirnov, Nucl. Phys. B 680, 479 (2004); S. Palomares-Ruiz and S. T. Petcov, hep-ph/0406096

View on Pith Pith review arXiv 2003
[31]

A. Osipowicz et al. [KATRIN Collaboration], hep-ex/0109033

View on Pith Pith review arXiv
[32]

H. V. Klapdor-Kleingrothaus et al., Mod. Phys. Lett. A 16, 2409 (2001); C. E. Aalseth et al. , Mod. Phys. Lett. A 17, 1475 (2002); H. L. Harney, hep-ph/0205293; H. V. Klapdor-Kleingrothaus, hep-ph/0205228; F. Feruglio, A. St rumia and F. Vis- sani, Nucl. Phys. B 637, 345 (2002) [Addendum-ibid. B 659, 359 (2003)]

View on Pith Pith review arXiv 2001
[33]

H. V. Klapdor-Kleingrothaus et al. , Phys. Lett. B 586, 198 (2004)

View on Pith 2004
[34]

E. K. Akhmedov, Z. G. Berezhiani and G. Senjanovic, Phys. Re v. Lett. 69, 3013 (1992); E. K. Akhmedov et al. , Phys. Rev. D 47, 3245 (1993); A. de Gouvea and J. W. F. Valle, Phys. Lett. B 501, 115 (2001); F. Vissani, M. Narayan and V. Berezin- sky, Phys. Lett. B 571, 209 (2003); hep-ph/0401029

View on Pith Pith review arXiv 1992
[35]

P. Minkowski, Phys. Lett. B67, 421 (1977); T. Yanagida, in Proceedings of the Work- shop on Uniﬁed Theory and the Baryon Number of the Universe , edited by O. Sawada and A. Sugamoto (KEK, Tsukuba, 1979), p. 95; M. Gell-Mann, P. Ra mond, and R. Slansky, in Supergravity, edited by F. van Nieuwenhuizen and D. Freedman (North Holland, Amsterdam, 1979), p. 315...

View on Pith 1977
[36]

J. Schechter and J.W.F. Valle, Phys. Rev. D 22, 2227 (1980); M. Magg and C. Wet- terich, Phys. Lett. B 94, 61 (1980); R. N. Mohapatra and G. Senjanovic, Phys. Rev. D 23, 165 (1981); G. Lazarides, Q. Shaﬁ and C. Wetterich, Nucl. Phys. B 181, 287 (1981). 18 0.496 0.498 0.5 .502 .504 0.506 0.508 0.51 0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 sin2 θ23 ...

View on Pith 1980

Forward citations

Cited by 34 Pith papers

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How the literature uses it

43 arXiv papers cite this in 48 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 · 31 sentences without a confident label

Cites it as background 17 papers

Thereafter, several variants of $U(1)_L_μ-L_τ$ model have been studied in the context of different phenomenological purposes: e.g., contribution of the $U(1)_L_μ-L_τ$ gauge boson to explain the $(g-2)_μ$ anomaly [ref] , dark matter phenomenology [ref] , generation of neutrino masses and mixing parameters [ref] etc.

Reconciling dark matter, $R_{K^{(*)}}$ anomalies and $(g-2)_{\mu}$ in an ${L_{\mu}-L_{\tau}}$ scenario · Introduction · 0.90
As far as continuous abelian symmetries of lepton numbers go, three interesting linear combinations have been identified for the zeroth-order approximation: $$, $≡L_e - L_μ- L_τ$ and $$, leading to normal hierarchy (NH), inverted hierarchy (IH) and quasi-degeneracy in the neutrino mass spectrum [ref] .

Neutrino Hierarchies from a Gauge Symmetry · Introduction · 0.91
For previous studies on the neutrino sector of the gauged U(1)$_L_α-L_β$ models, see Refs [ref] .

Predictions for the neutrino parameters in the minimal model extended by linear combination of U(1)$_{L_e-L_\mu}$, U(1)$_{L_\mu-L_\tau}$ and U(1)$_{B-L}$ gauge symmetries · Introduction · 0.82

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] [18]

N. F. Bell and R. R. Volkas, Phys. Rev. D 63, 013006 (2001)

View on Pith 2001

[2] [1]

B. Pontecorvo, Zh. Eksp. Teor. Fiz. 33, 549 (1957) and 34, 247 (1958); Z. Maki, M. Nakagawa and S. Sakata, Prog. Theor. Phys. 28, 870 (1962)

View on Pith 1957

[3] [2]

M. Apollonio et al. [CHOOZ Collaboration], Eur. Phys. J. C 27, 331 (2003); F. Boehm et al. , Phys. Rev. D 64, 112001 (2001). 15

View on Pith 2003

[4] [3]

E. Kearns, talk given at “Neutrino 2004” June 14-19, 2004, Par is, France, http://neutrino2004.in2p3.fr

View on Pith 2004

[5] [4]

T. Nakaya et al. , talk given at “Neutrino 2004”, June 14-19, 2004, Paris, France, http://neutrino2004.in2p3.fr; M.H. Ahn et al., Phys.Rev.Lett. 90 (2003) 041801; hep-ex/0411038

View on Pith Pith review arXiv 2003

[6] [5]

B. T. Cleveland et al. , Astrophys. J. 496, 505 (1998); C. Cattadori, Talk at “Neutrino 2004”, Paris, France, June 14-19, 2004 http://neutrino2004.in2p3.fr; S. Fukuda et al. [Super-Kamiokande Collaboration], Phys. Lett. B 539, 179 (2002); S. N. Ahmed et al. [SNO Collaboration], Phys. Rev. Lett. 92, 181301 (2004)

View on Pith 1998

[7] [6]

T. Araki et al. , [KamLAND Collaboration], hep-ex/0406035

View on Pith Pith review arXiv

[8] [7]

G. L. Fogli et al. , hep-ph/0408045

View on Pith Pith review arXiv

[9] [8]

See, e.g., A. Bandyopadhyay, et al. , hep-ph/0406328; J. N. Bahcall, M. C. Gonzalez- Garcia and C. Pena-Garay, JHEP 0408, 016 (2004)

View on Pith Pith review arXiv 2004

[10] [9]

M. Maltoni et al. , hep-ph/0405172

View on Pith Pith review arXiv

[11] [10]

F. Vissani, hep-ph/9708483; V. D. Barger, S. Pakvasa, T. J. Weiler and K. Whisnant, Phys. Lett. B 437, 107 (1998); A. J. Baltz, A. S. Goldhaber and M. Goldhaber, Phys. Rev. Lett. 81, 5730 (1998); H. Georgi and S. L. Glashow, Phys. Rev. D 61, 097301 (2000); I. Stancu and D. V. Ahluwalia, Phys. Lett. B 460, 431 (1999)

View on Pith Pith review arXiv 1998

[12] [11]

M. Jezabek and Y. Sumino, Phys. Lett. B 457, 139 (1999) Z. z. Xing, Phys. Rev. D 64, 093013 (2001); C. Giunti and M. Tanimoto, Phys. Rev. D 66, 053013 (2002); Phys. Rev. D 66, 113006 (2002); G. Altarelli, F. Feruglio and I. Masina, Nucl. Phys. B 689, 157 (2004); A. Romanino, Phys. Rev. D 70, 013003 (2004); W. Rodejohann, hep-ph/0403236 (to appear in Phys....

View on Pith Pith review arXiv 1999

[13] [12]

P. H. Frampton, S. T. Petcov and W. Rodejohann, Nucl. Phys. B 687, 31 (2004)

View on Pith 2004

[14] [13]

S. T. Petcov, W. Rodejohann, hep-ph/0409135

View on Pith Pith review arXiv

[15] [14]

F. Vissani, JHEP 9811, 025 (1998)

View on Pith 1998

[16] [15]

S. T. Petcov, Phys. Lett. B 110, 245 (1982); for more recent studies see, e.g., R. Bar- bieri et al. , JHEP 9812, 017 (1998); A. S. Joshipura and S. D. Rindani, Eur. Phys. J. C 14, 85 (2000); R. N. Mohapatra, A. Perez-Lorenzana and C. A. de S ousa Pires, Phys. Lett. B 474, 355 (2000); Q. Shaﬁ and Z. Tavartkiladze, Phys. Lett. B 482, 145 (2000). L. Lavoura...

View on Pith 1982

[17] [16]

L. Lavoura and W. Grimus, JHEP 0009, 007 (2000); hep-ph/0410279

View on Pith Pith review arXiv 2000

[18] [17]

P. Binetruy et al. , Nucl. Phys. B 496, 3 (1997)

View on Pith 1997

[19] [19]

K. S. Babu, E. Ma and J. W. F. Valle, Phys. Lett. B 552, 207 (2003); M. Hirsch et al., Phys. Rev. D 69, 093006 (2004)

View on Pith 2003

[20] [20]

X. G. He et al. , Phys. Rev. D 43, 22 (1991); Phys. Rev. D 44, 2118 (1991); see also E. Ma, D. P. Roy and S. Roy, Phys. Lett. B 525, 101 (2002)

View on Pith 1991

[21] [21]

See e.g., C. S. Lam, Phys. Lett. B 507, 214 (2001); T. Kitabayashi and M. Yasue, Phys. Rev. D 67, 015006 (2003); W. Grimus and L. Lavoura, Phys. Lett. B 572, 189 (2003); E. Ma, Phys. Rev. D 66, 117301 (2002); Y. Koide, Phys. Rev. D 69, 093001 (2004); W. Grimus, et al. , hep-ph/0408123; R. N. Mohapatra, JHEP 0410, 027 (2004)

View on Pith Pith review arXiv 2001

[22] [22]

S. Hannestad, JCAP 0305, 004 (2003); hep-ph/0409108

View on Pith Pith review arXiv 2003

[23] [23]

U. Seljak et al. , astro-ph/0407372

View on Pith Pith review arXiv

[24] [24]

See, e.g., S. R. Elliott and J. Engel, J. Phys. G 30, R183 (2004) and references therein

View on Pith 2004

[25] [25]

W. Rodejohann, Nucl. Phys. B 597, 110 (2001); Z. z. Xing, Phys. Rev. D 68, 053002 (2003); more realistic recent analyzes are V. Barger et al. , Phys. Lett. B 540, 247 (2002); S. Pascoli, S. T. Petcov and W. Rodejohann, Phys. L ett. B 549, 177 (2002); F. Deppisch, H. Pas and J. Suhonen; hep-ph/0409306; A . Joniec, M. Zralek, hep-ph/0411070

View on Pith Pith review arXiv 2001

[26] [26]

W. Rodejohann, Phys. Rev. D 69, 033005 (2004)

View on Pith 2004

[27] [27]

M. Raidal, Phys. Rev. Lett. 93, 161801 (2004); H. Minakata and A. Y. Smirnov, hep-ph/0405088; P. H. Frampton and R. N. Mohapatra, hep-ph/ 0407139; see also J. Ferrandis and S. Pakvasa, hep-ph/0409204

View on Pith Pith review arXiv 2004

[28] [28]

See, e.g., J.A. Casas, et al. , Nucl. Phys. B 573, 652 (2000); P.H. Chankowski, S. Pokorski, Int. J. Mod. Phys. A 17 (2002) 575; S. Antusch, et al. , Nucl. Phys. B 674, 401 (2003)

View on Pith 2000

[29] [29]

S. Antusch et al. , hep-ph/0404268; H. Minakata, M. Sonoyama and H. Sugiyama, hep-ph/0406073; M. C. Gonzalez-Garcia, M. Maltoni and A. Y. Smir nov, hep-ph/0408170; S. Choubey and P. Roy, Phys. Rev. Lett. 93, 021803 (2004). 17

View on Pith Pith review arXiv 2004

[30] [30]

J. Bernabeu, S. Palomares Ruiz and S. T. Petcov, Nucl. Phys. B 669, 255 (2003); O. L. G. Peres and A. Y. Smirnov, Nucl. Phys. B 680, 479 (2004); S. Palomares-Ruiz and S. T. Petcov, hep-ph/0406096

View on Pith Pith review arXiv 2003

[31] [31]

A. Osipowicz et al. [KATRIN Collaboration], hep-ex/0109033

View on Pith Pith review arXiv

[32] [32]

H. V. Klapdor-Kleingrothaus et al., Mod. Phys. Lett. A 16, 2409 (2001); C. E. Aalseth et al. , Mod. Phys. Lett. A 17, 1475 (2002); H. L. Harney, hep-ph/0205293; H. V. Klapdor-Kleingrothaus, hep-ph/0205228; F. Feruglio, A. St rumia and F. Vis- sani, Nucl. Phys. B 637, 345 (2002) [Addendum-ibid. B 659, 359 (2003)]

View on Pith Pith review arXiv 2001

[33] [33]

H. V. Klapdor-Kleingrothaus et al. , Phys. Lett. B 586, 198 (2004)

View on Pith 2004

[34] [34]

E. K. Akhmedov, Z. G. Berezhiani and G. Senjanovic, Phys. Re v. Lett. 69, 3013 (1992); E. K. Akhmedov et al. , Phys. Rev. D 47, 3245 (1993); A. de Gouvea and J. W. F. Valle, Phys. Lett. B 501, 115 (2001); F. Vissani, M. Narayan and V. Berezin- sky, Phys. Lett. B 571, 209 (2003); hep-ph/0401029

View on Pith Pith review arXiv 1992

[35] [35]

P. Minkowski, Phys. Lett. B67, 421 (1977); T. Yanagida, in Proceedings of the Work- shop on Uniﬁed Theory and the Baryon Number of the Universe , edited by O. Sawada and A. Sugamoto (KEK, Tsukuba, 1979), p. 95; M. Gell-Mann, P. Ra mond, and R. Slansky, in Supergravity, edited by F. van Nieuwenhuizen and D. Freedman (North Holland, Amsterdam, 1979), p. 315...

View on Pith 1977

[36] [36]

J. Schechter and J.W.F. Valle, Phys. Rev. D 22, 2227 (1980); M. Magg and C. Wet- terich, Phys. Lett. B 94, 61 (1980); R. N. Mohapatra and G. Senjanovic, Phys. Rev. D 23, 165 (1981); G. Lazarides, Q. Shaﬁ and C. Wetterich, Nucl. Phys. B 181, 287 (1981). 18 0.496 0.498 0.5 .502 .504 0.506 0.508 0.51 0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 sin2 θ23 ...

View on Pith 1980