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REVIEW 3 major objections 5 minor 53 references

Revisiting the two-zero texture Majorana neutrino mass matrix

T0 review · 3 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read The paper claims that five of the seven two-zero texture Majorana neutrino mass matrices, while compatible with current oscillation data, are in severe tension with cosmological and neutrinoless-double-beta-decay constraints, and that…

desk verdict A clean, honest update of two-zero texture scans; the abstract's 'severe tension' claim leans on the tight end of the paper's own bounds. read the letter →

arxiv 2501.11572 v2 pith:EPDHAR3U submitted 2025-01-20 hep-ph

Wararat Treesukrat , Nopmanee Supanam , Patipan Uttayarat This is my paper · ORCID
classification hep-ph
keywords two-zerotextureMajorananeutrinomassmatrixoscillationsNuFIT6.0neutrinolessdoublebetadecaycosmologicalboundonmassesorderingKATRIN
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper revisits a minimal ansatz for Majorana neutrino masses: a 3×3 mass matrix with exactly two independent entries set to zero, a 'two-zero texture,' which earlier work reduced to seven textures compatible with oscillation data. Using the updated NuFIT 6.0 oscillation parameters and scanning each texture's full parameter space, the paper finds that all seven still fit the oscillation data, but that five of them — those with a nonvanishing 1-1 entry, labelled B1–B4 and C — are in severe tension with bounds on the neutrino mass sum from cosmology and on the neutrinoless double $\beta$ decay effective mass. The other two, A1 and A2, force normal mass ordering, put the lightest neutrino mass in a 4–7.5 meV window, and predict a vanishing 0νββ effective mass. If the paper is right, next-generation cosmological and 0νββ experiments can decisively rule out the five stressed textures, and pinning down the $\theta_{23}$ octant could eliminate several more; the old ansatz has become experimentally falsifiable.

What carries the argument

The load-bearing device is the two-zero texture ansatz for the low-energy Majorana mass matrix in the charged-lepton-diagonal basis: a 3×3 complex symmetric matrix with exactly two independent entries zero, so that after phase redefinitions only five real parameters remain (an overall scale $\mu$, positive ratios $r_i$, and one phase $\theta$). The paper parametrizes each of the seven textures this way and scans those five parameters against the six oscillation observables from NuFIT 6.0, using the matrix invariants $\mathrm{Tr}(m^\dagger m)$, its quadratic invariant, and $\det(m^\dagger m)$ to test special limits such as a massless neutrino. The machinery's role is to map each texture's viable region to predictions for three mass observables — the lightest neutrino mass $m_{\rm light}$, the $\beta$-decay effective mass $m^{\rm eff}_{\nu e}$, and $m_{ee}$ — and the invariant identities are what show no texture can have a zero lightest mass.

What would settle it

A measurement of the neutrino mass sum below $0.13$ eV, combined with a bound $m_{ee} \lesssim 36$ meV from a next-generation 0νββ experiment, would decisively rule out textures B1–B4 and C as scanned; conversely, any confirmed 0νββ signal would rule out A1 and A2, since both predict $m_{ee}=0$.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central result is a classification: none of the seven two-zero textures can accommodate a massless lightest neutrino, and the seven split into two predictive families. Textures A1 and A2 are compatible only with normal ordering, with the lightest neutrino mass confined to 4.3–7.5 meV (A1) and 4.0–5.6 meV (A2), the $\beta$-decay effective mass near 10 meV, and the 0νββ effective mass $m_{ee}$ exactly zero. Textures B1–B4 and C can accommodate both orderings, but their scan forces lower bounds on the lightest neutrino mass — roughly 48–64 meV for B1–B4 and 156 meV for C in normal ordering — and on $m_{ee}$ of order 50–80 meV (B1–B4) and 149 meV (C, NO). These floors exceed the tight cosmological upper bound (lightest mass $\lesssim$34 meV for NO, $\lesssim$21 meV for IO, from $\sum_i m_i \le 0.13$ eV) and the tight KamLAND-Zen bound ($m_{ee} \le 36$ meV); hence the paper's 'severe tension' verdict. The scan also shows strong correlations: for B1–B4 the Dirac phase is pinned near 270°, the lightest mass grows as $s^2_{23}$ approaches 0.5, and the $\theta_{23}$ octant decides which textures survive.

Load-bearing premise

The paper's central verdict stands on the tight cosmological bound $\sum_i m_i \le 0.13$ eV and the low nuclear-matrix-element end of the KamLAND-Zen bound $m_{ee} \le 36$ meV; if the loose ends of those ranges apply, textures B1–B4 and C retain sizeable viable regions.

Editorial extensions

If this is right

  • Under the tight cosmological bound $\sum_i m_i \le 0.13$ eV, textures B1–B4 and C are already excluded today; a Simons Observatory measurement at 40 meV sensitivity would settle this decisively.
  • A LEGEND-II bound on the 0νββ effective mass at 13–29 meV would rule out all five stressed textures, since their scanned lower bounds on $m_{ee}$ lie above that range.
  • Determining the $\theta_{23}$ octant filters the survivors: first-octant normal ordering rules out A2, B2, B4 and C; second-octant inverted ordering rules out B2 and B4.
  • A positive 0νββ signal would immediately rule out A1 and A2, which predict $m_{ee}=0$, while a null signal at the 36 meV level would leave them untouched.
  • A demonstrated massless lightest neutrino would falsify the entire two-zero texture ansatz, because the paper shows none of the seven textures can accommodate a zero lightest mass.

Reading between the lines

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

  • The 'severe tension' verdict is bound to the tight end of both experimental ranges: under the loose cosmological bound ($\sum_i m_i \le 0.52$ eV) and the loose nuclear-matrix-element bound ($m_{ee} \le 156$ meV), textures B1–B4 and C with inverted ordering keep large viable regions, so the conclusion should be read as conditional on which bounds prove true.
  • Because the scan is model-independent at low energy, any ultraviolet model that generates a two-zero texture inherits these predictions; models producing B1–B4 or C must now explain how the tight bounds are evaded, while models producing A1/A2 predict a null 0νββ signal at all currently planned sensitivities.
  • The near-equality $m_{\rm light} \approx m^{\rm eff}_{\nu e} \approx m_{ee}$ found for B1–B4 is a cross-check opportunity: an upper bound below roughly 50 meV on any one of these three observables would exclude the entire B-family without waiting for cosmology to tighten further.
  • A decisive first-octant NO determination, as the paper notes, would reduce the surviving textures to A1, B1 and B3; that would sharpen the ansatz's predictions enough that the next round of experiments could settle it completely.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper revisits the seven two-zero texture Majorana neutrino mass matrices (A1, A2, B1–B4, C) using the NuFIT 6.0 oscillation data. Each texture is parametrized by an overall scale μ, three positive ratios r_i, and one phase θ; the authors scan μ ∈ [1 meV, 1 eV], r_i ∈ [10^{-3}, 10^3], θ ∈ [0, 2π], and retain points whose oscillation parameters lie inside the 3σ ranges. They also prove, using the invariants of m†ν mν, that no texture can accommodate a vanishing lightest neutrino mass. The scan yields ranges for m_light, m_eff_νe, and m_ee (Table II): A1/A2 predict normal ordering with m_light in the 4.0–7.5 meV window and m_ee = 0, while B1–B4 and C force m_light and m_ee to be at least about 48–156 meV and 43–149 meV, respectively. The authors conclude that B1–B4 and C are in severe tension with cosmological and 0νββ bounds and could be decisively ruled out by next-generation experiments.

Significance. If the numerical results are correct, this is a useful and timely update: it maps the surviving two-zero textures onto NuFIT 6.0 and gives concrete, falsifiable predictions that distinguish A1/A2 from B1–B4/C. The analytic determinant argument in Sec. III.B is clean, checkable, and a genuine strength, as is the explicit parametrization of all seven textures in Eqs. (3)–(5). The prospective statements about next-generation experiments are robust and well grounded. However, the paper’s headline claim about ‘severe tension’ is stronger than the body supports, because it depends on choosing the tight ends of the quoted cosmological and nuclear-matrix-element ranges, and the numerical scan is not documented to the level needed to certify the quoted lower bounds as exhaustive. With appropriate qualification and scan documentation, the paper would be a solid contribution to texture phenomenology.

major comments (3)
  1. [Abstract; Secs. III.A, IV, V] The abstract’s claim that B1–B4 and C are ‘in severe tension’ with cosmology and 0νββ is not uniformly supported by the constraints quoted in the paper. Section III.A gives Σm_i ≤ 0.13–0.52 eV, i.e. m_light ≤ 34–171 meV (NO) and 21–168 meV (IO), and KamLAND-Zen m_ee ≤ 36–156 meV. The lower bounds in Table II (m_light ≳ 48–64 meV for B1–B4 IO and m_light ≳ 156 meV for C NO; m_ee ≳ 68–80 meV for B1–B4 IO) exclude only the tight ends of these ranges. As the paper itself concedes in Sec. V, ‘in all cases except texture C with NO, there is a large part of parameter space compatible with the loose constraint.’ Under the loose ends, B1–B4 IO retain large allowed regions and C IO is also allowed, so the tension is marginal rather than severe. The abstract and Sec. IV.3 should be reworded to state explicitly that the ‘severe tension’ conclusion assumes the tight cosmological bound (Σm_i ≲ 130 meV) and the low end of the KamLAND-Zen nuclear matrix element range (m_ee ≲ 36 meV).
  2. [Sec. IV, Eq. (23) and Table II] The numerical scan is presented as ‘systematically scan[ning] over the full parameter space’, but the paper does not state the scanning algorithm, the number of sampled points, or any convergence checks. Compatibility is defined as the existence of at least one point whose oscillation parameters fall inside the 3σ ranges, which is a very weak notion; it does not quantify how much of the parameter space is allowed. Consequently, the lower bounds in Table II (e.g., m_light ≥ 57 meV for B1 NO) are not established as rigorous minima; they are only lower bounds from a finite, undocumented scan. The authors should specify the sampling density and convergence criteria, or derive the extrema analytically from the invariants in Eqs. (6)–(8), before presenting these bounds as definitive exclusions.
  3. [Sec. IV, Eq. (23)] The scan range 10^{-3} ≤ r_i ≤ 10^3 is justified only by the heuristic statement that r_i ≪ 1 or r_i ≫ 1 would produce approximately three or more independent zeros and hence incompatibility. This is plausible but not proven, and the predicted ranges for m_light, m_eff_νe, and m_ee in Table II could in principle depend on this cut. The authors should either prove that no viable parameter points exist outside the chosen range (using the polynomial invariants) or explicitly state that the quoted ranges are conditional on the chosen scan window. Since the abstract and conclusions present these ranges as intrinsic predictions of each texture, this is a load-bearing point.
minor comments (5)
  1. [Sec. III, before Eq. (12)] There is a typo: ‘Jarsklog invariant’ should be ‘Jarlskog invariant’.
  2. [Sec. III.B, Eq. (19)] The derivation of Eq. (19) from Eqs. (7) and (8) is not shown; please include the intermediate steps or point to the relevant equations, since this relation is an essential step in the no-zero-mass proof.
  3. [Sec. IV.2 and Table II] The text says that for B1 and B3 the NO scenario has θ23 ‘entirely in the first octant’, but Table II lists s2_23 ranges that include 0.50 (e.g., 0.44–0.50). Please either refine the ranges to three decimals or rephrase as ‘first octant and the maximal-mixing boundary’.
  4. [Sec. IV, Eq. (23)] The phrase ‘full parameter space’ is misleading; the scan is over the chosen ranges in Eq. (23), not the full unconstrained space. Consider using ‘chosen parameter ranges’.
  5. [Sec. I and Ref. [32]] Reference [32], which includes one of the present authors, is used to motivate the Zee-model origin of two-zero textures. The citation is legitimate, but the text could make the self-citation transparent or add earlier independent Zee-model texture references.

Circularity Check

0 steps flagged · score 2.0 of 10

No circular derivation: the texture scan produces mlight, meff, and mee as independent outputs, and the only self-citation is a non-load-bearing introduction remark; the 'severe tension' headline is a robustness caveat, not circularity.

full rationale

The seven two-zero textures are adopted as an explicit ansatz (Eqs. (3)-(5)) and are not derived from the mass observables they later bound. In Sec. IV the five texture parameters are determined by requiring the six NuFIT 6.0 oscillation observables to fall in their 3 sigma ranges (Table I); mlight, meff_nu_e, and mee are then read off from the diagonalized mass matrix and Eq. (15), so these mass observables are genuine predictions rather than fitted inputs renamed as predictions. The vanishing mee for A1 and A2 follows from the zero (1,1) entry in Eq. (3) via Eq. (15), which is a model consequence rather than a circular use of data. The only self-citation is Ref. [32] in Sec. I, noting that a minimal Zee model can yield two-zero textures; it is not used in the scan or in any conclusion, so it is not load-bearing. The abstract's 'severe tension' wording does depend on choosing the tight ends of the paper's own quoted ranges (sum m_i <= 0.13 eV and mee <= 36 meV in Sec. IIIA); under the loose ends, B1-B4 and C with IO retain large allowed regions (Sec. V), which is an overstatement/robustness concern, not a circularity. Score 2 reflects the minor non-load-bearing self-citation; no derivation reduces to its inputs.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The central scan rests on the two-zero texture ansatz, the Majorana assumption, and experimental inputs such as oscillation parameters, the cosmological mass bound, and the NME-dependent 0νββ limit. No new particles or entities are invented. The scan range for ri is a hand-chosen assumption about exhaustiveness. These are the main costs the paper pays to reach its conclusions.

free parameters (3)
  • mu (overall neutrino mass scale) = scanned over 1 meV to 1 eV; not predicted
    Sets the overall scale of the texture mass matrix in Eqs. (3)-(5); its allowed range is chosen by hand to cover possible heaviest-neutrino masses, not derived from first principles.
  • r1, r2, r3 (dimensionless texture entries) = scanned over 10^-3 to 10^3; no best-fit values quoted
    Positive real ratios in the texture matrices; the paper argues O(1) values are expected, but the scan bounds are imposed by hand in Eq. (23).
  • theta (relative phase) = scanned over [0, 2pi]
    One physical phase after charged-lepton phase redefinitions; scanned without a prior.
assumptions (5)
  • domain assumption Neutrinos are Majorana fermions, so m_nu is a complex symmetric 3x3 matrix diagonalized by U^T m_nu U = diag(m1,m2,m3) (Eq. (9)).
    The entire analysis is restricted to Majorana neutrinos (Sec. I); Dirac neutrinos would change the phenomenology and the 0νββ interpretation.
  • domain assumption The two-zero texture ansatz is imposed in the charged-lepton mass eigenbasis with exactly two independent zero entries.
    Basis and exactness of zeros are assumed from Refs. [11,12]; if zeros are approximate or the basis is changed, all derived ranges change.
  • domain assumption The cosmological upper bound on the sum of neutrino masses and its translation to mlight (Eq. (13)) is valid, with the tight value Σm_i <= 0.13 eV taken as the key benchmark.
    The severe tension conclusion for B1-B4 and C depends on this bound; the paper notes the bound ranges from 0.13 to 0.52 eV depending on the cosmological model.
  • domain assumption The 0νββ amplitude is dominated by light Majorana neutrino exchange, so mee = |(m_nu)_ee| (Eq. (15)), and the KamLAND-Zen upper bound applies with the quoted nuclear matrix element range.
    New physics contributions or different NME calculations would shift the mee constraint; the paper uses the range 36-156 meV.
  • ad hoc to paper The scan ranges 10^-3 <= ri <= 10^3 are exhaustive for viable textures.
    The paper justifies this by claiming extreme ri would produce effectively additional zeros, but no proof is given that no viable parameter points exist outside the range; the derived lower bounds on mlight could in principle be affected.

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Pith. "Pith review of Revisiting the two-zero texture Majorana neutrino mass matrix." pith.science (2026). https://pith.science/paper/EPDHAR3U

@misc{pith2026250111572,
  author       = {Pith},
  title        = {Pith review of: Revisiting the two-zero texture Majorana neutrino mass matrix},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/EPDHAR3U}},
  note         = {Machine review of arXiv:2501.11572}
}
abstract

It has long been pointed out that there are seven different two-zero texture neutrino mass matrices compatible with neutrino oscillation data. We perform an updated analysis with the recently published Nu-Fit 6.0 results. We also subject the seven two-zero textures to constraints on neutrino mass from cosmology, end point of beta decay spectrum, and neutrinoless double beta decay experiments. We find that all seven textures are compatible with the new oscillation parameters. However, we find five textures, whose 1-1 entry is nonvanishing, are in severe tension with the constraints from cosmology and neutrinoless double beta decay. With the next generation experiments, these five textures could be decisively ruled out. For the remaining two textures, one of them could be ruled out, or severely constrained, if the octant of $\theta_{23}$ is determined.

Figures

Figures reproduced from arXiv: 2501.11572 by the authors.

Figure 1
Figure 1. FIG. 1. The relation between [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. The relation between [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. The relation between [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: FIG. 4. The relation between [PITH_FULL_IMAGE:figures/full_fig_p011_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. The relation between [PITH_FULL_IMAGE:figures/full_fig_p012_5.png]

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Works this paper leans on

53 extracted references · 18 canonical work pages

  1. [40]

    Aghanimet al.(Planck), Astron

    N. Aghanimet al.(Planck), Astron. Astrophys.641, A6 (2020), [Erratum: Astron.Astrophys. 652, C4 (2021)], arXiv:1807.06209 [astro-ph.CO]

    arXiv 2020

  2. [32]

    Texture specific mass matrices with Dirac neutrinos and their implications

    G. Ahuja, M. Gupta, M. Randhawa, and R. Verma, Phys. Rev. D79, 093006 (2009), arXiv:0904.4534 [hep-ph]

    work page Pith review arXiv 2009

  3. [1]

    We find, in both cases, strong correlations betweens2 23, mlight, and meff νe; see Fig

    Textures A1 and A2 From our analysis, textures A1 and A2 can accommodate only NO neutrino masses. We find, in both cases, strong correlations betweens2 23, mlight, and meff νe; see Fig. 1. For texture A1,θ23 can 9 Texture Ordering s2 23 δ [◦] mlight [meV] meff νe [meV] mee [meV] A1 NO 0.43 − 0.58 124 − 290 4.3 − 7.5 9.7 − 11.7 0 A2 NO 0.50 − 0.58 236 − 29...

    work page

  4. [2]

    Such a scenario is compatible only with neutrino masses being NO

    Thus, in the limit where the lightest neutrino mass is vanishing there will be noCP violation in the lepton mixing matrix. Such a scenario is compatible only with neutrino masses being NO. Focusing on the two nonvanishing neutrino masses, Eqs. (7) and (8) imply that r1 + r2 2 + r1r2 2 = 1. (19) Applying the above relation, the resulting neutrino mass matr...

    work page

  5. [3]

    (22) The above equation does not admit a real solution

    = 2r1r2. (22) The above equation does not admit a real solution. Hence, in texture C, the lightest neutrino cannot be massless. IV. NUMERICAL SCAN Inthis section, we perform ascanon thetwo-zerotextureparameterspace. Wetake thefollowing ranges for the free parameters: 1 meV ≤ µ ≤ 1 eV, 10−3 ≤ ri ≤ 103, 0 ≤ θ ≤ 2π. (23) The parameter µ determines the overal...

    work page

  6. [4]

    Textures B1–B4 0.44 0.46 0.48 0.50 0.52 0.54 0.56 0.58 0.60 s2 23 50 100 150 200 250 300 350 mlight [meV] Cosmology (loose) Cosmology (tight) B1 NO B2 NO B3 NO B4 NO 0.44 0.46 0.48 0.50 0.52 0.54 0.56 0.58 0.60 s2 23 50 100 150 200 250 300 350 mlight [meV] Cosmology (loose) Cosmology (tight) B1 IO B2 IO B3 IO B4 IO FIG. 3. The relation betweens2 23 and th...

    work page

  7. [5]

    For NO, we find thats2 23 ≃ 0.5 and neutrino masses are quasidegenerate, while for IOθ23 can be in either octant; see Fig

    Texture C Texture C can accommodate both NO and IO neutrino masses. For NO, we find thats2 23 ≃ 0.5 and neutrino masses are quasidegenerate, while for IOθ23 can be in either octant; see Fig. 5. The Dirac phase δ can take any value between 124◦ and 289◦ in the NO scenario. In the IO case,δ is clustered around 270◦. It is interesting to note that, in the IO...

    work page

  8. [6]

    P. F. de Salas, D. V. Forero, S. Gariazzo, P. Martínez-Miravé, O. Mena, C. A. Ternes, M. Tórtola, and J. W. F. Valle, JHEP02, 071 (2021), arXiv:2006.11237 [hep-ph]

    arXiv 2021

Show all 53 references
  1. [7]

    Capozzi, E

    F. Capozzi, E. Di Valentino, E. Lisi, A. Marrone, A. Melchiorri, and A. Palazzo, Phys. Rev. D104, 083031 (2021), arXiv:2107.00532 [hep-ph]

    2021 arXiv

  2. [8]

    Esteban, M

    I. Esteban, M. C. Gonzalez-Garcia, M. Maltoni, I. Martinez-Soler, J. a. P. Pinheiro, and T. Schwetz, (2024), arXiv:2410.05380 [hep-ph]

    2024 arXiv

  3. [9]

    Minkowski, Phys

    P. Minkowski, Phys. Lett.67B, 421 (1977)

    1977

  4. [10]

    Yanagida,Proceedings: Workshop on the Unified Theories and the Baryon Number in the Universe: Tsukuba, Japan, February 13-14, 1979, Conf

    T. Yanagida,Proceedings: Workshop on the Unified Theories and the Baryon Number in the Universe: Tsukuba, Japan, February 13-14, 1979, Conf. Proc.C7902131, 95 (1979)

    1979

  5. [11]

    Gell-Mann, P

    M. Gell-Mann, P. Ramond, and R. Slansky,Supergravity Workshop Stony Brook, New York, September 27-28, 1979, Conf. Proc.C790927, 315 (1979), arXiv:1306.4669 [hep-th]

    1979 arXiv

  6. [12]

    R. N. Mohapatra and G. Senjanovic, Phys. Rev. Lett.44, 912 (1980)

    1980

  7. [13]

    Zee, Phys

    A. Zee, Phys. Lett. B93, 389 (1980), [Erratum: Phys.Lett.B 95, 461 (1980)]

    1980

  8. [14]

    Zee, Nucl

    A. Zee, Nucl. Phys. B264, 99 (1986)

    1986

  9. [15]

    K. S. Babu, Phys. Lett. B203, 132 (1988)

    1988

  10. [16]

    Xing, Phys

    Z.-z. Xing, Phys. Lett. B530, 159 (2002), arXiv:hep-ph/0201151

    2002 arXiv

  11. [17]

    P. H. Frampton, S. L. Glashow, and D. Marfatia, Phys. Lett. B536, 79 (2002), arXiv:hep-ph/0201008

    2002 arXiv

  12. [18]

    Guo and Z.-z

    W.-l. Guo and Z.-z. Xing, Phys. Rev. D67, 053002 (2003), arXiv:hep-ph/0212142

    2003 arXiv

  13. [19]

    Fritzsch, Z.-z

    H. Fritzsch, Z.-z. Xing, and S. Zhou, JHEP09, 083 (2011), arXiv:1108.4534 [hep-ph]

    2011 arXiv

  14. [20]

    Kageyama, S

    A. Kageyama, S. Kaneko, N. Shimoyama, and M. Tanimoto, Phys. Lett. B538, 96 (2002), arXiv:hep- ph/0204291

    2002

  15. [21]

    Frigerio and A

    M. Frigerio and A. Y. Smirnov, Phys. Rev. D67, 013007 (2003), arXiv:hep-ph/0207366

    2003 arXiv

  16. [22]

    Honda, S

    M. Honda, S. Kaneko, and M. Tanimoto, JHEP09, 028 (2003), arXiv:hep-ph/0303227

    2003 arXiv

  17. [23]

    Bhattacharyya, A

    G. Bhattacharyya, A. Raychaudhuri, and A. Sil, Phys. Rev. D 67, 073004 (2003), arXiv:hep- ph/0211074

    2003

  18. [24]

    Mohanta, G

    R. Mohanta, G. Kranti, and A. K. Giri, (2006), arXiv:hep-ph/0608292

    2006 arXiv

  19. [25]

    Farzan and A

    Y. Farzan and A. Y. Smirnov, JHEP01, 059 (2007), arXiv:hep-ph/0610337

    2007 arXiv

  20. [26]

    S. Dev, S. Verma, and S. Gupta, Phys. Lett. B687, 53 (2010), arXiv:0909.3182 [hep-ph]

    2010 arXiv

  21. [27]

    S. Dev, S. Kumar, S. Verma, and S. Gupta, Phys. Rev. D76, 013002 (2007), arXiv:hep-ph/0612102

    2007 arXiv

  22. [28]

    E. I. Lashin and N. Chamoun, Phys. Rev. D78, 073002 (2008), arXiv:0708.2423 [hep-ph]. 15

    2008 arXiv

  23. [29]

    Dighe and N

    A. Dighe and N. Sahu, (2009), arXiv:0812.0695 [hep-ph]

    2009 arXiv

  24. [30]

    Goswami and A

    S. Goswami and A. Watanabe, Phys. Rev. D79, 033004 (2009), arXiv:0807.3438 [hep-ph]

    2009 arXiv

  25. [31]

    E. I. Lashin and N. Chamoun, Phys. Rev. D80, 093004 (2009), arXiv:0909.2669 [hep-ph]

    2009 arXiv

  26. [33]

    Goswami, S

    S. Goswami, S. Khan, and W. Rodejohann, Phys. Lett. B680, 255 (2009), arXiv:0905.2739 [hep-ph]

    2009 arXiv

  27. [34]

    S. Dev, S. Gupta, and R. R. Gautam, Phys. Rev. D82, 073015 (2010), arXiv:1009.5501 [hep-ph]

    2010 arXiv

  28. [35]

    S. Dev, S. Verma, S. Gupta, and R. R. Gautam, Phys. Rev. D81, 053010 (2010), arXiv:1003.1006 [hep-ph]

    2010 arXiv

  29. [36]

    Grimus and P

    W. Grimus and P. O. Ludl, Phys. Lett. B700, 356 (2011), arXiv:1104.4340 [hep-ph]

    2011 arXiv

  30. [37]

    Primulando, J

    R. Primulando, J. Julio, and P. Uttayarat, Phys. Rev. D107, 055034 (2023), arXiv:2211.16021 [hep- ph]

    2023 arXiv

  31. [38]

    E. E. Jenkins and A. V. Manohar, Nucl. Phys. B792, 187 (2008), arXiv:0706.4313 [hep-ph]

    2008 arXiv

  32. [39]

    J. F. Nieves and P. B. Pal, Phys. Rev. D64, 076005 (2001), arXiv:hep-ph/0105305

    2001 arXiv

  33. [41]

    Di Valentino, A

    E. Di Valentino, A. Melchiorri, and J. Silk, JCAP01, 013 (2020), arXiv:1908.01391 [astro-ph.CO]

    2020 arXiv

  34. [42]

    Akeret al.(Katrin), (2024), arXiv:2406.13516 [nucl-ex]

    M. Akeret al.(Katrin), (2024), arXiv:2406.13516 [nucl-ex]

    2024

  35. [43]

    Abe et al.(KamLAND-Zen), Phys

    S. Abe et al.(KamLAND-Zen), Phys. Rev. Lett.130, 051801 (2023), arXiv:2203.02139 [hep-ex]

    2023

  36. [44]

    Agostini et al.(GERDA), Phys

    M. Agostini et al.(GERDA), Phys. Rev. Lett.125, 252502 (2020), arXiv:2009.06079 [nucl-ex]

    2020 arXiv

  37. [45]

    P. B. Denton and J. Gehrlein, Phys. Rev. D109, 055028 (2024), arXiv:2308.09737 [hep-ph]

    2024 arXiv

  38. [46]

    M. H. Abitbolet al. (Simons Observatory), Bull. Am. Astron. Soc.51, 147 (2019), arXiv:1907.08284 [astro-ph.IM]

    2019 arXiv

  39. [47]

    Alpert et al., Eur

    B. Alpert et al., Eur. Phys. J. C75, 112 (2015), arXiv:1412.5060 [physics.ins-det]

    2015 arXiv

  40. [48]

    Akeret al.(KATRIN), Phys

    M. Akeret al.(KATRIN), Phys. Rev. Lett.123, 221802 (2019), arXiv:1909.06048 [hep-ex]

    2019

  41. [49]

    Abgrallet al.(LEGEND), AIP Conf

    N. Abgrallet al.(LEGEND), AIP Conf. Proc.1894, 020027 (2017), arXiv:1709.01980 [physics.ins-det]

    2017 arXiv

  42. [50]

    An et al.(JUNO), J

    F. An et al.(JUNO), J. Phys. G43, 030401 (2016), arXiv:1507.05613 [physics.ins-det]

    2016 arXiv

  43. [51]

    Abusleme et al.(JUNO), Prog

    A. Abusleme et al.(JUNO), Prog. Part. Nucl. Phys.123, 103927 (2022), arXiv:2104.02565 [hep-ex]

    2022

  44. [52]

    Abi et al.(DUNE), Eur

    B. Abi et al.(DUNE), Eur. Phys. J. C80, 978 (2020), arXiv:2006.16043 [hep-ex]

    2020

  45. [53]

    Abe et al.(Hyper-Kamiokande), (2018), arXiv:1805.04163 [physics.ins-det]

    K. Abe et al.(Hyper-Kamiokande), (2018), arXiv:1805.04163 [physics.ins-det]

    2018 arXiv

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.