The QCD Axion and Neutrino Masses

Grace Miller; Hridoy Debnath; Pavel Fileviez Perez

REVIEW 4 major objections 4 minor 72 references

The QCD Axion and Neutrino Masses

T0 review · 4 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read By tying the axion scale to the seesaw scale, this paper derives a generic axion–neutrino coupling and a dark-matter decay line that future neutrino experiments can chase.

desk verdict A useful survey of axion–seesaw models whose DFSZ part is probably sound, but the KSVZ colored-seesaw construction is internally inconsistent and the headline monochromatic-neutrino-flux predictions rest on an asserted, underived coupling. read the letter →

arxiv 2608.05150 v1 pith:L246FFEI submitted 2026-08-05 hep-ph hep-ex

Hridoy Debnath , Pavel Fileviez Perez , Grace Miller This is my paper

classification hep-phhep-ex

keywords QCDaxionPQsymmetryneutrinomassesseesawmechanismsaxion-neutrinocouplingdarkmatterdecaymonochromaticfluxanomalyratioE/N

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

This paper tries to establish that when the same symmetry-breaking scale that gives the QCD axion its mass also sets neutrino masses, the axion inevitably couples to neutrinos. Working through two standard axion constructions (DFSZ and KSVZ) and five neutrino-mass mechanisms (Type-I, Type-II, and Type-III seesaw, the Zee radiative model, and the colored seesaw), it derives the axion–photon and axion–neutrino couplings for each case. The generic consequence is that sufficiently heavy axions can decay into neutrino pairs, and if the axion is dark matter, those decays produce a monochromatic neutrino line at half the axion mass that can rise above the cosmic and solar neutrino backgrounds. A sympathetic reader would care because this gives neutrino experiments a concrete, testable target that connects two independent gaps in the Standard Model.

What carries the argument

The load-bearing object is the axion–neutrino derivative coupling $\mathcal{L}\supset -c_\nu \frac{\partial_\mu a}{4 v_s}\bar\nu\gamma^\mu\gamma^5\nu$, with coefficient $c_\nu$ set to one for KSVZ-type models and to a function of $\tan\beta$ for DFSZ models. It is this coupling that opens the $a\to\nu\nu$ decay channel and generates the dark-matter decay line. The second piece of machinery is the pair of anomaly coefficients $E$ and $N$, integers that fix the axion–photon coupling through $g_{a\gamma\gamma}=\frac{\alpha_{\rm em}}{2\pi f_a}(E/N-1.92)$; model-by-model values of $E/N$ are what separate the scenarios. In the colored seesaw, the heavy color-octet scalars and fermions that create the QCD anomaly are the same fields that generate radiative Majorana neutrino masses, which is why the axion decay constant and the seesaw scale are identified.

What would settle it

Compute the one-loop contribution to the axion–neutrino coupling in the colored-seesaw model from the heavy color-octet fermion and scalar loops; a coefficient significantly below one would scale the line flux down quadratically and erase the predicted separation from the solar and cosmic neutrino backgrounds. Observationally, a neutrino telescope with enough exposure to detect a monoenergetic line at $E=m_a/2$ in the mass range where the dineutrino branching ratio exceeds the diphoton one would confirm or exclude the framework.

Watch

Extended reading notes

Core claim

The paper's central claim is that in any of these unified models the axion has a derivative coupling to neutrinos of the form $\mathcal{L}\supset -c_\nu \frac{\partial_\mu a}{4 v_s}\bar\nu\gamma^\mu\gamma^5\nu$, so its partial width into a neutrino pair is $\Gamma(a\to\nu_i\nu_i)=\frac{m_a}{16\pi}\left|\frac{c_\nu m_{\nu_i}}{N f_a}\right|^2\sqrt{1-4m_{\nu_i}^2/m_a^2}$. Because the coupling is proportional to the physical neutrino mass divided by the PQ scale, the decay rate grows once the axion mass exceeds twice a neutrino mass, and the dineutrino branching ratio can overtake the diphoton channel. The paper also shows that the anomaly ratio $E/N$, which fixes the axion–photon coupling, is unchanged for Type-I, Type-II, and Zee variants in DFSZ, but shifted by the new fermions in Type-III seesaw, and takes distinct values in the two colored-seesaw realizations, separating the models in the $g_{a\gamma\gamma}$–$m_a$ plane. Assuming the QCD axion is the dark matter, the resulting neutrino line at $E=m_a/2$ is large enough to lie above the Cosmic Neutrino Background and the solar thermal neutrino flux over a wide energy range.

Load-bearing premise

In the KSVZ and colored-seesaw cases, the paper takes the axion–neutrino coupling coefficient $c_\nu$ to be exactly one even though the Standard Model fermions carry no PQ charge and the coupling would have to be generated radiatively; if that coefficient is actually smaller, every decay width and flux prediction shrinks.

Editorial extensions

If this is right

If the central claim is right, every model in this class predicts axion decay into neutrino pairs once $m_a>2m_{\nu_i}$, with branching fractions that can exceed the diphoton channel for the heaviest neutrino mass eigenstate.
If the QCD axion is dark matter, the decay line at $E=m_a/2$ sits above both the Cosmic Neutrino Background and the solar thermal neutrino flux over a wide energy range, so future neutrino detectors can test the framework.
Precision measurements of the axion–photon coupling could distinguish Type-III seesaw from Type-I and Type-II and Zee variants in DFSZ, and distinguish the colored-seesaw realizations from standard KSVZ models.
Over most of the allowed parameter space the axion lifetime remains longer than the age of the Universe, so the axion stays a viable dark matter candidate even with the new decay channel.

Reading between the lines

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

If the axion–neutrino coupling is as large as the paper assumes, then in the mass region where $a\to\nu\nu$ dominates the axion is not a stable dark matter candidate, so its lifetime must also be checked against cosmic gamma-ray and neutrino bounds, a constraint the paper only partially explores.
The same coupling ties the decay line to the neutrino mass ordering: normal versus inverted ordering changes which mass eigenstate dominates the line, so a measured line energy could be cross-checked against oscillation data.
A natural next calculation is the one-loop correction to $c_\nu$ in KSVZ and colored-seesaw models; if that correction suppresses $c_\nu$ below $O(1)$, the flux predictions scale down quadratically and the claimed background separation weakens.

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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 paper is best read as a systematic map: five neutrino-mass mechanisms in both DFSZ and KSVZ frameworks, with E/N values and axion–photon coupling plots. That part is genuinely useful. The Type-III DFSZ shift to E/N = 11/3 or 5/3 is a new, checkable result, and the tables separating KSVZ I/II/III from the colored-seesaw cases will help people navigate the parameter space. The figures are clear and the literature is cited fairly, including the prior work on the scale identification.

The soft spots are not minor. The KSVZ colored-seesaw model, which drives Figs. 5–9 and the central "large monochromatic flux" claim, is internally inconsistent as written. Under the paper's own KSVZ condition that SM fermions are PQ-neutral, the quark Yukawas force q(H) = 0. The colored-seesaw term λ/2 Tr(Φ†H)² then forces q(Φ) = 0; the neutrino Yukawa forces q(ρ_L) = 0; and the λρ Tr(ρ_L^T C ρ_L) S term forces q(S) = 0. So there is no U(1)_PQ with q(S) ≠ 0, and the axion decay constant cannot be identified with v_S in this model. The statement after Eq. (21) that c_ν = 1 for KSVZ is therefore not a derived result, and Eq. (18) literally contains a placeholder for the loop function. The flux formula in Eq. (24) also has an unexplained factor of 1/3. I did not try to adjudicate that normalization, but the reader is right that it needs justification.

The DFSZ sections and the E/N tables are likely correct, and the Type-III DFSZ shift is a legitimate extension. But the paper's headline prediction—that axion decays into neutrinos produce a detectable line—is carried by the same KSVZ construction that does not hold together. If the authors cannot find a consistent PQ charge assignment (say, by relaxing the pure-KSVZ condition and recomputing E/N and c_ν), the colored-seesaw predictions should be removed or substantially revised.

This deserves a serious referee: the survey is useful, the anomaly computations are standard, and the flaw is precisely the kind a careful referee should catch. I would not cite the KSVZ flux predictions in their current form, and I would bring the paper to reading group mainly as a case study in checking charge assignments. Send it to peer review, but with the expectation of heavy revision.

For the record, the stress-test note holds up on reading; I could not find a way around it.

Referee Report

4 major / 4 minor

Summary. The manuscript explores the possibility that the Peccei-Quinn symmetry-breaking scale is also the scale responsible for neutrino mass generation, analyzing DFSZ and KSVZ realizations with Type-I, Type-II, Type-III seesaw, Zee, and colored seesaw mechanisms. For each scenario it computes anomaly ratios E/N, derives axion couplings to photons and neutrinos, and studies axion decays and the resulting monochromatic neutrino flux, claiming a robust axion-neutrino coupling in all frameworks.

Significance. If correct, the paper would provide a useful unified survey of axion-photon coupling predictions in connected PQ/neutrino-mass models and would sharpen the phenomenology of axion dark matter decays into neutrino lines, with clear experimental targets such as JWST, ADMX, and future neutrino detectors. The paper correctly identifies that Type-III DFSZ and colored seesaw KSVZ shift E/N relative to minimal models and organizes the predictions in tables that are easy to use. However, the KSVZ colored seesaw construction is internally inconsistent as written, and the central c_nu=1 assignment for KSVZ is asserted without derivation, so the claimed robustness of axion-neutrino couplings does not currently hold for the KSVZ sector.

major comments (4)

[Sec. 4.A, Eq. (17) vs. Sec. 2] The colored seesaw model as written is inconsistent with the KSVZ condition stated in Section 2 that the SM fermions remain neutral under U(1)_PQ. Since the SM lepton doublet l_L and the Higgs doublet H have q=0, the term (lambda/2) Tr(Phi^dag H)^2 forces q(Phi)=0; the Yukawa term Y_nu l^T C i sigma2 Phi rho_L then forces q(rho_L)=0; and the Majorana term lambda_rho Tr(rho^T C rho) S forces q(S)=0. This contradicts the PQ-breaking role of S and Eq. (19). Consequently, the E/N values for Colored Seesaw I and II in Table II and all the predictions in Figures 5-9 based on them are not defined in a consistent model. The authors must either assign nonzero PQ charges to the new fermions (which would make the construction a DFSZ-like or mixed model and require a recomputation of E/N and c_nu) or modify the field content so that q(S) != 0 is allowed.
[After Eq. (21)] The statement that the coefficient c_nu is one for the KSVZ models is asserted without derivation. In a genuine KSVZ model the SM fermions are PQ-neutral, so the axion-neutrino coupling cannot be a tree-level derivative coupling of the form of Eq. (21); in the colored seesaw it would arise radiatively, and its normalization and flavor structure would need to be computed from the UV theory. Because Gamma(a->nu_i nu_i) is proportional to c_nu^2 and the flux scales with this width, the quantitative decay and flux predictions in Eqs. (22)-(24) and Figures 5-9 depend entirely on this coefficient. A derivation, or at minimum an explicit statement that c_nu is an assumed benchmark parameter whose value is not predicted by the model, is required before these predictions can be presented as results of the framework.
[Eq. (18)] The loop function I(M_rho_k, M_Phi) in Eq. (18) is left as a literal "[?]" placeholder, and no closed form or reference is provided. Since the same loop is expected to mediate the axion-neutrino coupling in the KSVZ colored seesaw, the manuscript does not actually compute the coupling it claims to be robust; it only parameterizes it with c_nu. The absence of this integral means that the decay and flux results in Section 5 are not derived from the described model but assumed.
[Sec. 4, KSVZ I/II/III with Type-I seesaw] The KSVZ I, II, and III models, for which the text says "we assume Type I seesaw", face the same SM-neutrality obstruction as the colored seesaw. With q(l_L)=q(H)=0 from the KSVZ condition, the Type-I seesaw Yukawa term Y_nu l H nu_R forces q(nu_R)=0, and the Majorana mass term lambda_R nu_R^T C nu_R S then forces q(S)=0. Thus the PQ singlet S cannot both generate the right-handed neutrino mass and break the PQ symmetry in these models without additional structure. The paper's central claim that axion-neutrino couplings are a robust prediction of all frameworks considered is therefore unsupported for the entire KSVZ sector as written.

minor comments (4)

[Eq. (24)] The factor 1/3 in Eq. (24) is unexplained. With dN/dE = 2 delta(E - m_a/2) from Eq. (25), a per-flavor flux from a two-body decay into a specific mass eigenstate should be (1/(4 pi m_a tau_a)) * 2 delta(E - m_a/2) * D, without an additional 1/3; if the authors intend flavor averaging, that should be stated and the factor justified. The normalization directly affects Figures 8 and 9.
[General presentation] The manuscript contains several typos, including "thestrong CP-problemandtheorigin" in the Introduction, "helps us to to find" in Section 3, and "Figs. 5 and 6 shows" in Section 5. Reference [42] appears to duplicate reference [34].
[Eqs. (21) and (23)] The relation between the normalization v_S in Eq. (21) and f_a in Eq. (23) is not stated; with v_S = N f_a from Eq. (19), the effective coupling in Eq. (23) differs by a factor of 2 from a naive reading of Eq. (21). This should be clarified to allow the reader to verify the decay widths.
[Fig. 9] The caption and legend of Fig. 9 do not specify whether the plotted flux is summed over neutrino flavors or shown per flavor. Given Eq. (24), this should be stated explicitly, especially since the 1/3 factor in Eq. (24) is ambiguous.

Circularity Check

0 steps flagged · score 2.0 of 10

No circular derivation chain: anomaly coefficients and decay/flux curves are computed from stated charge assignments and standard kinematics. The main gap is an underived c_nu=1 input, and a possible PQ charge contradiction in the colored-seesaw KSVZ case, which are support/correctness issues rather than circular fits.

full rationale

No parameter is fitted to make the predicted signal appear. The E/N values in Tables I and II are obtained directly from the PQ charge assignments and gauge representations: Type-III triplets and KSVZ colored fermions contribute to the anomaly, while singlets and scalars do not, and the g_aγγ curves in Figs. 1 and 3 are just Eq. (6) evaluated with those coefficients. The neutrino-flux predictions use Eq. (23) with neutrino masses from oscillation data and a scanned axion mass; the D-factor in Eq. (26) is the standard halo integral. There is no step in which a fitted parameter is renamed as a prediction. The only self-citation relevant to the derivation is Ref. [25] for the colored-seesaw Lagrangian; that construction is reproduced explicitly in Eq. (17) and its anomaly coefficients are recomputed here, so the citation is not load-bearing in the circularity sense. What the paper does not supply is a derivation of c_nu=1 for KSVZ just after Eq. (21): the text first asserts it as a value, and the Fig. 4 caption later calls it an illustrative assumption. The colored-seesaw loop function in Eq. (18) is also left as '[?]'. Moreover, if one imposes the paper's own KSVZ condition that SM fermions are neutral, gauge invariance of the quark Yukawas forces q(H)=0, the (lambda/2) Tr(Phi^dagger H)^2 term forces q(Phi)=0, the neutrino Yukawa forces q(rho)=0, and lambda_rho Tr(rho^T C rho) S forces q(S)=0, which would eliminate a nontrivial PQ symmetry and the QCD axion from the colored-seesaw model. These are important gaps in the support of the central claim, and they should be addressed, but they are not cases where the derived prediction reduces to its own input; the anomaly-coefficient analysis for the DFSZ and minimal-KSVZ frameworks is self-contained. For that reason the circularity score is low.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central claim rests on the assumed identification of the PQ scale with the seesaw scale and on an unproven normalization of the axion-neutrino coupling. Neutrino masses are inputs from oscillation data rather than fitted outputs. No novel entities are introduced.

free parameters (3)

Axion-neutrino coupling coefficient c_nu = 1 (assumed)
Eq. (21) sets c_nu = 1 for KSVZ and a tan(beta)-dependent value for DFSZ, but no derivation is given for the KSVZ value. This coefficient directly scales the decay width in Eq. (23) and the flux in Figs. 8-9.
Benchmark light neutrino masses (normal ordering) = m1 = 0, m2 ~ 8.6e-3 eV, m3 ~ 0.05 eV
Input from oscillation data used to render Figs. 5-7; not fitted here. The heaviest mass sets the axion-neutrino coupling scale in Fig. 4.
Benchmark light neutrino masses (inverted ordering) = m3 = 0, m1 ~ 0.0492 eV, m2 ~ 0.05 eV
Used for the inverted-ordering branching-ratio plots; taken from oscillation data, not derived in the paper.

assumptions (4)

domain assumption The PQ symmetry-breaking scale equals the neutrino-mass seesaw scale, with M_seesaw ~ v_S ~ f_a (Eq. 9 and Eq. 19).
The premise that one scalar singlet sets both the axion decay constant and the heavy neutrino mass scale. It is the paper's organizing assumption and is not derived from a more fundamental theory.
standard math Standard axion effective couplings to gluons and photons, Eqs. (3)-(6), including the chiral-lagrangian relation between ma and fa.
Taken from the QCD axion literature; accepted background for the computations.
domain assumption Colored-seesaw one-loop neutrino mass formula, Eq. (18), including the loop function I(M_rho, M_Phi).
The model from Ref. [25], authored by a coauthor, is assumed. The loop function is left as an unresolved placeholder in the text.
ad hoc to paper The axion derivative coupling to neutrinos has the form of Eq. (21) with coefficient c_nu.
This form is asserted rather than derived, especially for KSVZ where SM fermions are PQ-neutral. It is the main input to the decay and flux predictions.

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Cite this review

Pith. "Pith review of The QCD Axion and Neutrino Masses." pith.science (2026). https://pith.science/paper/L246FFEI

@misc{pith2026260805150,
  author       = {Pith},
  title        = {Pith review of: The QCD Axion and Neutrino Masses},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/L246FFEI}},
  note         = {Machine review of arXiv:2608.05150}
}

read the original abstract

The strong CP problem and the origin of neutrino masses are among the clearest motivations for physics beyond the Standard Model. The Peccei-Quinn mechanism offers an elegant dynamical solution to the strong CP problem, predicting the QCD axion, while neutrino masses point to new degrees of freedom or interactions beyond the Standard Model. We explore the possibility that these two phenomena arise from a common origin by identifying the Peccei-Quinn symmetry-breaking scale with the scale responsible for neutrino mass generation. We perform a systematic and unified analysis of this connection in both DFSZ and KSVZ realizations of the Peccei-Quinn mechanism, considering the Type-I, Type-II, and Type-III seesaw mechanisms, the Zee radiative model, and the colored seesaw. For each scenario, we determine the axion couplings to photons and neutrinos and examine their phenomenological consequences. A robust prediction of all the frameworks considered is the existence of axion-neutrino couplings. We show that these interactions can significantly affect the axion decays. If the QCD axion makes up the observed dark matter, these couplings also lead to a large monochromatic neutrino flux from axion decays, opening a complementary path to test these theories in future neutrino experiments.

Figures

Figures reproduced from arXiv: 2608.05150 by the authors.

**Figure 2.** FIG. 2: Colored seesaw mechanism [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 4.** FIG. 4: Axion neutrino coupling as a function of axion mass [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗

Figures from the paper (4 more)

**Figure 5.** Figure 5: FIG. 5: Branching ratios of axion decays as a function of [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]

**Figure 7.** Figure 7: FIG. 7: Axion lifetime as a function of axion mass assuming [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]

**Figure 8.** Figure 8: FIG. 8: Differential neutrino energy spectrum from the [PITH_FULL_IMAGE:figures/full_fig_p009_8.png]

**Figure 9.** Figure 9: FIG. 9: Differential neutrino flux from axion dark matter as a function of the neutrino energy, [PITH_FULL_IMAGE:figures/full_fig_p010_9.png]

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INTRODUCTION The Standard Model (SM) of particle physics stands as one of the most successful theoretical frame- works ever constructed, describing the fundamental con- stituents of matter and their interactions with extraor- dinary precision. Yet, despite its remarkable achieve- ments, it leaves two of the most profound questions in contemporary particle...

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DFSZ MECHANISMS The DFSZ framework provides one of the most economical realizations of the PQ mechanism. Unlike KSVZ models, where the QCD anomaly is generated by heavy vector-like colored fermions, the DFSZ construc- FIG. 1: Axion photon coupling as a function of axion mass for the DFSZ scenarios. The teal shaded region indicates the bounds from globular...

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Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

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INTRODUCTION The Standard Model (SM) of particle physics stands as one of the most successful theoretical frame- works ever constructed, describing the fundamental con- stituents of matter and their interactions with extraor- dinary precision. Yet, despite its remarkable achieve- ments, it leaves two of the most profound questions in contemporary particle...

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Notice that the quark mass matrices are related to the observed CP-violation in the quark sector given by the Cabibbo-Kobayaski-Maskawa matrix,V CKM

THE QCD AXION The SM allows for a renormalizable CP-violating interaction in QCD, Lθ =θ g2 s 32π2 Ga µν ˜Gaµν,(1) whereG a µν is the gluon field-strength tensor and˜Gaµν = 1 2 ϵµναβ Ga αβ.After taking into account the phases appear- ing in the quark mass matrices, the physical parameter controlling strong CP violation is given by ¯θ=θ+ arg det(M u) + arg ...

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Unlike KSVZ models, where the QCD anomaly is generated by heavy vector-like colored fermions, the DFSZ construc- FIG

DFSZ MECHANISMS The DFSZ framework provides one of the most economical realizations of the PQ mechanism. Unlike KSVZ models, where the QCD anomaly is generated by heavy vector-like colored fermions, the DFSZ construc- FIG. 1: Axion photon coupling as a function of axion mass for the DFSZ scenarios. The teal shaded region indicates the bounds from globular...

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In contrast to DFSZ models, the SM fermions are neutral under the globalU(1) PQ symmetry

KSVZ MECHANISMS The KSVZ mechanism provides an alternative re- alization of the Peccei–Quinn mechanism. In contrast to DFSZ models, the SM fermions are neutral under the globalU(1) PQ symmetry. Instead, the QCD anomaly responsible for solving the strong CP problem is gen- erated by heavy vector-like colored fermions. After the spontaneous breaking of the ...

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This coupling reads as −L ⊃cν ∂µa 4vs ¯νγµγ5ν.(21) Here the coefficientcν is one for the KSVZ models, while for the DFSZ models it is function oftanβ=vu/vd

NEUTRINOS FROM THE QCD AXION AcommonfeatureofthesemodelsisthattheQCD axion has a coupling to SM neutrinos. This coupling reads as −L ⊃cν ∂µa 4vs ¯νγµγ5ν.(21) Here the coefficientcν is one for the KSVZ models, while for the DFSZ models it is function oftanβ=vu/vd. Fig. 4 shows the predicted axion–neutrino cou- pling,g aνν for the heaviest neutrino, as a fu...

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SUMMAR Y In this work, we presented a unified study of the- oretical frameworks in which the solution to the strong CP problem, the origin of neutrino masses, and the na- ture of dark matter are all connected through a common symmetry-breaking scale. The central idea is that the spontaneous breaking of the PQ symmetry not only gives 10 rise to the QCD axi...

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