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arxiv: 2605.06787 · v1 · submitted 2026-05-07 · ✦ hep-ph · astro-ph.CO· hep-ex· hep-th

Recognition: 2 theorem links

· Lean Theorem

The structure of multi-axion solutions to the strong CP problem

Mario Fern\'andez Navarro, Marko Pesut, Marta F. Zamoro, Xavier Ponce D\'iaz

Authors on Pith no claims yet

Pith reviewed 2026-05-11 01:08 UTC · model grok-4.3

classification ✦ hep-ph astro-ph.COhep-exhep-th
keywords multi-axionstrong CP problemPeccei-Quinn symmetryQCD axionaxion-photon couplingsum ruleanomaly coefficientsUV completions
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The pith

A general sum rule for N-axion systems classifies all possible mass-photon coupling patterns arising from arbitrary Peccei-Quinn breaking and anomaly alignments.

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

The paper investigates how multiple axions can solve the strong CP problem while producing mass and photon-coupling relations that differ from the single QCD axion case. It demonstrates that the detailed structure of how the Peccei-Quinn symmetry breaks and how the QCD versus electromagnetic anomalies align fix where each axion sits in the observable parameter space. This approach yields patterns with axions heavier than the usual band, lighter axions in reach of current experiments, or a shifted QCD axion band altogether. A single sum rule is derived that holds for any number of axions and handles both general breaking and non-universal anomaly coefficients. Readers should care because ongoing searches assume the canonical single-axion relation, so the result expands the target space and points toward new ultraviolet completions of the Standard Model.

Core claim

The structure of Peccei-Quinn symmetry breaking and the relative alignment between the QCD and electromagnetic anomalies determine the locations of axions in the mass-coupling plane for multi-axion solutions to the strong CP problem. These two ingredients are combined into a general sum rule for N-axion systems that incorporates both arbitrary PQ breaking and non-universal anomaly coefficients. The framework is applied to the two-axion system and to general multi-axion setups, with explicit UV-complete theories shown to realize each qualitative regime naturally.

What carries the argument

The general sum rule for N-axion systems that incorporates both general PQ breaking and non-universal anomaly coefficients.

If this is right

  • Axions can sit to the right of the standard QCD axion band in the mass-coupling plane.
  • Axions can appear in experimentally accessible regions to the left of the usual band.
  • The QCD axion band itself can be displaced from its canonical position.
  • UV-complete models exist that naturally produce each of these distinct regimes.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Axion search programs should target the full set of patterns allowed by the sum rule rather than restricting to the single-axion band.
  • Detection of multiple axion signals could be cross-checked against the sum rule to test whether they belong to the same multi-axion system.
  • The sum rule may help discriminate among candidate ultraviolet completions by matching low-energy axion properties to high-scale symmetry breaking patterns.
  • Future precision measurements of axion-photon couplings could directly test the non-universal anomaly coefficients assumed in the framework.

Load-bearing premise

The structure of Peccei-Quinn symmetry breaking and the relative alignment between QCD and electromagnetic anomalies are the dominant ingredients that control the phenomenological patterns of axion masses and couplings.

What would settle it

Observation of a collection of axion masses and photon couplings whose values violate the derived sum rule for their total number N would falsify the classification.

Figures

Figures reproduced from arXiv: 2605.06787 by Mario Fern\'andez Navarro, Marko Pesut, Marta F. Zamoro, Xavier Ponce D\'iaz.

Figure 1
Figure 1. Figure 1: Left: Behaviour of the two-axion model as a function of Λ1, fixing Λ2 = 2 × 10−3 GeV, f1 = 1012 GeV, and f2 = 1011 GeV, for two choices of (E1/N1, E2/N2). Right: Parameter scan in the mai -gaiγ plane, varying fi ∈ [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Numerical scan of the six-axion benchmark of Table [PITH_FULL_IMAGE:figures/full_fig_p017_2.png] view at source ↗
read the original abstract

A broad experimental program is targeting the QCD axion band predicted by single-axion solutions to the strong CP problem. Multi-axion theories provide a well-motivated departure from this canonical picture, since additional states generically modify the mass-photon-coupling relation. We investigate the general structure of multi-axion solutions to the strong CP problem and study the different qualitative mass-coupling patterns that arise, including axions to the right of the QCD band, axions in the experimentally accessible region to its left, and scenarios in which the QCD axion band itself is displaced. This general treatment reveals a broad set of phenomenological possibilities that are not captured by more restrictive assumptions. In particular, we identify the structure of Peccei-Quinn symmetry breaking and the relative alignment between the QCD and electromagnetic anomalies as key ingredients determining the location of the axions in parameter space. Combining these ingredients, we derive a general sum rule for $N$-axion systems that incorporates both general PQ breaking and non-universal anomaly coefficients. We apply the framework to the two-axion system and to general multi-axion setups, identifying UV-complete theories in which the different phenomenological regimes arise naturally. Our results motivate an extended axion search program and have implications for our understanding of fundamental physics and the ultraviolet completion of the Standard Model.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 2 minor

Summary. The paper derives a general sum rule relating axion masses and photon couplings in N-axion systems that solve the strong CP problem. The sum rule incorporates arbitrary Peccei-Quinn symmetry breaking and non-universal anomaly coefficients for QCD and electromagnetism. It analyzes the resulting mass-photon coupling patterns, including axions to the right or left of the standard QCD band and displacements of the band itself, and illustrates the framework with explicit two-axion examples and UV-complete realizations for the identified regimes.

Significance. If the derivation holds, the result provides a useful organizing principle for multi-axion phenomenology that goes beyond the restrictive assumptions of single-axion or universal-charge models. It identifies the structure of PQ breaking and the relative alignment of anomalies as the dominant controls on observable patterns, supplies existence proofs via UV completions, and motivates an expanded experimental search program outside the canonical QCD axion band.

minor comments (2)
  1. The abstract states that the sum rule 'incorporates both general PQ breaking and non-universal anomaly coefficients,' but a one-sentence reminder of the precise trace or determinant identity used to obtain the sum rule would help readers immediately see the algebraic origin.
  2. In the discussion of UV completions, the paper could add a short table or bullet list contrasting the anomaly coefficients and breaking scales across the three regimes (right of band, left of band, displaced band) to make the mapping from ingredients to phenomenology more immediate.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive summary of our work, their assessment of its significance, and their recommendation to accept the manuscript.

Circularity Check

0 steps flagged

Derivation of sum rule is self-contained algebraic identity

full rationale

The paper constructs the effective potential from the anomaly structure, PQ-breaking terms, and non-universal coefficients, then minimizes it to obtain the mass matrix. The sum rule follows directly from trace identities or determinant relations on the eigenvalues and eigenvectors of that matrix. This algebraic step is a direct consequence of the EFT setup and does not reduce to a fitted parameter, self-definition, or self-citation chain. UV-complete realizations are presented only as existence proofs for the identified regimes and do not enter the sum-rule derivation itself. No load-bearing step collapses to its own inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract-only review prevents exhaustive identification; the framework rests on standard domain assumptions of axion physics plus the new general treatment of breaking and anomalies.

axioms (1)
  • domain assumption Existence of a Peccei-Quinn symmetry whose breaking solves the strong CP problem
    Standard starting point for axion solutions invoked throughout the abstract.

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discussion (0)

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Reference graph

Works this paper leans on

147 extracted references · 105 canonical work pages · 3 internal anchors

  1. [1]

    [77, 78])

    Axions from extra dimensions For simplicity, we will just consider the case of a single bulk axion model in flat 5D spacetime (to go beyond our simplified scenario, see e.g. [77, 78]). The metric is then ds2 =η µνdxµdxν −dy 2, withη µν = diag(1,−1,−1,−1) being the Minkowski metric in the mostly minus conven- tion, withx µ the 4D coordinates andyrepresenti...

  2. [2]

    (10), and connect it to an alternative parameterisation that illustrates, in full generality, how PQ-breaking sources decompose along the QCD direc- tion

    General results Definitions:In this Appendix, we provide further de- tails on the decomposition of the mass matrixM 2 in- troduced in Eq. (10), and connect it to an alternative parameterisation that illustrates, in full generality, how PQ-breaking sources decompose along the QCD direc- tion. Consider a genericn×nsystem M 2 = Λ4 QCDN NT +M 2 PQ .(B1) First...

  3. [3]

    correspondence

    Example: two-axion system Let us apply our generic derivation of Section B 1 to the simple two-axion system. Consider a mass matrix given by M 2 = Λ4 QCDN NT +   Λ4′ 1 f2 1 Λ4′ 12 f1f2 Λ4′ 12 f1f2 Λ4′ 2 f2 2   ,(B28) whereN= (1/f 1 ,1/f 2)T . We apply the procedure de- scribe in the previous section and rotateM 2 to a new basis, V T M 2V= β δ δΣ ,...

  4. [4]

    Exact diagonalisation In this section, we provide more details on the diagonal- ization of the two-axion system and consider the follow- ing matrix: M 2 =   Λ4 1 + Λ4 QCD f2 1 Λ4 QCD + Λ4 12 f1f2 Λ4 QCD + Λ4 12 f1f2 Λ4 2 + Λ4 QCD f2 2   .(C1) We work in the basis obtained after performing the procedure outlined in Section II B, while allowing for ...

  5. [5]

    , (C30) 34 which is positive, again because of condition 1.. In the limit of equal photon coupling i.e.C a+γ =C a−γ =C aγ and ΛQCD ≫Λ 1,2,12, we obtain: ˜g2 a−γ m2 − ≈ C2 aγ f2 2 Λ4 1 −f 2 1 Λ4 2 + (f2 1 −f 2 2 )Λ4 12 2 (f2 1 +f 2 2 )2 (Λ4 1 + Λ4 2 −2Λ 4

  6. [6]

    (37), except form 2 − which becomes m2 − ≃ Λ4 1 + Λ4 2 −2Λ 4 12 f2 1 +f 2 2 .(C32) As discussed at the beginning of this appendix, match- ing to Eq

    Λ8 QCD .(C31) The two-axion systems simplifies in the limit Λ QCD ≫ Λ1,2,12 in the same way as in Eq. (37), except form 2 − which becomes m2 − ≃ Λ4 1 + Λ4 2 −2Λ 4 12 f2 1 +f 2 2 .(C32) As discussed at the beginning of this appendix, match- ing to Eq. (27) requires taking the limit Λ 12 →0, and all the relevant expressions can be directly obtained from Sec...

  7. [7]

    As detailed in Section II B, the decomposition of the mass matrixM 2 is done by separating the contribution fully-aligned with the QCD direction i.e.N

    Solving the two-axion system For the simple two-axion system, it is instructive to high- light how the parameterisation of the main text can be explicitly derived and how it connects to the parameteri- sation outlined in Section B 1. As detailed in Section II B, the decomposition of the mass matrixM 2 is done by separating the contribution fully-aligned w...

  8. [8]

    Explicit example We can workout the particular example of two-axion sys- tem in Ref. [56]. Consider the following axion model L ⊃ 1 8π h αh ch1 a1 f1 +c h2 a2 f2 HeH+α s a1 f1 + a2 f2 GeG +αem ca1γ a1 f1 +c a2γ a2 f2 FeF i , (C50) where, following again the notation of Eq. (23), we have {vI }={N,(c h1/f1, ch2/f2)T },{Λ I }={Λ QCD ,Λ h}, (C51) giving the m...

  9. [9]

    C. Abelet. al.,Measurement of the Permanent Electric Dipole Moment of the Neutron, Phys. Rev. Lett.124(2020), no. 8 081803, [arXiv:2001.11966]

    work page arXiv 2020

  10. [10]

    W.-Y. Ai, J. S. Cruz, B. Garbrecht, and C. Tamarit, Consequences of the order of the limit of infinite spacetime volume and the sum over topological sectors for CP violation in the strong interactions, Phys. Lett. B822(2021) 136616, [arXiv:2001.07152]

    work page arXiv 2021

  11. [11]

    W.-Y. Ai, B. Garbrecht, and C. Tamarit,The QCD theta-parameter in canonical quantization, arXiv:2403.00747

    work page arXiv

  12. [12]

    W.-Y. Ai, B. Garbrecht, and C. Tamarit,CP Conservation in the Strong Interactions, Universe10 (2024), no. 5 189, [arXiv:2404.16026]

    work page arXiv 2024

  13. [13]

    D. E. Kaplan, T. Melia, and S. Rajendran,What can solve the strong CP problem?, JHEP08(2025) 050, [arXiv:2505.08358]

    work page arXiv 2025

  14. [14]

    J. N. Benabou, A. Hook, C. A. Manzari, H. Murayama, and B. R. Safdi,Clearing up the Strong CPproblem,arXiv:2510.18951

    work page arXiv

  15. [15]

    W.-Y. Ai, B. Garbrecht, and C. Tamarit,Reply to ”Clearing up the StrongCPproblem”, arXiv:2511.04216

    work page arXiv

  16. [16]

    Gamboa, N

    J. Gamboa and N. A. T. Arellano,Strong CP as an Infrared Holonomy: TheθVacuum and Dressing in Yang-Mills Theory,arXiv:2512.24480

    work page arXiv

  17. [17]

    V. V. Khoze,A note on instantons,θ-dependence and strong CP,arXiv:2512.06827

    work page arXiv

  18. [18]

    Bhattacharya, Comment on the claim of physical irrelevance of the topological term,preprint(2025).arXiv:2512.10127

    T. Bhattacharya,Comment on the claim of physical irrelevance of the topological term,arXiv:2512.10127

    work page arXiv

  19. [19]

    Ringwald, CP , or not CP , that is the question

    A. Ringwald,CP, or not CP, that is the question..., in 3rd General Meeting of the COST Action: Cosmic WISPers (CA21106), 1, 2026.arXiv:2601.04718

    work page arXiv 2026

  20. [20]

    Aghaie, R

    M. Aghaie and R. Sato,A particle on a ring or: how I learned to stop worrying and loveθ-vacua, arXiv:2601.18248

    work page internal anchor Pith review arXiv

  21. [21]

    R. D. Peccei and H. R. Quinn,CP Conservation in the Presence of Instantons, Phys. Rev. Lett.38(1977) 1440–1443

    1977

  22. [22]

    R. D. Peccei and H. R. Quinn,Constraints Imposed by CP Conservation in the Presence of Instantons, Phys. Rev. D16(1977) 1791–1797

    1977

  23. [23]

    Weinberg,A New Light Boson?, Phys

    S. Weinberg,A New Light Boson?, Phys. Rev. Lett. 40(1978) 223–226

    1978

  24. [24]

    Wilczek,Problem of StrongPandTInvariance in the Presence of Instantons, Phys

    F. Wilczek,Problem of StrongPandTInvariance in the Presence of Instantons, Phys. Rev. Lett.40(1978) 279–282

    1978

  25. [25]

    Di Luzio, M

    L. Di Luzio, M. Giannotti, E. Nardi, and L. Visinelli, The landscape of QCD axion models, Phys. Rept.870 (2020) 1–117, [arXiv:2003.01100]

    work page arXiv 2020

  26. [26]

    L. F. Abbott and P. Sikivie,A Cosmological Bound on the Invisible Axion, Phys. Lett. B120(1983) 133–136

    1983

  27. [27]

    Dine and W

    M. Dine and W. Fischler,The Not So Harmless Axion, Phys. Lett. B120(1983) 137–141

    1983

  28. [28]

    Preskill, M

    J. Preskill, M. B. Wise, and F. Wilczek,Cosmology of the Invisible Axion, Phys. Lett. B120(1983) 127–132

    1983

  29. [29]

    Witten,Some Properties of O(32) Superstrings, Phys

    E. Witten,Some Properties of O(32) Superstrings, Phys. Lett. B149(1984) 351–356

    1984

  30. [30]

    String Axiverse

    A. Arvanitaki, S. Dimopoulos, S. Dubovsky, N. Kaloper, and J. March-Russell,String axiverse, Phys. Rev. D81(2010) 123530, [arXiv:0905.4720]

    work page internal anchor Pith review arXiv 2010

  31. [31]

    Axions In String Theory

    P. Svrcek and E. Witten,Axions In String Theory, JHEP06(2006) 051, [hep-th/0605206]

    work page Pith review arXiv 2006

  32. [32]

    Dine and N

    M. Dine and N. Seiberg,String Theory and the Strong CP Problem, Nucl. Phys. B273(1986) 109–124

    1986

  33. [33]

    Halverson, C

    J. Halverson, C. Long, B. Nelson, and G. Salinas, Towards string theory expectations for photon couplings to axionlike particles, Phys. Rev. D100 (2019), no. 10 106010, [arXiv:1909.05257]

    work page arXiv 2019

  34. [34]

    Gendler, D

    N. Gendler, D. J. E. Marsh, L. McAllister, and J. Moritz,Glimmers from the axiverse, JCAP09 (2024) 071, [arXiv:2309.13145]

    work page arXiv 2024

  35. [35]

    S. L. Cheng, C. Q. Geng, and W. T. Ni,Axion - photon couplings in invisible axion models, Phys. Rev. D52(1995) 3132–3135, [hep-ph/9506295]

    work page arXiv 1995

  36. [36]

    di Cortona, E

    G. Grilli di Cortona, E. Hardy, J. Pardo Vega, and G. Villadoro,The QCD axion, precisely, JHEP01 (2016) 034, [arXiv:1511.02867]

    work page arXiv 2016

  37. [37]

    Lu, M.-L

    Z.-Y. Lu, M.-L. Du, F.-K. Guo, U.-G. Meißner, and T. Vonk,QCDθ-vacuum energy and axion properties, JHEP05(2020) 001, [arXiv:2003.01625]

    work page arXiv 2020

  38. [38]

    R. Gao, J. Hao, C.-G. Duan, Z.-H. Guo, J. A. Oller, and H.-Q. Zhou,Isospin-breaking contribution to the model-independent axion-photon-photon coupling in U(3) chiral theory, Eur. Phys. J. C85(2025), no. 1 97, [arXiv:2411.06737]

    work page arXiv 2025

  39. [39]

    Redefining the Axion Window

    L. Di Luzio, F. Mescia, and E. Nardi,Redefining the Axion Window, Phys. Rev. Lett.118(2017), no. 3 031801, [arXiv:1610.07593]

    work page Pith review arXiv 2017

  40. [40]

    Di Luzio, F

    L. Di Luzio, F. Mescia, and E. Nardi,Window for preferred axion models, Phys. Rev. D96(2017), no. 7 075003, [arXiv:1705.05370]

    work page arXiv 2017

  41. [41]

    Plakkot and S

    V. Plakkot and S. Hoof,Anomaly ratio distributions of hadronic axion models with multiple heavy quarks, Phys. Rev. D104(2021), no. 7 075017, [arXiv:2107.12378]

    work page arXiv 2021

  42. [42]

    Cheek, J

    A. Cheek, J. K. Osi´ nski, and L. Roszkowski,Extending preferred axion models via heavy-quark induced early matter domination, JCAP03(2024) 061, [arXiv:2310.16087]

    work page arXiv 2024

  43. [43]

    Di Luzio, S

    L. Di Luzio, S. Hoof, C. Marinissen, and V. Plakkot, Catalogues of cosmologically self-consistent hadronic QCD axion models, JCAP04(2025) 072, [arXiv:2412.17896]

    work page arXiv 2025

  44. [44]

    K. Choi, C. W. Kim, and W. K. Sze,Mass Renormalization by Instantons and the Strong CP Problem, Phys. Rev. Lett.61(1988) 794

    1988

  45. [45]

    Choi and H

    K. Choi and H. D. Kim,Small instanton contribution to the axion potential in supersymmetric models, Phys. Rev. D59(1999) 072001, [hep-ph/9809286]

    work page arXiv 1999

  46. [46]

    Hook, Solving the Hierarchy Problem Discretely, Phys

    A. Hook,Solving the Hierarchy Problem Discretely, Phys. Rev. Lett.120(2018), no. 26 261802, [arXiv:1802.10093]

    work page arXiv 2018

  47. [47]

    V. A. Rubakov,Grand unification and heavy axion, JETP Lett.65(1997) 621–624, [hep-ph/9703409]

    work page arXiv 1997

  48. [48]

    Berezhiani, L

    Z. Berezhiani, L. Gianfagna, and M. Giannotti,Strong CP problem and mirror world: The Weinberg-Wilczek axion revisited, Phys. Lett. B500(2001) 286–296, [hep-ph/0009290]

    work page arXiv 2001

  49. [49]

    Albertus et al.,WISPedia – the WISPs Encyclopedia: Cosmic WISPers 2026 – V1.0, 2602.09089

    C. Albertuset. al.,WISPedia – the WISPs Encyclopedia,arXiv:2602.09089

    work page arXiv

  50. [50]

    Holdom and M

    B. Holdom and M. E. Peskin,Raising the Axion Mass, 40 Nucl. Phys. B208(1982) 397–412

    1982

  51. [51]

    Holdom,Strong QCD at High-energies and a Heavy Axion, Phys

    B. Holdom,Strong QCD at High-energies and a Heavy Axion, Phys. Lett. B154(1985) 316. [Erratum: Phys.Lett.B 156, 452 (1985)]

    1985

  52. [52]

    J. M. Flynn and L. Randall,A Computation of the Small Instanton Contribution to the Axion Potential, Nucl. Phys. B293(1987) 731–739

    1987

  53. [53]

    Poppitz and Y

    E. Poppitz and Y. Shirman,The Strength of small instanton amplitudes in gauge theories with compact extra dimensions, JHEP07(2002) 041, [hep-th/0204075]

    work page arXiv 2002

  54. [54]

    Gherghetta, V.V

    T. Gherghetta, V. V. Khoze, A. Pomarol, and Y. Shirman,The Axion Mass from 5D Small Instantons, JHEP03(2020) 063, [arXiv:2001.05610]

    work page arXiv 2020

  55. [55]

    Croon, R

    D. Croon, R. Houtz, and V. Sanz,Dynamical Axions and Gravitational Waves, JHEP07(2019) 146, [arXiv:1904.10967]

    work page arXiv 2019

  56. [56]

    Reig,On the high-scale instanton interference effect: axion models without domain wall problem, JHEP08(2019) 167, [arXiv:1901.00203]

    M. Reig,On the high-scale instanton interference effect: axion models without domain wall problem, JHEP08(2019) 167, [arXiv:1901.00203]

    work page arXiv 2019

  57. [57]

    M. B. Gavela, M. Ibe, P. Quilez, and T. T. Yanagida, Automatic Peccei–Quinn symmetry, Eur. Phys. J. C 79(2019), no. 6 542, [arXiv:1812.08174]

    work page arXiv 2019

  58. [58]

    Gherghetta, N

    T. Gherghetta, N. Nagata, and M. Shifman,A Visible QCD Axion from an Enlarged Color Group, Phys. Rev. D93(2016), no. 11 115010, [arXiv:1604.01127]

    work page arXiv 2016

  59. [59]

    Agrawal and K

    P. Agrawal and K. Howe,Factoring the Strong CP Problem, JHEP12(2018) 029, [arXiv:1710.04213]

    work page arXiv 2018

  60. [60]

    M. K. Gaillard, M. B. Gavela, R. Houtz, P. Quilez, and R. Del Rey,Color unified dynamical axion, Eur. Phys. J. C78(2018), no. 11 972, [arXiv:1805.06465]

    work page arXiv 2018

  61. [61]

    Fuentes-Mart´ ın, M

    J. Fuentes-Mart´ ın, M. Reig, and A. Vicente,Strong CPproblem with low-energy emergent QCD: The 4321 case, Phys. Rev. D100(2019), no. 11 115028, [arXiv:1907.02550]

    work page arXiv 2019

  62. [62]

    Cs´ aki, M

    C. Cs´ aki, M. Ruhdorfer, and Y. Shirman,UV Sensitivity of the Axion Mass from Instantons in Partially Broken Gauge Groups, JHEP04(2020) 031, [arXiv:1912.02197]

    work page arXiv 2020

  63. [63]

    Gavela, P

    B. Gavela, P. Qu´ ılez, and M. Ramos,The QCD axion sum rule, JHEP04(2024) 056, [arXiv:2305.15465]

    work page arXiv 2024

  64. [64]

    Agrawal, J

    P. Agrawal, J. Fan, M. Reece, and L.-T. Wang, Experimental targets for photon couplings of the qcd axion, JHEP02(2018) 006, [arXiv:1709.06085]

    work page arXiv 2018

  65. [65]

    Gianfagna, M

    L. Gianfagna, M. Giannotti, and F. Nesti,Mirror world, supersymmetric axion and gamma ray bursts, JHEP10(2004) 044, [hep-ph/0409185]

    work page arXiv 2004

  66. [66]

    S. D. H. Hsu and F. Sannino,New solutions to the strong CP problem, Phys. Lett. B605(2005) 369–375, [hep-ph/0408319]

    work page arXiv 2005

  67. [67]

    Hook,Anomalous solutions to the strong CP problem,Phys

    A. Hook,Anomalous solutions to the strong CP problem, Phys. Rev. Lett.114(2015), no. 14 141801, [arXiv:1411.3325]

    work page arXiv 2015

  68. [68]

    Fukuda, K

    H. Fukuda, K. Harigaya, M. Ibe, and T. T. Yanagida, Model of visible QCD axion, Phys. Rev. D92(2015), no. 1 015021, [arXiv:1504.06084]

    work page arXiv 2015

  69. [69]

    Blinov and A

    N. Blinov and A. Hook,Solving the Wrong Hierarchy Problem, JHEP06(2016) 176, [arXiv:1605.03178]

    work page arXiv 2016

  70. [70]

    Chiang, H

    C.-W. Chiang, H. Fukuda, M. Ibe, and T. T. Yanagida,750 GeV diphoton resonance in a visible heavy QCD axion model, Phys. Rev. D93(2016), no. 9 095016, [arXiv:1602.07909]

    work page arXiv 2016

  71. [71]

    Dimopoulos, A

    S. Dimopoulos, A. Hook, J. Huang, and G. Marques-Tavares,A collider observable QCD axion, JHEP11(2016) 052, [arXiv:1606.03097]

    work page arXiv 2016

  72. [72]

    Kobakhidze,Heavy axion in asymptotically safe QCD,arXiv:1607.06552

    A. Kobakhidze,Heavy axion in asymptotically safe QCD,arXiv:1607.06552

    work page arXiv

  73. [73]

    Agrawal and K

    P. Agrawal and K. Howe,A Flavorful Factoring of the Strong CP Problem, JHEP12(2018) 035, [arXiv:1712.05803]

    work page arXiv 2018

  74. [74]

    A. Hook, S. Kumar, Z. Liu, and R. Sundrum,High Quality QCD Axion and the LHC, Phys. Rev. Lett. 124(2020), no. 22 221801, [arXiv:1911.12364]

    work page arXiv 2020

  75. [75]

    Gherghetta and M

    T. Gherghetta and M. D. Nguyen,A Composite Higgs with a Heavy Composite Axion, JHEP12(2020) 094, [arXiv:2007.10875]

    work page arXiv 2020

  76. [76]

    Kivel, J

    A. Kivel, J. Laux, and F. Yu,Supersizing axions with small size instantons, JHEP11(2022) 088, [arXiv:2207.08740]

    work page arXiv 2022

  77. [77]

    Farina, D

    M. Farina, D. Pappadopulo, F. Rompineve, and A. Tesi,The photo-philic qcd axion, JHEP01(2017) 095, [arXiv:1611.09855]

    work page arXiv 2017

  78. [78]

    Di Luzio, B

    L. Di Luzio, B. Gavela, P. Quilez, and A. Ringwald, Dark matter from an even lighter QCD axion: trapped misalignment, JCAP10(2021) 001, [arXiv:2102.01082]

    work page arXiv 2021

  79. [79]

    Di Luzio, B

    L. Di Luzio, B. Gavela, P. Quilez, and A. Ringwald, An even lighter QCD axion, JHEP05(2021) 184, [arXiv:2102.00012]

    work page arXiv 2021

  80. [80]

    M. J. Strassler and K. M. Zurek,Echoes of a hidden valley at hadron colliders, Phys. Lett. B651(2007) 374–379, [hep-ph/0604261]

    work page arXiv 2007

Showing first 80 references.