The Majoron at two loops

Hiren H. Patel; Julian Heeck

REVIEW 3 major objections 4 minor 9 cited by

The Majoron at two loops

T0 review · 3 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read The paper claims that the Majoron's two-loop couplings to gauge bosons and flavor-changing quarks complete the leading-order description of how the Majoron talks to every Standard Model particle.

desk verdict Solid two-loop calculation that completes most of the Majoron coupling program; the completeness claim is slightly overbroad because the hZ/hγ couplings are omitted, but that is a framing issue, not a physics flaw. read the letter →

arxiv 1909.02029 v2 pith:7PNXNI4X submitted 2019-09-04 hep-ph

Julian Heeck , Hiren H. Patel This is my paper · ORCID

classification hep-ph

keywords Majorontwo-loopcouplingsseesawmechanismleptonnumberviolationaxion-likeparticleflavor-changingneutralcurrentsdarkmatterrarekaondecays

topics Dark Matter

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 completes a program that began with the original 1981 Majoron proposal: it derives the couplings of the Majoron, the Goldstone boson of spontaneously broken lepton number, to every Standard Model particle, at leading order in the seesaw expansion. The missing pieces were the two-loop couplings to gauge bosons and to quarks of different generations. If the calculation is right, the Majoron is a fully predictive axion-like particle whose couplings are fixed by the seesaw parameters, and rare processes such as $\tau\to\ell J$, $K\to\pi J$, and $B\to K J$ become direct probes of those parameters. The result also reshapes Majoron dark matter expectations, because the two-loop diphoton coupling can be suppressed by cancellations, leaving neutrinos as the dominant decay signal.

What carries the argument

The load-bearing object is the two-loop effective-vertex calculation in the minimal singlet Majoron model, organized by the seesaw expansion in the small ratio $v/f$ of electroweak scale to lepton-number-breaking scale. The diagrams split into Set I (genuine two-loop 1PI diagrams) and Set II (reducible diagrams dominated by $J$-$Z$ mixing), and the computation uses standard identities among the seesaw mixing matrices $C$, $B$, and $M_n$ to ensure the amplitudes are ultraviolet finite. The quoted outputs are coefficients $g_{JVV'}$ of on-shell decay amplitudes $M(J \to VV') = -g_{JVV'} \varepsilon^{\mu\nu\rho\sigma} \varepsilon^*_\mu(k_1) \varepsilon^*_\nu(k_2) k_{1\rho} k_{2\sigma}$, with the loop functions $h(x)$, $g(x)$, and the Passarino-Veltman $C_0$ carrying all mass dependence; after reduction, no two-loop master integrals survive.

What would settle it

An independent numerical evaluation of the two-loop amplitudes at a benchmark point (say $m_J=1\,\mathrm{GeV}$, $f=M_R=1\,\mathrm{TeV}$, diagonal $M_DM_D^\dagger=(100\,\mathrm{GeV})^2$) would settle the formal calculation, since the paper's expressions are explicit enough to compare numerically. For the phenomenological layer, a hadronic computation of $J\to\gamma\gamma$ between 1 and 100 MeV would decide whether the quoted exclusion curves survive.

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Extended reading notes

Core claim

At leading order in the seesaw expansion, the Majoron's couplings to two gluons, two photons, a photon and a $Z$, two $Z$s, two $W$s, and to quark pairs of different generations all arise for the first time at two-loop order, and this paper gives them in closed form. The amplitudes are written as on-shell decay amplitudes $J \to VV'$, they are ultraviolet finite by virtue of the neutrino-mixing identities of Eq. (5), and after tensor reduction they collapse to sums of elementary one-loop functions and rational terms. Two important structural results follow: $J \to gg$ and $J \to \gamma\gamma$ vanish like $m_J^2$ for small Majoron masses, matching onto derivative operators such as $(\partial^2 J) F \tilde F$ rather than $J F \tilde F$, while $J \to Z\gamma$, $J \to ZZ$, and $J \to WW$ remain nonzero in the zero-momentum limit. The flavor-changing quark couplings are of minimal-flavor-violating form and are enhanced by $\log(M_R/m_W)$, making $s \to dJ$ the largest quark-level transition.

Load-bearing premise

The load-bearing premise is the free-quark description of the two-loop amplitudes: the paper's low-mass phenomenology, such as MeV-to-100 MeV $J\to\gamma\gamma$ limits and $K\to\pi J$, assumes that replacing quarks by hadrons in the loops does not change the results by order-one factors, and that replacement is explicitly not done.

Editorial extensions

If this is right

For a strictly massless Majoron, the new photon and gluon couplings vanish as $m_J^2$, and the paper concludes that the two-loop couplings are phenomenologically irrelevant there.
For nonzero Majoron masses, the flavor-changing quark couplings provide new rare-decay probes: $K\to\pi J$ and $B\to K J$ can beat stellar-cooling limits when the $\log(M_R/m_W)$ enhancement is active.
The full $J\to\gamma\gamma$ coupling can be significantly smaller than the earlier Set II estimate when the diagonal entries of $M_DM_D^\dagger$ are hierarchical, so dark-matter diphoton limits weaken and the neutrino-line channel becomes relatively more important.
In low-scale seesaw realizations, the special texture of $M_D$ makes all Majoron and non-Majoron coupling matrices share one flavor structure, so $\tau\to\ell J$ and $\mu\to e J$ can be observable even where $\tau\to\ell\gamma$ and $\mu\to e\gamma$ are not.
Because Majoron operators scale as $M_DM_D^\dagger/f$ while ordinary seesaw operators scale as $M_D M_R^{-2}M_D^\dagger$, the ratio $f/M_R$ controls whether Majoron couplings dominate or are negligible relative to standard seesaw observables.

Reading between the lines

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

Implicit in the paper's hierarchy plots: because $g_{J\gamma\gamma}$ can be suppressed to near zero for particular hierarchies of the diagonal entries of $M_DM_D^\dagger$, monochromatic gamma-ray line searches for Majoron dark matter may be far less sensitive than previously estimated, making the neutrino-line mode the more robust discovery channel.
A direct extension of the calculation would apply the same two-loop machinery to other spontaneously broken lepton numbers, such as familons or lepton-flavored majorons, where the flavor-changing quark couplings would inherit the same $\log(M_R/m_W)$ structure.
The paper leaves the hadronic replacement as future work; because the free-quark amplitudes are the only input in the low-mass regime, a chiral or lattice calculation of the relevant matrix elements would settle the reliability of the low-mass exclusion regions.
The paper does not pursue it, but the explicit dependence of the flavor-changing couplings on $\mathrm{tr}(M_D \log(M_R/m_W) M_D^\dagger)$ means that a single measured rare-decay rate, if combined with neutrino oscillation data, could begin to overconstrain the seesaw parameter space.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

The important physics here is the two-loop, leading-seesaw Majoron couplings to gauge bosons and flavor-changing quarks. The genuinely new piece is the Set I 1PI contribution to Jγγ and the full set of JZγ, JZZ, JWW, and Jgg amplitudes, plus the log-enhanced Jdd′ and Juu′ couplings. Before this paper only the J–Z mixing (Set II) piece of Jγγ had been estimated, so this fills a real gap in the 40-year-old Majoron program.

The calculation is careful and transparent. The authors give explicit formulas, check UV finiteness using the identities of Eq. (5), verify γ5-scheme independence, and confirm the expected low-mass and soft limits. The FeynArts/FeynRules pipeline is validated on known tree- and one-loop results. The physics points, like the mJ^2 suppression of Jgg and the possible cancellations in Jγγ from the two diagram sets, are credible and interesting. The phenomenology section is honest about its approximations.

The soft spots are real but not damaging. The abstract and introduction claim to derive “all Majoron couplings to SM particles,” yet Sec. III F explicitly states that the two-loop J–hZ and J–hγ couplings exist but are not presented. That is a load-bearing claim in the framing only; the authors acknowledge the omission and give a reasonable justification (low phenomenological relevance). Still, “complete” is overbroad and should be qualified. Second, the low-mass hadronic treatment is acknowledged to be crude: setting mu=md=mπ and ms=mK in the Jγγ loop is a naive substitution, and the authors themselves say the resulting limit “should not be taken too seriously.” That weakens the low-mass exclusion plot but does not touch the two-loop formulas in the free-quark regime.

The citation pattern is appropriate, including the reuse of the Set II formula from the authors’ earlier work, which is properly credited. I have not re-run the integrals, but the internal consistency checks and the published record give me reasonable confidence in the central results.

This paper is for anyone working on Majoron models, axion-like particles, rare B and K decays, or Majoron dark matter. It deserves serious peer review. The main revision I would ask for is to temper the completeness claim and make clear that hZ/hγ are not computed here. I would bring it to a reading group and would cite it in related work.

Referee Report

3 major / 4 minor

Summary. The paper studies the minimal singlet Majoron model with spontaneous lepton-number breaking. In the seesaw limit MD << MR, it computes the two-loop couplings of the Majoron to gluons, photons, Z-gamma, ZZ, WW, and to flavor-changing quark pairs dd' and uu' at leading order in the seesaw expansion. The couplings are given as explicit expressions in terms of one-loop integral functions; the authors verify UV finiteness, independence of the gamma5 treatment, and the expected low-energy and soft limits. They then use these couplings to discuss constraints from rare kaon/B decays, supernova cooling, lepton-flavor-violating decays, and Majoron dark matter, and compare with standard seesaw observables.

Significance. The calculation is technically demanding, involving on the order of one hundred two-loop diagrams, and is performed with multiple cross-checks, including UV-finiteness, gamma5-scheme independence, and agreement with known limits. The main physics findings—an mJ^2-suppressed and potentially cancellation-prone J-gamma-gamma coupling, non-vanishing J-Z-gamma, J-ZZ, and J-WW couplings, and log(MR/mW)-enhanced flavor-changing quark couplings—are novel and phenomenologically relevant. The explicit formulas constitute a useful resource for experimental searches. If the missing hZ/h-gamma amplitudes are supplied or the scope claim is revised, this would be a valuable contribution appropriate for the journal.

major comments (3)

[Sec. III F (with Sec. I and Sec. V)] The paper's headline claim of deriving 'all Majoron couplings to SM particles' is not supported by its own text: Sec. III F states that CP invariance permits couplings of the Majoron to hZ and h-gamma, that the dominant contributions to both arise at two-loop order, and that 'we will not, however, present the results here.' Unless these couplings vanish identically at leading order in the seesaw expansion—which is not shown—the completeness claim is false as stated. The authors should either compute these amplitudes or explicitly revise the abstract, introduction, and conclusion to state that the paper covers the phenomenologically important gauge-boson and flavor-changing-quark couplings, listing hZ and h-gamma as omitted.
[Sec. IV A and Fig. 6] The low-mass phenomenological constraints (mJ below roughly 1 GeV) rely on the free-quark expression for gJ-gamma-gamma with the ad hoc replacements mu=md=m_pi and ms=m_K, a procedure the text itself labels 'very naive' and cautions 'should not be taken too seriously.' Because Fig. 6 is presented as the central constraint summary, the exclusion regions between about 1 MeV and 1 GeV should be clearly marked as model-dependent estimates, and the text should state that robust quantitative bounds in this mass range require a hadronic treatment rather than free-quark thresholds.
[Sec. III G] The subleading contribution Lsub_Jdd' in Eq. (37) is neglected in the subsequent phenomenological analysis with the justification that log(MR/mW) >~ 1. Since log(MR/mW) is only O(1) when MR is near the TeV scale, and no quantitative comparison between the leading-log and subleading terms is provided, the dominance of the leading-log coupling in the K -> pi J and B -> K J constraints should be demonstrated, or Lsub should be included in the numerical analysis.

minor comments (4)

[Eq. (3)] The rendering of the Z-boson coupling term appears garbled: 'ni/Z' seems to be missing a gamma matrix (presumably gamma^mu Z_mu or a slashed Z). Please check the typeset version.
[Fig. 4 caption] The caption describes the blue dashed line as (MDMD†)ee=(MDMD†)mu-mu=(100 GeV)^2, (MDMD†)tau-tau=0 and simultaneously states that this configuration corresponds to gJee=gJmu-mu=0. These statements are inconsistent with the definitions in Eqs. (10) and (11), since nonzero diagonal entries of MDMD† do not make the corresponding diagonal fermion couplings vanish. The caption should be corrected.
[Sec. III] The paper relies on an in-house Mathematica implementation of expansion by regions and two-loop tensor reduction, but no code or detailed algebraic steps are provided. An ancillary file or an appendix with additional intermediate steps would substantially improve reproducibility.
[Sec. III B and III E] The one-argument loop functions h(x) and g(x) are defined in Eqs. (16) and (27), while a two-argument function g(x,y) is introduced later in Eq. (34). Collecting all loop-function definitions in a single table or appendix would improve readability.

Circularity Check

0 steps flagged · score 1.0 of 10

No substantive circularity: the two-loop couplings follow from the Lagrangian and are checked against independent data; the only self-cited element (Ref. [10] for gII_Jγγ) is a component reuse, not a construction that forces the result.

full rationale

The derivation chain is self-contained in the relevant sense. The authors start from the singlet-Majoron Lagrangian (Eq. (1)), expand in the seesaw hierarchy via A = U† MD MR^{-1}, and compute the two-loop amplitudes for Jgg, Jγγ, JZγ, JZZ, JWW, and Jqq' with FeynArts/FeynRules and asymptotic expansion. The resulting couplings are expressed in terms of tr(MDMD†) and (MDMD†)ll; none of these parameters is fitted to the observables used later as constraints. The phenomenological section applies external bounds (μ→eJ, τ→ℓJ, K→πJ, B→KJ, SN1987) to the derived couplings, so the stated constraints are not forced by construction. The one self-citation is Eq. (19), where the Set II Jγγ contribution is taken from Ref. [10] (co-authored by Heeck). That is a component rather than the central claim: the new Set I contribution is computed in Eq. (20), and the total gJγγ is presented as their sum. The cited formula is a parameter-free calculation in the same model, not an assumption equivalent to the conclusion, so the reuse does not make the central result circular. Equation (21) is a low-energy consistency relation between gJγγ and the one-loop gJff, not the definition of either coupling, and it is cross-checked against Ref. [52]. No uniqueness theorem or ansatz is imported from the authors' prior work to exclude alternatives. The acknowledged omission of hγ and hZ couplings in Sec. III F weakens the ``all Majoron couplings'' headline claim, but that is a claim-scope issue rather than a circularity; the same holds for the hadronic-replacement caveat for MeV-scale Majoron masses, which is an admitted numerical uncertainty and not a fitted input. Overall, no significant circularity is present.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

The central claim rests on the standard singlet Majoron Lagrangian (three right-handed neutrinos plus one complex scalar) and on the seesaw hierarchy MD << MR; these are model inputs imported from the prior literature rather than derived here. The model introduces no new particles beyond the established Majoron, right-handed neutrinos, and heavy scalar. The paper's contribution is the derivation of the couplings in terms of these inputs. The seesaw parameter matrix MD and the scale f remain free parameters to be constrained by experiment; the paper does not fit any of them. The only hand-chosen quantities are illustrative benchmark values in figures (f=1 TeV, MR=1 TeV, log(MR/mW)=1), which do not affect the analytical results.

free parameters (4)

Lepton-number breaking scale f
Lagrangian input from the scalar vacuum expectation value that gives the right-handed neutrino masses. Every Majoron coupling scales as 1/f; the paper does not fit it, it only constrains combinations like K=(MD MD†)/(v f) using experimental limits.
Seesaw parameter matrix MD MD†
The combination of the Dirac Yukawa matrix that controls all loop-induced Majoron couplings. It is an input of the model; the paper derives couplings as functions of it and then translates experimental bounds into limits on its entries, using benchmarks in the figures.
Majoron mass mJ
Introduced as an explicit shift-symmetry-breaking mass term; it is a free parameter that enters the loop functions and determines the relevant decay channels. Scanned over keV to GeV range in the phenomenology.
Heavy neutrino mass scale MR (via log(MR/mW))
Enters the flavor-changing quark couplings at leading-log order. Not fitted; in Fig. 6 the authors set log(MR/mW)=1 for a conservative comparison, noting larger values would strengthen the rare-decay limits.

assumptions (6)

domain assumption The minimal singlet Majoron Lagrangian of Eq. (1), with three right-handed neutrinos and one complex singlet scalar, is the theory under study.
This model choice, inherited from Chikashige, Mohapatra, and Peccei, defines the particle content and the origin of the Majoron. The paper does not derive the model, it computes couplings within it.
domain assumption The seesaw hierarchy MD << MR (equivalently v << f) holds, and the expansion in A = U† MD MR^-1 is truncated at leading order.
Stated in Sec. II after Eq. (5). All reported couplings are leading order in this expansion; corrections of order (v/f) are dropped.
domain assumption The CP-even scalar partner sigma0 of the Majoron is inaccessibly heavy and decouples.
Stated in Sec. II: sigma0 is 'assumed to be inaccessibly heavy'. If it is light, additional portals and mixings would modify the phenomenology.
standard math The seesaw mixing-matrix identities of Eq. (5), taken from Pilaftsis, are valid and guarantee UV finiteness of the amplitudes.
These algebraic identities, such as C=C²=C†, BB†=1, and CMnCT=0, are standard for seesaw matrices and are used throughout the amplitude reduction. They are stated, not proven, but they follow from unitarity and the mass matrix structure.
domain assumption The naive anticommuting gamma5 prescription is a valid regularization for these two-loop amplitudes.
The authors treat gamma5 naively and then state they checked insensitivity by projecting onto form factors and by cyclically reordering traces. The checks make the assumption reasonable, but it remains a scheme assumption.
domain assumption The low-scale seesaw texture (Eq. 51) taken from Coy and Frigerio is assumed in Sec. IV B to solve Mν=0 and to generate observable neutrino masses via small perturbations.
This texture is borrowed from Ref. [17] to render the seesaw parameter space tractable; it is an input to the phenomenological comparison, not a result of this paper.

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Cite this review

Pith. "Pith review of The Majoron at two loops." pith.science (2026). https://pith.science/paper/7PNXNI4X

@misc{pith2026190902029,
  author       = {Pith},
  title        = {Pith review of: The Majoron at two loops},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7PNXNI4X}},
  note         = {Machine review of arXiv:1909.02029}
}

abstract

We present singlet-Majoron couplings to Standard Model particles through two loops at leading order in the seesaw expansion, including couplings to gauge bosons as well as flavor-changing quark interactions. We discuss and compare the relevant phenomenological constraints on Majoron production as well as decaying Majoron dark matter. A comparison with standard seesaw observables in low-scale settings highlights the importance of searches for lepton-flavor-violating two-body decays $\ell \to \ell' +$Majoron in both the muon and tau sectors.

Figures

Figures reproduced from arXiv: 1909.02029 by the authors.

**Figure 2.** FIG. 2. Loop-induced Majoron couplings to [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** FIG. 3. Representative two-loop diagrams contributing to [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

Figures from the paper (4 more)

**Figure 4.** Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]

**Figure 5.** Figure 5: FIG. 5. Representative two-loop diagrams for off-diagonal [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]

**Figure 6.** Figure 6: FIG. 6. Upper limits on combinations of [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]

**Figure 7.** Figure 7: FIG. 7. Limits on ( [PITH_FULL_IMAGE:figures/full_fig_p011_7.png]

Discussion (0). Continue with ORCID to comment.

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Reference graph

Works this paper leans on

97 extracted references · 21 canonical work pages · cited by 9 Pith papers

[1]

Baryon and Lepton Nonconserving Processes,

S. Weinberg, “ Baryon and Lepton Nonconserving Processes,” Phys. Rev. Lett. 43 (1979) 1566–1570

1979
[2]

≡− 1 2 ¯nc RMnnR + h.c., (2) whereV is the unitary 6× 6 mixing matrix to the states nR, which form the Majorana mass eigenstates n =nR + nc R

The full 6 × 6 neutrino mass matrix in the basis ( νc L,NR) = VnR is then L =−1 2 ¯nc RVT ( 0 MD MT D MR ) VnR + h.c. ≡− 1 2 ¯nc RMnnR + h.c., (2) whereV is the unitary 6× 6 mixing matrix to the states nR, which form the Majorana mass eigenstates n =nR + nc R. The diagonal mass matrix Mn = diag(m1,...,m 6) consists of the physical neutrino masses arranged...
[3]

standard

As already noted in Ref. [17], the non-Majoron limits are completely dominated by ﬂavor- conserving observ- ables such as Z → e+e− and other electroweak preci- sion data. LFV such as τ → eγ and τ → eee reside far in the already excluded region and even future im- provements, e.g. in Belle-II, do not reach the allowed pa- rameter space. In comparison, Majo...
[4]

µ→eγ at a rate of one out of 109 muon decays?,

P. Minkowski, “µ→eγ at a rate of one out of 109 muon decays?,” Phys. Lett. B67 (1977) 421–428

1977
[5]

Are There Real Goldstone Bosons Associated with Broken Lepton Number?,

Y. Chikashige, R. N. Mohapatra, and R. D. Peccei, “ Are There Real Goldstone Bosons Associated with Broken Lepton Number?,” Phys. Lett. B98 (1981) 265–268

1981
[6]

Neutrino Decay and Spontaneous Violation of Lepton Number ,

J. Schechter and J. W. F. Valle, “ Neutrino Decay and Spontaneous Violation of Lepton Number ,” Phys. Rev. D25 (1982) 774

1982
[7]

The Superlight Axion and Neutrino Masses ,

R. N. Mohapatra and G. Senjanovic, “ The Superlight Axion and Neutrino Masses ,” Z. Phys. C17 (1983) 53–56

1983
[8]

Invisible Axions and Light Neutrinos: Are They Connected? ,

P. Langacker, R. D. Peccei, and T. Yanagida, “ Invisible Axions and Light Neutrinos: Are They Connected? ,” Mod. Phys. Lett. A01 (1986) 541

1986

Show all 97 references

[9]

Light Neutrino Masses and Strong CP Problem,

M. Shin, “ Light Neutrino Masses and Strong CP Problem,” Phys. Rev. Lett. 59 (1987) 2515. [Erratum: Phys. Rev. Lett. 60, 383 (1988)]

1987
[10]

Unifying inﬂation with the axion, dark matter, baryogenesis and the seesaw mechanism ,

G. Ballesteros, J. Redondo, A. Ringwald, and C. Tamarit, “Unifying inﬂation with the axion, dark matter, baryogenesis and the seesaw mechanism ,” Phys. Rev. Lett. 118 (2017) 071802, [ 1608.05414]

2017 arXiv
[11]

Standard Model-axion-seesaw-Higgs portal inﬂation. Five problems of particle physics and cosmology solved in one stroke ,

G. Ballesteros, J. Redondo, A. Ringwald, and C. Tamarit, “Standard Model-axion-seesaw-Higgs portal inﬂation. Five problems of particle physics and cosmology solved in one stroke ,” JCAP 1708 (2017) 001, [1610.01639]

2017 arXiv
[12]

Neutrino Lines from Majoron Dark Matter ,

C. Garcia-Cely and J. Heeck, “ Neutrino Lines from Majoron Dark Matter ,” JHEP 05 (2017) 102, [1701.07209]

2017 arXiv
[13]

The Eﬀective Lagrangian for the seesaw model of neutrino mass and leptogenesis ,

A. Broncano, M. B. Gavela, and E. E. Jenkins, “ The Eﬀective Lagrangian for the seesaw model of neutrino mass and leptogenesis ,” Phys. Lett. B552 (2003) 177–184, [hep-ph/0210271]. [Erratum: Phys. Lett. B636, 332 (2006)]

2003 arXiv
[14]

Neutrino physics in the seesaw model ,

A. Broncano, M. B. Gavela, and E. E. Jenkins, “Neutrino physics in the seesaw model ,” Nucl. Phys. B672 (2003) 163–198, [ hep-ph/0307058]

2003 arXiv
[15]

Renormalization of lepton mixing for Majorana neutrinos,

A. Broncano, M. B. Gavela, and E. E. Jenkins, “Renormalization of lepton mixing for Majorana neutrinos,” Nucl. Phys. B705 (2005) 269–295, [hep-ph/0406019]

2005 arXiv
[16]

Minimal ﬂavor violation in the lepton sector ,

V. Cirigliano, B. Grinstein, G. Isidori, and M. B. Wise, “Minimal ﬂavor violation in the lepton sector ,” Nucl. Phys. B728 (2005) 121–134, [ hep-ph/0507001]

2005 arXiv
[17]

Low energy eﬀects of neutrino masses ,

A. Abada, C. Biggio, F. Bonnet, M. B. Gavela, and T. Hambye, “Low energy eﬀects of neutrino masses ,” JHEP 12 (2007) 061, [ 0707.4058]

2007 arXiv
[18]

Minimal Flavour Seesaw Models ,

M. B. Gavela, T. Hambye, D. Hernandez, and P. Hernandez, “Minimal Flavour Seesaw Models ,” JHEP 09 (2009) 038, [ 0906.1461]

2009 arXiv
[19]

Eﬀective approach to lepton observables: the seesaw case ,

R. Coy and M. Frigerio, “ Eﬀective approach to lepton observables: the seesaw case ,” Phys. Rev. D99 (2019) 095040, [1812.03165]

2019 arXiv
[20]

Astrophysical and terrestrial constraints on singlet Majoron models ,

A. Pilaftsis, “ Astrophysical and terrestrial constraints on singlet Majoron models ,” Phys. Rev. D49 (1994) 2398–2404, [hep-ph/9308258]

1994 arXiv
[21]

Electroweak Resonant Leptogenesis in the Singlet Majoron Model,

A. Pilaftsis, “ Electroweak Resonant Leptogenesis in the Singlet Majoron Model,” Phys. Rev. D78 (2008) 013008, [0805.1677]

2008 arXiv
[22]

Radiatively induced neutrino masses and large Higgs neutrino couplings in the standard model with Majorana ﬁelds ,

A. Pilaftsis, “ Radiatively induced neutrino masses and large Higgs neutrino couplings in the standard model with Majorana ﬁelds ,” Z. Phys. C55 (1992) 275–282, [hep-ph/9901206]

1992 arXiv
[23]

Lepton ﬂavor nonconservation in H 0 decays,

A. Pilaftsis, “ Lepton ﬂavor nonconservation in H 0 decays,” Phys. Lett. B285 (1992) 68–74

1992
[24]

Oscillating neutrinos and µ→eγ,

J. A. Casas and A. Ibarra, “ Oscillating neutrinos and µ→eγ,” Nucl. Phys. B618 (2001) 171–204, [hep-ph/0103065]

2001 arXiv
[25]

Determining seesaw parameters from weak scale measurements?,

S. Davidson and A. Ibarra, “ Determining seesaw parameters from weak scale measurements?,” JHEP 09 (2001) 013, [ hep-ph/0104076]

2001 arXiv
[26]

The smallest neutrino mass,

S. Davidson, G. Isidori, and A. Strumia, “ The smallest neutrino mass,” Phys. Lett. B646 (2007) 100–104, [hep-ph/0611389]

2007 arXiv
[27]

R. A. Horn and C. R. Johnson, Matrix Analysis. Cambridge University Press, 1990

1990
[28]

Pseudo-Majoron as Dark Matter,

P.-H. Gu, E. Ma, and U. Sarkar, “ Pseudo-Majoron as Dark Matter,” Phys. Lett. B690 (2010) 145–148, [1004.1919]

2010 arXiv
[29]

Sub-GeV dark matter as pseudo-Goldstone from the seesaw scale ,

M. Frigerio, T. Hambye, and E. Masso, “ Sub-GeV dark matter as pseudo-Goldstone from the seesaw scale ,” Phys. Rev. X1 (2011) 021026, [ 1107.4564]

2011 arXiv
[30]

Planck scale eﬀects on the majoron,

E. K. Akhmedov, Z. G. Berezhiani, R. N. Mohapatra, and G. Senjanovic, “ Planck scale eﬀects on the majoron,” Phys. Lett. B299 (1993) 90–93, [hep-ph/9209285]

1993 arXiv
[31]

Planck scale symmetry breaking and majoron physics ,

I. Z. Rothstein, K. S. Babu, and D. Seckel, “ Planck scale symmetry breaking and majoron physics ,” Nucl. Phys. B403 (1993) 725–748, [ hep-ph/9301213]

1993 arXiv
[32]

Wormholes and masses for Goldstone bosons,

R. Alonso and A. Urbano, “ Wormholes and masses for Goldstone bosons,” JHEP 02 (2019) 136, [ 1706.07415]. 13

2019 arXiv
[33]

The keV majoron as a dark matter particle ,

V. Berezinsky and J. W. F. Valle, “ The keV majoron as a dark matter particle ,” Phys. Lett. B318 (1993) 360–366, [hep-ph/9309214]

1993 arXiv
[34]

Decaying warm dark matter and neutrino masses ,

M. Lattanzi and J. W. F. Valle, “ Decaying warm dark matter and neutrino masses ,” Phys. Rev. Lett. 99 (2007) 121301, [ 0705.2406]

2007 arXiv
[35]

X-ray photons from late-decaying majoron dark matter ,

F. Bazzocchi, M. Lattanzi, S. Riemer-Sørensen, and J. W. F. Valle, “ X-ray photons from late-decaying majoron dark matter ,” JCAP 0808 (2008) 013, [0805.2372]

2008 arXiv
[36]

Updated CMB and x- and γ-ray constraints on Majoron dark matter ,

M. Lattanzi, S. Riemer-Sørensen, M. T´ ortola, and J. W. F. Valle, “ Updated CMB and x- and γ-ray constraints on Majoron dark matter ,” Phys. Rev. D88 (2013) 063528, [ 1303.4685]

2013 arXiv
[37]

The Poker Face of the Majoron Dark Matter Model: LUX to keV Line ,

F. S. Queiroz and K. Sinha, “ The Poker Face of the Majoron Dark Matter Model: LUX to keV Line ,” Phys. Lett. B735 (2014) 69–74, [ 1404.1400]

2014 arXiv
[38]

GlobalU(1)L Breaking in Neutrinophilic 2HDM: From LHC Signatures to X-Ray Line,

W. Wang and Z.-L. Han, “ GlobalU(1)L Breaking in Neutrinophilic 2HDM: From LHC Signatures to X-Ray Line,” Phys. Rev. D94 (2016) 053015, [ 1605.00239]

2016 arXiv
[39]

The QCD axion, precisely ,

G. Grilli di Cortona, E. Hardy, J. Pardo Vega, and G. Villadoro, “The QCD axion, precisely ,” JHEP 01 (2016) 034, [ 1511.02867]

2016 arXiv
[40]

Neutrino Mixing and the Axion-Gluon Vertex ,

A. Latosinski, K. A. Meissner, and H. Nicolai, “Neutrino Mixing and the Axion-Gluon Vertex ,” Nucl. Phys. B868 (2013) 596–626, [ 1203.3886]

2013 arXiv
[41]

( B−L) symmetry vs. neutrino seesaw ,

A. Latosinski, K. A. Meissner, and H. Nicolai, “( B−L) symmetry vs. neutrino seesaw ,” Eur. Phys. J. C73 (2013) 2336, [ 1205.5887]

2013 arXiv
[42]

Axions are blind to anomalies,

J. Quevillon and C. Smith, “ Axions are blind to anomalies,” Eur. Phys. J. C79 no. 10, (2019) 822, [1903.12559]

2019 arXiv
[43]

Baryon nonconservation in standard model and Yukawa interaction,

A. A. Anselm and A. A. Johansen, “ Baryon nonconservation in standard model and Yukawa interaction,” Nucl. Phys. B407 (1993) 313–330

1993
[44]

Can electroweak theta term be observable? ,

A. A. Anselm and A. A. Johansen, “ Can electroweak theta term be observable? ,” Nucl. Phys. B412 (1994) 553–573, [hep-ph/9305271]

1994 arXiv
[45]

The Electroweak Vacuum Angle,

P. Fileviez Perez and H. H. Patel, “ The Electroweak Vacuum Angle,” Phys. Lett. B732 (2014) 241–243, [1402.6340]

2014 arXiv
[46]

FeynRules 2.0 - A complete toolbox for tree-level phenomenology,

A. Alloul, N. D. Christensen, C. Degrande, C. Duhr, and B. Fuks, “FeynRules 2.0 - A complete toolbox for tree-level phenomenology,” Comput. Phys. Commun. 185 (2014) 2250–2300, [ 1310.1921]

2014 arXiv
[47]

Generating Feynman diagrams and amplitudes with FeynArts 3 ,

T. Hahn, “ Generating Feynman diagrams and amplitudes with FeynArts 3 ,” Comput. Phys. Commun. 140 (2001) 418–431, [ hep-ph/0012260]

2001 arXiv
[48]

Problems of the strategy of regions ,

V. A. Smirnov, “ Problems of the strategy of regions ,” Phys. Lett. B465 (1999) 226–234, [ hep-ph/9907471]

1999 arXiv
[49]

One Loop Corrections for e+ e- Annihilation Into mu+ mu- in the Weinberg Model,

G. Passarino and M. J. G. Veltman, “ One Loop Corrections for e+ e- Annihilation Into mu+ mu- in the Weinberg Model,” Nucl. Phys. B160 (1979) 151–207

1979
[50]

Tensor reduction of two loop vacuum diagrams and projectors for expanding three point functions,

A. I. Davydychev and J. B. Tausk, “ Tensor reduction of two loop vacuum diagrams and projectors for expanding three point functions,” Nucl. Phys. B465 (1996) 507–520, [hep-ph/9511261]

1996 arXiv
[51]

ALPs Eﬀective Field Theory and Collider Signatures ,

I. Brivio, M. B. Gavela, L. Merlo, K. Mimasu, J. M. No, R. del Rey, and V. Sanz, “ ALPs Eﬀective Field Theory and Collider Signatures ,” Eur. Phys. J. C77 (2017) 572, [1701.05379]

2017 arXiv
[52]

Conformal Standard Model with an extended scalar sector,

A. Latosinski, A. Lewandowski, K. A. Meissner, and H. Nicolai, “Conformal Standard Model with an extended scalar sector,” JHEP 10 (2015) 170, [1507.01755]

2015 arXiv
[53]

Is Anomaly Transferred thorough Multi-loop Process?,

T. Nakawaki, “ Is Anomaly Transferred thorough Multi-loop Process?,” [1805.12078]

arXiv
[54]

Anomaly-free ﬂavor models for Nambu–Goldstone bosons and the 3.5 keV X-ray line signal ,

K. Nakayama, F. Takahashi, and T. T. Yanagida, “Anomaly-free ﬂavor models for Nambu–Goldstone bosons and the 3.5 keV X-ray line signal ,” Phys. Lett. B734 (2014) 178–182, [ 1403.7390]

2014 arXiv
[55]

Manifesting the Invisible Axion at Low-energies ,

H. Georgi, D. B. Kaplan, and L. Randall, “ Manifesting the Invisible Axion at Low-energies ,” Phys. Lett. 169B (1986) 73–78

1986
[56]

Collider Probes of Axion-Like Particles ,

M. Bauer, M. Neubert, and A. Thamm, “ Collider Probes of Axion-Like Particles ,” JHEP 12 (2017) 044, [1708.00443]

2017 arXiv
[57]

Axion couplings to electroweak gauge bosons ,

G. Alonso- ´Alvarez, M. B. Gavela, and P. Quilez, “ Axion couplings to electroweak gauge bosons ,” Eur. Phys. J. C79 (2019) 223, [ 1811.05466]

2019 arXiv
[58]

The Elusive Axion ,

J.-M. Fr` ere, J. A. M. Vermaseren, and M. B. Gavela, “The Elusive Axion ,” Phys. Lett. 103B (1981) 129–133

1981
[59]

Flavor Changing Higgs Boson Couplings,

L. J. Hall and M. B. Wise, “ Flavor Changing Higgs Boson Couplings,” Nucl. Phys. B187 (1981) 397–408

1981
[60]

Searching for Axionlike Particles in Flavor-Changing Neutral Current Processes,

E. Izaguirre, T. Lin, and B. Shuve, “ Searching for Axionlike Particles in Flavor-Changing Neutral Current Processes,” Phys. Rev. Lett. 118 (2017) 111802, [1611.09355]

2017 arXiv
[61]

Revised constraints and Belle II sensitivity for visible and invisible axion-like particles ,

M. J. Dolan, T. Ferber, C. Hearty, F. Kahlhoefer, and K. Schmidt-Hoberg, “Revised constraints and Belle II sensitivity for visible and invisible axion-like particles ,” JHEP 12 (2017) 094, [ 1709.00009]

2017 arXiv
[62]

Model-independent bounds on light pseudoscalars from rare B-meson decays,

B. D¨ obrich, F. Ertas, F. Kahlhoefer, and T. Spadaro, “Model-independent bounds on light pseudoscalars from rare B-meson decays,” Phys. Lett. B790 (2019) 537–544, [1810.11336]

2019 arXiv
[63]

Flavor constraints on electroweak ALP couplings,

M. B. Gavela, R. Houtz, P. Quilez, R. Del Rey, and O. Sumensari, “Flavor constraints on electroweak ALP couplings,” Eur. Phys. J. C79 (2019) 369, [ 1901.02031]

2019 arXiv
[64]

Minimal ﬂavor violation: An Eﬀective ﬁeld theory approach,

G. D’Ambrosio, G. F. Giudice, G. Isidori, and A. Strumia, “Minimal ﬂavor violation: An Eﬀective ﬁeld theory approach,” Nucl. Phys. B645 (2002) 155–187, [hep-ph/0207036]

2002 arXiv
[65]

Constraining the Axion Portal with B→Kl +l−,

M. Freytsis, Z. Ligeti, and J. Thaler, “ Constraining the Axion Portal with B→Kl +l−,” Phys. Rev. D81 (2010) 034001, [ 0911.5355]

2010 arXiv
[66]

Multi-lepton Signatures of a Hidden Sector in Rare B Decays,

B. Batell, M. Pospelov, and A. Ritz, “ Multi-lepton Signatures of a Hidden Sector in Rare B Decays,” Phys. Rev. D83 (2011) 054005, [ 0911.4938]

2011 arXiv
[67]

Third generation familons, b factories, and neutrino cosmology,

J. L. Feng, T. Moroi, H. Murayama, and E. Schnapka, “Third generation familons, b factories, and neutrino cosmology,” Phys. Rev. D57 (1998) 5875–5892, [hep-ph/9709411]

1998 arXiv
[68]

Majoron emission in muon and tau decays revisited ,

M. Hirsch, A. Vicente, J. Meyer, and W. Porod, “Majoron emission in muon and tau decays revisited ,” Phys. Rev. D79 (2009) 055023, [ 0902.0525]. [Erratum: Phys. Rev. D79, 079901 (2009)]

2009 arXiv
[69]

A Search for lepton ﬂavor violating decays τ→eα, τ→µα,

ARGUS Collaboration Collaboration, H. Albrecht et al., “A Search for lepton ﬂavor violating decays τ→eα, τ→µα,” Z. Phys. C68 (1995) 25–28

1995
[70]

Lepton ﬂavor violation with light vector bosons,

J. Heeck, “ Lepton ﬂavor violation with light vector bosons,” Phys. Lett. B758 (2016) 101–105, [1602.03810]

2016 arXiv
[71]

Lepton Flavor Violation with Displaced Vertices,

J. Heeck and W. Rodejohann, “ Lepton Flavor Violation with Displaced Vertices,” Phys. Lett. B776 (2018) 385–390, [1710.02062]

2018 arXiv
[72]

MC study for the lepton ﬂavor violating tau decay into a lepton and an undetectable particle ,

Belle Collaboration, T. Yoshinobu and K. Hayasaka, “MC study for the lepton ﬂavor violating tau decay into a lepton and an undetectable particle ,” Nucl. Part. Phys. Proc. 287-288 (2017) 218–220

2017
[73]

Search for two body muon decay signals,

TWIST Collaboration, R. Bayes et al., “Search for two body muon decay signals,” Phys. Rev. D91 (2015) 052020, [1409.0638]. 14

2015 arXiv
[74]

The Rare and Forbidden: Testing Physics Beyond the Standard Model with Mu3e,

Mu3e Collaboration, A.-K. Perrevoort, “ The Rare and Forbidden: Testing Physics Beyond the Standard Model with Mu3e,” SciPost Phys. Proc. 1 (2019) 052, [1812.00741]

2019 arXiv
[75]

Light Boson Emission in the Decay of the µ+,

J. T. Goldman, A. Hallin, C. Hoﬀman, L. Piilonen, D. Preston, et al., “Light Boson Emission in the Decay of the µ+,” Phys. Rev. D36 (1987) 1543–1546

1987
[76]

Red giant bound on the axion–electron coupling revisited,

G. Raﬀelt and A. Weiss, “ Red giant bound on the axion–electron coupling revisited,” Phys. Rev. D51 (1995) 1495–1498, [ hep-ph/9410205]

1995 arXiv
[77]

A Fresh look at axions and SN-1987A,

W. Keil, H.-T. Janka, D. N. Schramm, G. Sigl, M. S. Turner, and J. R. Ellis, “ A Fresh look at axions and SN-1987A,” Phys. Rev. D56 (1997) 2419–2432, [astro-ph/9612222]

1997 arXiv
[78]

The Photophobic ALP,

N. Craig, A. Hook, and S. Kasko, “ The Photophobic ALP,” JHEP 09 (2018) 028, [ 1805.06538]

2018 arXiv
[79]

Axion-Like Particles at Future Colliders ,

M. Bauer, M. Heiles, M. Neubert, and A. Thamm, “Axion-Like Particles at Future Colliders ,” Eur. Phys. J. C79 (2019) 74, [ 1808.10323]

2019 arXiv
[80]

Revisiting Supernova 1987A Limits on Axion-Like-Particles,

J. S. Lee, “ Revisiting Supernova 1987A Limits on Axion-Like-Particles,” [1808.10136]

arXiv
[81]

New measurement of the K +→π+ν¯ν branching ratio,

E949 Collaboration, A. V. Artamonov et al., “New measurement of the K +→π+ν¯ν branching ratio,” Phys. Rev. Lett. 101 (2008) 191802, [ 0808.2459]

2008 arXiv
[82]

Further search for the decay K +→π+ν¯ν in the momentum region P <195 MeV/c,

E787 Collaboration, S. Adler et al., “Further search for the decay K +→π+ν¯ν in the momentum region P <195 MeV/c,” Phys. Rev. D70 (2004) 037102, [hep-ex/0403034]

2004 arXiv
[83]

Decay photons from the axionlike particles burst of type II supernovae ,

J. Jaeckel, P. C. Malta, and J. Redondo, “ Decay photons from the axionlike particles burst of type II supernovae ,” Phys. Rev. D98 (2018) 055032, [ 1702.02964]

2018 arXiv
[84]

Dilatons and majorana neutrinos,

W. Buchm¨ uller and D. Wyler, “Dilatons and majorana neutrinos,” Phys. Lett. B249 (1990) 458–462

1990
[85]

Heavy Majorana neutrinos in electron–positron and electron–proton collisions,

W. Buchm¨ uller and C. Greub, “Heavy Majorana neutrinos in electron–positron and electron–proton collisions,” Nucl. Phys. B363 (1991) 345–368

1991
[86]

Right-Handed Neutrinos at CERN LHC and the Mechanism of Neutrino Mass Generation ,

J. Kersten and A. Yu. Smirnov, “ Right-Handed Neutrinos at CERN LHC and the Mechanism of Neutrino Mass Generation ,” Phys. Rev. D76 (2007) 073005, [0705.3221]

2007 arXiv
[87]

Massless Neutrinos in Left-Right Symmetric Models,

D. Wyler and L. Wolfenstein, “ Massless Neutrinos in Left-Right Symmetric Models,” Nucl. Phys. B218 (1983) 205–214

1983
[88]

Neutrino Mass and Baryon Number Nonconservation in Superstring Models,

R. N. Mohapatra and J. W. F. Valle, “ Neutrino Mass and Baryon Number Nonconservation in Superstring Models,” Phys. Rev. D34 (1986) 1642

1986
[89]

Fast Decaying Neutrinos and Observable Flavor Violation in a New Class of Majoron Models ,

M. C. Gonzalez-Garcia and J. W. F. Valle, “ Fast Decaying Neutrinos and Observable Flavor Violation in a New Class of Majoron Models ,” Phys. Lett. B216 (1989) 360–366

1989
[90]

Heavy Majorana neutrinos at ep colliders,

G. Ingelman and J. Rathsman, “ Heavy Majorana neutrinos at ep colliders,” Z. Phys. C60 (1993) 243–254

1993
[91]

Equivalence between massless neutrinos and lepton number conservation in fermionic singlet extensions of the Standard Model,

K. Moﬀat, S. Pascoli, and C. Weiland, “ Equivalence between massless neutrinos and lepton number conservation in fermionic singlet extensions of the Standard Model,” [1712.07611]

arXiv
[92]

A Search for muon to electron conversion in muonic gold ,

SINDRUM II Collaboration, W. H. Bertl et al., “A Search for muon to electron conversion in muonic gold ,” Eur. Phys. J. C47 (2006) 337–346

2006
[93]

Mu2e Conceptual Design Report,

Mu2e Collaboration, R. J. Abrams et al., “Mu2e Conceptual Design Report,” [1211.7019]

arXiv
[94]

COMET Phase-I Technical Design Report,

COMET Collaboration, G. Adamov et al., “COMET Phase-I Technical Design Report,” [1812.09018]

arXiv
[95]

Cold keV dark matter from decays and scatterings,

J. Heeck and D. Teresi, “ Cold keV dark matter from decays and scatterings,” Phys. Rev. D96 (2017) 035018, [1706.09909]

2017 arXiv
[96]

Cold light dark matter in extended seesaw models ,

S. Boulebnane, J. Heeck, A. Nguyen, and D. Teresi, “Cold light dark matter in extended seesaw models ,” JCAP 1804 (2018) 006, [ 1709.07283]

2018 arXiv
[97]

Cosmic neutrino background search experiments as decaying dark matter detectors ,

D. McKeen, “ Cosmic neutrino background search experiments as decaying dark matter detectors ,” Phys. Rev. D100 (2019) 015028, [ 1812.08178]

2019 arXiv

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [1]

Baryon and Lepton Nonconserving Processes,

S. Weinberg, “ Baryon and Lepton Nonconserving Processes,” Phys. Rev. Lett. 43 (1979) 1566–1570

1979

[2] [2]

≡− 1 2 ¯nc RMnnR + h.c., (2) whereV is the unitary 6× 6 mixing matrix to the states nR, which form the Majorana mass eigenstates n =nR + nc R

The full 6 × 6 neutrino mass matrix in the basis ( νc L,NR) = VnR is then L =−1 2 ¯nc RVT ( 0 MD MT D MR ) VnR + h.c. ≡− 1 2 ¯nc RMnnR + h.c., (2) whereV is the unitary 6× 6 mixing matrix to the states nR, which form the Majorana mass eigenstates n =nR + nc R. The diagonal mass matrix Mn = diag(m1,...,m 6) consists of the physical neutrino masses arranged...

[3] [3]

standard

As already noted in Ref. [17], the non-Majoron limits are completely dominated by ﬂavor- conserving observ- ables such as Z → e+e− and other electroweak preci- sion data. LFV such as τ → eγ and τ → eee reside far in the already excluded region and even future im- provements, e.g. in Belle-II, do not reach the allowed pa- rameter space. In comparison, Majo...

[4] [4]

µ→eγ at a rate of one out of 109 muon decays?,

P. Minkowski, “µ→eγ at a rate of one out of 109 muon decays?,” Phys. Lett. B67 (1977) 421–428

1977

[5] [5]

Are There Real Goldstone Bosons Associated with Broken Lepton Number?,

Y. Chikashige, R. N. Mohapatra, and R. D. Peccei, “ Are There Real Goldstone Bosons Associated with Broken Lepton Number?,” Phys. Lett. B98 (1981) 265–268

1981

[6] [6]

Neutrino Decay and Spontaneous Violation of Lepton Number ,

J. Schechter and J. W. F. Valle, “ Neutrino Decay and Spontaneous Violation of Lepton Number ,” Phys. Rev. D25 (1982) 774

1982

[7] [7]

The Superlight Axion and Neutrino Masses ,

R. N. Mohapatra and G. Senjanovic, “ The Superlight Axion and Neutrino Masses ,” Z. Phys. C17 (1983) 53–56

1983

[8] [8]

Invisible Axions and Light Neutrinos: Are They Connected? ,

P. Langacker, R. D. Peccei, and T. Yanagida, “ Invisible Axions and Light Neutrinos: Are They Connected? ,” Mod. Phys. Lett. A01 (1986) 541

1986