Pith. sign in

REVIEW 4 major objections 5 minor 1 cited by

Accidental Peccei-Quinn Symmetry From Gauged U(1) and a High Quality Axion

T0 review · 4 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read Adding a gauged U(1) symmetry can make the QCD axion survive quantum gravity.

desk verdict Models I and II fail gauge invariance under the very U(1)a meant to protect them; Model III survives and is the part worth refereeing. read the letter →

arxiv 2412.21157 v2 pith:RGZXKMH6 submitted 2024-12-30 hep-ph

K.S. Babu , Bhaskar Dutta , Rabindra N. Mohapatra This is my paper · ORCID
classification hep-ph
keywords axionqualityproblemPeccei-QuinnsymmetrystrongCPgaugedaxialU(1)KSVZDFSZSO(10)grandunifiedtheorydarkmatter
topics Quantum GravityDark MatterThe Strong CP Problem
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 aims to show that the axion quality problem—the tendency of quantum gravity to wreck the axion solution to the strong CP problem—can be solved by gauging an anomaly-free axial U(1)_a symmetry. In the proposed models, the Peccei-Quinn (PQ) symmetry is not imposed by hand but emerges accidentally because the renormalizable theory splits into two sectors connected only by high-dimensional Planck-suppressed operators. Three explicit constructions are given: two KSVZ-type extensions of the Standard Model with vector-like quarks, and one SO(10) grand unified model whose axion interpolates between KSVZ and DFSZ types. If these models are right, the $\theta$ parameter stays below $10^{-10}$ for axion decay constants up to about 7 x $10^{11}$ GeV, comfortably covering the range where axions are all the dark matter, and all constructions have domain wall number one.

What carries the argument

The machinery is the anomaly-free gauged axial U(1)_a symmetry together with two SM-singlet scalar fields S and T whose U(1)_a charges are chosen so that the renormalizable scalar potential has no interlocking S-T terms. This leaves an accidental global U(1)_PQ, whose spontaneous breaking produces the axion as the combination of the S and T phases orthogonal to the Goldstone boson eaten by the U(1)_a gauge boson. The gauge symmetry then controls gravity: operators that break U(1)_PQ must involve high powers of S and T, for example $S^{{3n}}$T^*/$M_Pl^{{3n-3}}$ in Model I and $T^{{12}}$S^*/$M_Pl^{9}$ in Model III, and these are suppressed enough to keep the induced $\theta$ small.

What would settle it

Compute the shift in $\theta$ induced by every gauge-invariant operator of dimension below 3n (Models I and II) or below 12 (Model III) that can be written with the fields of each model; if any such operator with an order-one coefficient gives $\theta$ at or above $10^{-10}$ at f_a = 5 x $10^{10}$ GeV, the claimed axion quality fails, and the loop estimates of Secs. 3.2 and 6.2 are the specific place to look for a missed dominant contribution.

Watch

Extended reading notes

Core claim

The paper's central claim is that a gauged, anomaly-free axial U(1)_a symmetry can turn the Peccei-Quinn symmetry into an accidental global symmetry of two decoupled sectors, so that quantum gravity respects the gauge symmetry while breaking the PQ symmetry only through high-dimensional operators. For the vector-like quark models I and II, the leading dangerous operator is $S^{{3n}}$T^* (or $S^{{mn}}$T^*) suppressed by $M_Pl^{{3n-3}}$; choosing n at least 4 (or m > 3) leaves the induced $\theta$ shift many orders of magnitude below $10^{-10}$. In the SO(10) model the leading operator is $T^{{12}}$S^*/$M_Pl^{9}$, which keeps $\theta$ at or below $10^{-10}$ for f_a up to 6.96 x $10^{11}$ GeV; the axion couplings to electron and nucleon there interpolate between KSVZ and DFSZ values, with E/N = 8/3 and a positive electron coupling that can distinguish the model. All three models have domain wall number one, which avoids the cosmological domain-wall problem.

Load-bearing premise

The whole construction stands on the assumption that quantum gravity generates precisely the Planck-suppressed operators listed in Eqs. (3.10), (3.15), (4.7), (4.11), (5.4), and (6.1), with order-one coefficients, and generates no additional Peccei-Quinn-breaking operator of lower dimension; if that fails, the induced $\theta$ shift exceeds $10^{-10}$ and the axion is not high quality.

Editorial extensions

If this is right

  • In Model I, n = 4 with f_a = 5 x 10^10 GeV gives an induced theta around 2.7 x 10^-25, and n = 5 gives 9.6 x 10^-29 at f_a = 10^12 GeV, so the KSVZ-type axion has high quality even with gravity.
  • In Model II, m = 4 with n = 4 gives theta around 1.2 x 10^-57, and even n = 3 gives theta around 2.7 x 10^-25, so this family permits a lower integer n than Model I.
  • If the SO(10) model is correct, the axion can be all the dark matter with f_a = (4.6-7.2) x 10^10 GeV, and the quality constraint remains satisfied up to f_a about 7 x 10^11 GeV.
  • All three models have domain wall number one, so none suffers the cosmological domain-wall problem that affects many axion models.
  • In the SO(10) model the axion's electron and nucleon couplings differ from pure KSVZ or DFSZ predictions, giving a concrete way to test the model with axion experiments.

Reading between the lines

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

  • The same charge-multiplicity trick could protect other accidental global symmetries, such as those behind proton stability or dark-matter stability, from gravity-induced operators.
  • The paper leaves open how the order-one gravity coefficients are fixed; if a particular theory of quantum gravity enhanced or suppressed them, the quality bound would shift accordingly.
  • The SO(10) model's prediction of a positive electron coupling C_ae around 0.25-0.33 means a future measurement outside that window would exclude this specific construction, a testable consequence worth stating explicitly.
  • A supersymmetric version of the same gauged-U(1) construction would face additional constraints from sfermion masses and anomaly mediation, and could be a natural next step.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. The paper constructs two classes of models, based on GSM × U(1)_a and SO(10) × U(1)_a, in which an anomaly-free gauged axial U(1)_a forces the Peccei-Quinn symmetry to arise accidentally. In Models I and II, vector-like quarks and singlet scalars T,S are arranged into two decoupled sectors at the renormalizable level, so that the leading gravity-induced interlocking operators are of high dimension (e.g., S^{3n}T^* with n≥4 for Model I). In Model III, an SO(10) GUT with fermions in 16+10+singlets and scalars 10+10'+126+45/210+singlets realizes a hybrid KSVZ-DFSZ axion whose decay constant and couplings are computed, with the leading PQ-breaking scalar operator T^{12}S^*/M_Pl^9. The paper claims θ ≤ 10^-10 is achieved for fa up to about 7×10^11 GeV in the SO(10) case, that all models have domain wall number one, and that the SO(10) model interpolates between KSVZ and DFSZ-I limits as the ratio of singlet VEVs varies.

Significance. If the construction is correct, this is a valuable addition to the axion-quality literature: it provides explicit, anomaly-free gauge extensions in which the accidental PQ symmetry is protected by a gauged U(1)_a, and it extends the strategy to a realistic SO(10) GUT with testable axion couplings. The paper is careful to check anomaly cancellation, to identify the axion field orthogonal to Goldstone modes, and to compute fa for each model. The explicit prediction that Model III has gae, gap, and gan in a band distinct from standard KSVZ and DFSZ models, together with NDW=1, gives falsifiable signatures. The numerical quality estimates for Models I and II are internally consistent, and the use of M_* rather than M_Pl in the VLQ mass generation is a useful practical point. However, the manuscript as written contains several gauge-invariance and notation problems in the scalar and fermion sectors that must be fixed before the central claims can be accepted without reservation.

major comments (4)
  1. [Eq. (5.4) and Sec. 5, SO(10) model] Several terms in the symbolic scalar potential of Eq. (5.4) are not invariant under the gauged U(1)_a with the charges of Table 3. For example, HΔAA carries U(1)_a charge -2-2+0+0 = -4, ΔΔHH carries -8, and ΔΔbarΔH (with barΔ charge +2) carries -4. Since this potential is used to generate the doublet mixing that is needed for realistic fermion masses, the model as written is inconsistent at the level of gauge invariance. The terms should be corrected to gauge-invariant combinations, e.g., H^*ΔAA and Δ^*ΔHH, and the subsequent mass and axion analysis re-checked. This is a load-bearing issue for Model III, not a mere typographical detail.
  2. [Eqs. (3.3), (4.1), (5.3) and Tables 1-3] The fermion bilinears are written as QL QR T^* and QL QR S^n without explicit bars or a stated convention. If these are read as 4-component ar Q_L Q_R terms, then the U(1)_a charges work out as claimed, e.g., ar Q_{4L}Q_{4R}T^* has charge +3+3-6=0 and ar Q_{aL}Q_{bR}S^n has charge -1-1+2=0, and the bare mass ar Q_L Q_R is indeed forbidden. But in the same equations the N_R terms, e.g., N_{1R}N_{2R}T^*, require the 2-component Weyl product convention (charge 2+4-6=0). The manuscript never states which convention is used, and the literal reading of the displayed formulas gives apparent charge mismatches such as +2 for Q_aL Q_bR S^n. This ambiguity is serious because it obscures the gauge invariance of the central Yukawa sector; the authors should rewrite all fermion terms in a manifestly Lorentz-invariant and charge-assigned notation and verify each term explicitly.
  3. [Sec. 6.2, Eq. (6.5)] The three-loop contribution to the PQ-breaking scalar operator T^{12}S^* is estimated by power counting, but the derivation of Eq. (6.5) is not shown in enough detail to verify the coefficient gn, the logarithmic structure, and the claim that the loop term becomes comparable to the tree-level d=12 operator for λ≥0.003. Since this loop effect is a key part of the quality analysis for Model III, the authors should either provide the full calculation or a more step-by-step estimate, including the treatment of the color-triplet and doublet exchanges that produce the logarithmic factors. Without this, the numerical results in Figs. 5 and 6 rest on an unverified estimate.
  4. [Eq. (5.3) and Sec. 6.1] The Yukawa Lagrangian Eq. (5.3) contains non-renormalizable operators, such as χN_1T^4S^*/M_Pl^4 and N_aN_bT^{*4}S/M_Pl^4, which explicitly break the accidental global U(1) listed in Table 3. The quality analysis in Sec. 6.1-6.2, however, considers only the scalar operators T^{12}S^* and H^6S/M_Pl^3. The authors should explain why the PQ-breaking fermionic operators do not induce a dangerous shift in θ, for instance by estimating the loop contributions that close the fermion lines, or should include them in the quality constraint. As written, the claim that the leading PQ violation is contained in the scalar potential is not fully supported.
minor comments (5)
  1. [Throughout] The text contains numerous typos and grammatical slips, e.g., 'Goldsonte' in Sec. 2.2, 'dertimen' in Sec. 3.4, 'arising' for 'arising' in Eq. (3.17), 'hyercharges' in Sec. 3.3, 'presnece' in Sec. 6.3.1, and 'scalat' in Sec. 7. A careful proofreading pass is needed.
  2. [Table 3 and Eq. (5.4)] The notation ar Δ is used in Eq. (5.4) but the conjugate of the 126-plet is not introduced in Table 3; the authors should clarify whether ar Δ denotes the conjugate field Δ^* and list its U(1)_a charge explicitly.
  3. [Eqs. (5.12)-(5.14) and (6.9)] In Eq. (5.14), the coefficients c_S, c_T, ... have mass dimension four, while the axion field in Eq. (5.12) uses a = N(c_S η_S + ...) with N carrying inverse mass dimension four. When applying the domain-wall formula in Eq. (6.9), the dimensionless combinations N c_i should be used. This should be stated explicitly to avoid dimensional confusion.
  4. [Sec. 3.5 and Fig. 5] The dark-matter band fa = (4.6-7.2)×10^10 GeV is quoted from Ref. [53], but the wider ranges from Refs. [54,55] are also mentioned; it would be clearer to present the model predictions against a single adopted DM window and to state which simulation results are used for the allowed region in Figs. 5-10.
  5. [Sec. 6.3.2] The parameter scan for the SO(10) model should specify the ranges and distributions of the scanned VEVs and the treatment of the complex phase in v'_u/v'_d; without this, the orange regions in Figs. 7-10 are not reproducible.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the axion-quality predictions are computed consequences of the explicitly chosen gauge charges and Planck-suppressed operators, not re-imports of the target result.

full rationale

The paper's central derivation is self-contained. In Models I and II, the accidental U(1)PQ is identified from the charge assignments, and the quality estimate follows by writing the lowest-dimension gauge-invariant PQ-breaking operators (Eqs. (3.10), (3.15), (4.7), (4.11)) and evaluating the induced theta shift; the allowed regions in (n, fa, fS, fT, M*) are outputs of those formulae rather than fitted inputs. Model III likewise computes fa and theta from Eqs. (5.15) and (6.1)-(6.4), with VEV ratios taken from an independent fermion-mass fit [83] and the loop estimate of Sec. 6.2 stated explicitly. The overlap with the authors' prior Ref. [28] is disclosed and is not load-bearing, since the SO(10) construction, anomaly checks, axion identification, and quality calculation are reproduced in the present text. The choices n >= 4 and the VEV ranges are model-building choices rather than fits of the quality bound; choosing a parameter so that a constraint is satisfied does not make the resulting claim circular. A separate correctness concern, not a circularity, is that the U(1)a charges in Tables 1 and 2 appear inconsistent with the Yukawa terms in Eqs. (3.3) and (4.1), and the claim in Sec. 3 that bare mass terms are forbidden is questionable because QL and QR carry opposite U(1)a charges; this is a gauge-invariance flaw that would invalidate Models I and II as written, but it is not a reduction of a prediction to an input in the circularity sense.

Assumptions & free parameters 9 free parameters · 6 assumptions · 6 invented entities

The paper introduces many new fields and VEVs, all of which are free parameters or domain assumptions of the construction. The central claim, that a gauged axial U(1)_a leads to an accidental high-quality Peccei-Quinn symmetry, rests on the standard assumption that quantum gravity induces gauge-invariant operators with O(1) coefficients and on the specific charge assignments and scalar potential choices made in the three models.

free parameters (9)
  • fS, fT (or fa and VEV ratio r) = not fitted; benchmark fa = 5e10 GeV (n=4) and fa = 1e12 GeV (n=5); r scanned over broad range
    Vacuum expectation values of the new singlet scalars set the axion decay constant and are free parameters, constrained only by quality and dark matter abundance.
  • integer n = n >= 4 in Model I; n = 3 allowed for m = 4; n = 1 for m + 1 >= 10 in Model II
    Determines the dimension of the leading gravity operator S^{3n} T^*; chosen large enough to satisfy the quality constraint.
  • integer m = m >= 3 in Model II
    Number of unit-charge vector-like quarks; larger m gives stronger suppression of gravity-induced theta.
  • M* = M* <= 6e12 GeV for n = 4 in Model I
    Scale suppressing higher-dimensional Yukawa operators; bounded from above by the LHC limit on vector-like quark masses above 1.2 TeV.
  • Yukawa couplings Y_ab, Y_44, Y_N = assumed O(1); example Tr(Y) = 0.1 used in loop estimates
    Set vector-like quark and singlet fermion masses and enter the estimated loop-induced theta shifts.
  • Scalar quartic couplings lambda_S, lambda_T, lambda_TS and lambda in SO(10) = not specified; lambda = 0.01 to 0.1 used in the SO(10) scans
    Stabilize the scalar potential and control the three-loop contribution to theta in the SO(10) model.
  • Gravity operator coefficients kappa, delta, gamma = taken O(1), with sin delta = 1 for most bounds
    Unknown coefficients of Planck-suppressed operators; the quality claim assumes they are order one with no additional suppression.
  • SO(10) scalar masses MH', MHd, MT = example: MH' = 2e16 GeV, MT = 1e11 GeV, MHd = 6e11 GeV
    Masses of colored scalars entering the three-loop quality estimate in Sec. 6.2.
  • SO(10) VEV ratios vu/vd and v'_u/v'_d = |vu/vd| ~ 70.3 and |v'_u/v'_d| ~ 18.1 from Ref. [83]
    Fixed by the fermion mass fits of a minimal SO(10) model and used in the axion coupling scan.
assumptions (6)
  • domain assumption Quantum gravity breaks global symmetries and induces all gauge-invariant operators with O(1) coefficients
    Standard axion quality premise invoked in Sec. 2.1; if wrong, the quality problem itself changes or disappears.
  • domain assumption The gauged U(1)_a is exact at all scales and is respected by quantum gravity
    The mechanism relies on gravity respecting gauge symmetry; this enters in Sec. 2.2 and in Eqs. (3.10) and (6.1).
  • standard math The QCD axion potential is described by the chiral perturbation formula of Eq. (2.1)
    Used to translate gravity-induced axion mass into a shift of theta; standard result quoted from the literature.
  • ad hoc to paper The scalar potential can be arranged so that T and S, and the GUT fields, acquire the assumed VEVs with no interlocking renormalizable terms
    The split-sector structure is an input of the construction; for the SO(10) model only the relevant terms are given, with the full potential referenced to Ref. [57].
  • domain assumption The fermion mass fit results of Ref. [83] apply to the SO(10) model
    Used to constrain VEV ratios in Sec. 6.3.2 when scanning axion couplings.
  • ad hoc to paper No additional Peccei-Quinn-breaking operators beyond those considered dominate the theta shift
    The paper checks selected loop diagrams and scalar operators, but does not prove that all possible operators are subdominant.
invented entities (6)
  • Vector-like quarks Q_i in Models I and II
    purpose: Carry axial U(1)_a charges, generate the accidental Peccei-Quinn symmetry and a KSVZ-type axion; 4 copies in Model I, m+1 copies in Model II.
    No independent detection; masses could be near a TeV and searched at colliders, but the model gives no specific mass prediction.
  • Singlet fermions N_R in Models I and II
    purpose: Cancel the U(1)_a^3 anomaly and participate in the Yukawa sector with charges (2,4,-6).
    No independent evidence; they are model-building ingredients with no direct observable handle.
  • Scalar singlets T and S
    purpose: Break the U(1)_a gauge symmetry, supply the axion, and set the axion decay constant fa.
    No independent evidence; their VEVs are free parameters of the construction.
  • SO(10) 10-plet fermion F in Model III
    purpose: Cancel the SO(10)^2 x U(1)_a anomaly and produce the hybrid KSVZ-DFSZ axion phenomenology.
    No independent evidence; its mass is tied to the Peccei-Quinn scale.
  • SO(10) singlet fermions chi and N_a in Model III
    purpose: Complete anomaly cancellation, generate sub-eV fermion masses, and affect BBN through a small Delta N_eff.
    No independent evidence; their masses and mixings are model parameters.
  • GUT scalars H(10), H'(10), Delta(126), and A(45 or 210)
    purpose: Break SO(10), generate fermion masses, and host the axion field in the SO(10) model.
    No independent evidence beyond the standard SO(10) model-building context; their VEVs and masses are free parameters.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Accidental Peccei-Quinn Symmetry From Gauged U(1) and a High Quality Axion." pith.science (2026). https://pith.science/paper/RGZXKMH6

@misc{pith2026241221157,
  author       = {Pith},
  title        = {Pith review of: Accidental Peccei-Quinn Symmetry From Gauged U(1) and a High Quality Axion},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RGZXKMH6}},
  note         = {Machine review of arXiv:2412.21157}
}
abstract

We construct explicit models that solve the axion quality problem originating from quantum gravitational effects. The general strategy we employ is to supplement the Standard Model and its grand unified extensions by an anomaly-free axial $U(1)_a$ symmetry that is gauged. We show that for several choices of the gauge quantum numbers of the fermions, this setup leads to an accidental $U(1)$ symmetry with a QCD anomaly which can be identified as the Peccei-Quinn (PQ) symmetry that solves the strong CP problem. The $U(1)_a$ gauge symmetry controls the amount of explicit PQ symmetry violation induced by quantum gravity, resulting in a high quality axion. We present two classes of models employing this strategy. In the first class (models I and II), the axial $U(1)_a$ gauge symmetry acts on vector-like quarks leading to an accidental KSVZ-type axion. The second class (model III) is based on $SO(10)$ grand unified theory extended by a gauged $U(1)_a$ symmetry that leads to a hybrid KSVZ--DFSZ type axion. The couplings of the axion to the electron and the nucleon are found to be distinct in this class of hybrid models from those in the KSVZ and DFSZ models, when the axion is identified as the dark matter of the universe, which can be used to test these models. Interestingly, all models presented here have domain wall number of one, which is free of cosmological problems that typically arise in axion models.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. The Minimal High-Quality QCD Axion

    hep-ph 2026-07 conditional novelty 5.5 of 10

    A flat-interval 5D U(1) Wilson-line axion with 4D KSVZ/DFSZ anomaly sector supplies exponential quality protection while remaining minimal.

Reference graph

Works this paper leans on

99 extracted references · 12 canonical work pages · cited by 1 Pith paper

  1. [1]

    Pseudoparticle Solutions of the Yang-Mills Equations,

    A. A. Belavin, A. M. Polyakov, A. S. Schwartz, and Y. S. Tyupkin, “Pseudoparticle Solutions of the Yang-Mills Equations,” Phys. Lett. B59 (1975) 85–87

    1975

  2. [2]

    Computation of the Quantum Effects Due to a Four-Dimensional Pseudoparticle,

    G. ’t Hooft, “Computation of the Quantum Effects Due to a Four-Dimensional Pseudoparticle,” Phys. Rev. D14 (1976) 3432–3450. [Erratum: Phys.Rev.D 18, 2199 (1978)]

    1976

  3. [3]

    The Structure of the Gauge Theory Vacuum,

    C. G. Callan, Jr., R. F. Dashen, and D. J. Gross, “The Structure of the Gauge Theory Vacuum,” Phys. Lett. B63 (1976) 334–340

    1976

  4. [4]

    Vacuum Periodicity in a Yang-Mills Quantum Theory,

    R. Jackiw and C. Rebbi, “Vacuum Periodicity in a Yang-Mills Quantum Theory,” Phys. Rev. Lett. 37 (1976) 172–175

    1976

  5. [5]

    Chiral Estimate of the Electric Dipole Moment of the Neutron in Quantum Chromodynamics,

    R. J. Crewther, P. Di Vecchia, G. Veneziano, and E. Witten, “Chiral Estimate of the Electric Dipole Moment of the Neutron in Quantum Chromodynamics,” Phys. Lett. B88 (1979) 123. [Erratum: Phys.Lett.B 91, 487 (1980)]

    1979

  6. [6]

    Measurement of the Permanent Electric Dipole Moment of the Neutron,

    C. Abel et al., “Measurement of the Permanent Electric Dipole Moment of the Neutron,” Phys. Rev. Lett.124 no. 8, (2020) 081803, arXiv:2001.11966 [hep-ex]

    arXiv 2020

  7. [7]

    CP Conservation in the Presence of Instantons,

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

    1977

  8. [8]

    A New Light Boson?,

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

    1978

Show all 99 references
  1. [9]

    Problem of Strong P and T Invariance in the Presence of Instantons,

    F. Wilczek, “Problem of Strong P and T Invariance in the Presence of Instantons,” Phys. Rev. Lett.40 (1978) 279–282

    1978

  2. [10]

    Of Axions, Domain Walls and the Early Universe,

    P. Sikivie, “Of Axions, Domain Walls and the Early Universe,” Phys. Rev. Lett.48 (1982) 1156–1159

    1982

  3. [11]

    A Simple Solution to the Strong CP Problem with a Harmless Axion,

    M. Dine, W. Fischler, and M. Srednicki, “A Simple Solution to the Strong CP Problem with a Harmless Axion,” Phys. Lett. B104 (1981) 199–202

    1981

  4. [12]

    On Possible Suppression of the Axion Hadron Interactions. (In Russian),

    A. R. Zhitnitsky, “On Possible Suppression of the Axion Hadron Interactions. (In Russian),” Sov. J. Nucl. Phys.31 (1980) 260

    1980

  5. [13]

    Weak Interaction Singlet and Strong CP Invariance,

    J. E. Kim, “Weak Interaction Singlet and Strong CP Invariance,” Phys. Rev. Lett.43 (1979) 103. 4See however Ref. [99] where it has been shown that the production of strings by decaying domain walls for the case NDW ≥ 2 leads to a bound of fa ≤ 5 × 108 GeV. – 35 –

    1979

  6. [14]

    Can Confinement Ensure Natural CP Invariance of Strong Interactions?,

    M. A. Shifman, A. I. Vainshtein, and V. I. Zakharov, “Can Confinement Ensure Natural CP Invariance of Strong Interactions?,” Nucl. Phys. B166 (1980) 493–506

    1980

  7. [15]

    Bounds on Exotic Particle Interactions from SN 1987a,

    G. Raffelt and D. Seckel, “Bounds on Exotic Particle Interactions from SN 1987a,” Phys. Rev. Lett.60 (1988) 1793

    1988

  8. [16]

    Axions from SN 1987a,

    M. S. Turner, “Axions from SN 1987a,” Phys. Rev. Lett.60 (1988) 1797

    1988

  9. [17]

    Cosmology of the Invisible Axion,

    J. Preskill, M. B. Wise, and F. Wilczek, “Cosmology of the Invisible Axion,” Phys. Lett. B 120 (1983) 127–132

    1983

  10. [18]

    A Cosmological Bound on the Invisible Axion,

    L. F. Abbott and P. Sikivie, “A Cosmological Bound on the Invisible Axion,” Phys. Lett. B 120 (1983) 133–136

    1983

  11. [19]

    The Not So Harmless Axion,

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

    1983

  12. [20]

    The landscape of QCD axion models,

    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 [hep-ph]

    2020 arXiv

  13. [21]

    The QCD axion, precisely,

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

    2016 arXiv

  14. [22]

    Axion Cosmology,

    D. J. E. Marsh, “Axion Cosmology,” Phys. Rept. 643 (2016) 1–79, arXiv:1510.07633 [astro-ph.CO]

    2016 arXiv

  15. [23]

    Planck scale physics and the Peccei-Quinn mechanism,

    M. Kamionkowski and J. March-Russell, “Planck scale physics and the Peccei-Quinn mechanism,” Phys. Lett. B282 (1992) 137–141, arXiv:hep-th/9202003

    1992 arXiv

  16. [24]

    Solutions to the strong CP problem in a world with gravity,

    R. Holman, S. D. H. Hsu, T. W. Kephart, E. W. Kolb, R. Watkins, and L. M. Widrow, “Solutions to the strong CP problem in a world with gravity,” Phys. Lett. B282 (1992) 132–136, arXiv:hep-ph/9203206

    1992 arXiv

  17. [25]

    Planck scale corrections to axion models,

    S. M. Barr and D. Seckel, “Planck scale corrections to axion models,” Phys. Rev. D46 (1992) 539–549

    1992

  18. [26]

    Instability of the invisible axion,

    S. Ghigna, M. Lusignoli, and M. Roncadelli, “Instability of the invisible axion,” Phys. Lett. B 283 (1992) 278–281

    1992

  19. [27]

    High-Quality Axions in a Class of Chiral U(1) Gauge Theories,

    Y.-C. Qiu, J.-W. Wang, and T. T. Yanagida, “High-Quality Axions in a Class of Chiral U(1) Gauge Theories,” Phys. Rev. Lett.131 no. 7, (2023) 071802, arXiv:2301.02345 [hep-ph]

    2023 arXiv

  20. [28]

    Hybrid SO(10) Axion Model Without Quality Problem,

    K. S. Babu, B. Dutta, and R. N. Mohapatra, “Hybrid SO(10) Axion Model Without Quality Problem,” arXiv:2410.07323 [hep-ph]

    arXiv

  21. [29]

    Accidental SO(10) axion from gauged flavour,

    L. Di Luzio, “Accidental SO(10) axion from gauged flavour,” JHEP 11 (2020) 074, arXiv:2008.09119 [hep-ph]

    2020 arXiv

  22. [30]

    Axion quality from the (anti)symmetric of SU( N ),

    M. Ardu, L. Di Luzio, G. Landini, A. Strumia, D. Teresi, and J.-W. Wang, “Axion quality from the (anti)symmetric of SU( N ),” JHEP 11 (2020) 090, arXiv:2007.12663 [hep-ph]

    2020 arXiv

  23. [31]

    Composite axion models and Planck scale physics,

    L. Randall, “Composite axion models and Planck scale physics,” Phys. Lett. B284 (1992) 77–80

    1992

  24. [32]

    A High Quality Composite Axion,

    B. Lillard and T. M. P. Tait, “A High Quality Composite Axion,” JHEP 11 (2018) 199, arXiv:1811.03089 [hep-ph]

    2018 arXiv

  25. [33]

    Color unified dynamical axion,

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

    2018 arXiv

  26. [34]

    Axion quality straight from the GUT,

    L. Vecchi, “Axion quality straight from the GUT,” Eur. Phys. J. C81 no. 10, (2021) 938, arXiv:2106.15224 [hep-ph]. – 36 –

    2021 arXiv

  27. [35]

    Peccei-Quinn symmetry from a hidden gauge group structure,

    H.-S. Lee and W. Yin, “Peccei-Quinn symmetry from a hidden gauge group structure,” Phys. Rev. D99 no. 1, (2019) 015041, arXiv:1811.04039 [hep-ph]

    2019 arXiv

  28. [36]

    A common origin for the QCD axion and sterile neutrinos from SU(5) strong dynamics,

    P. Cox, T. Gherghetta, and A. Paul, “A common origin for the QCD axion and sterile neutrinos from SU(5) strong dynamics,” JHEP 12 (2023) 180, arXiv:2310.08557 [hep-ph]

    2023 arXiv

  29. [37]

    Light sterile neutrinos and a high-quality axion from a holographic Peccei-Quinn mechanism,

    P. Cox, T. Gherghetta, and M. D. Nguyen, “Light sterile neutrinos and a high-quality axion from a holographic Peccei-Quinn mechanism,” Phys. Rev. D105 no. 5, (2022) 055011, arXiv:2107.14018 [hep-ph]

    2022 arXiv

  30. [38]

    Axion Quality from Superconformal Dynamics,

    Y. Nakai and M. Suzuki, “Axion Quality from Superconformal Dynamics,” Phys. Lett. B 816 (2021) 136239, arXiv:2102.01329 [hep-ph]

    2021 arXiv

  31. [39]

    Chiral models of composite axions and accidental Peccei-Quinn symmetry,

    R. Contino, A. Podo, and F. Revello, “Chiral models of composite axions and accidental Peccei-Quinn symmetry,” JHEP 04 (2022) 180, arXiv:2112.09635 [hep-ph]

    2022 arXiv

  32. [40]

    Integer solutions to the anomaly equations for a class of chiral gauge theories,

    A. Podo and F. Revello, “Integer solutions to the anomaly equations for a class of chiral gauge theories,” Phys. Rev. D106 no. 11, (2022) 116020, arXiv:2205.03428 [hep-th]

    2022 arXiv

  33. [41]

    Stabilizing the axion by discrete gauge symmetries,

    K. S. Babu, I. Gogoladze, and K. Wang, “Stabilizing the axion by discrete gauge symmetries,” Phys. Lett. B560 (2003) 214–222, arXiv:hep-ph/0212339

    2003 arXiv

  34. [42]

    Strong CP problem and mirror world: The Weinberg-Wilczek axion revisited,

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

    2001 arXiv

  35. [43]

    High Quality QCD Axion and the LHC,

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

    2020 arXiv

  36. [44]

    Solving the Hierarchy Problem Discretely,

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

    2018 arXiv

  37. [45]

    From axion quality and naturalness problems to a high-quality ZN QCD relaxion,

    A. Banerjee, J. Eby, and G. Perez, “From axion quality and naturalness problems to a high-quality ZN QCD relaxion,” Phys. Rev. D107 no. 11, (2023) 115011, arXiv:2210.05690 [hep-ph]

    2023 arXiv

  38. [46]

    A QCD axion from higher dimensional gauge field,

    K.-w. Choi, “A QCD axion from higher dimensional gauge field,” Phys. Rev. Lett.92 (2004) 101602, arXiv:hep-ph/0308024

    2004 arXiv

  39. [47]

    Extra-Dimensional Axion Expectations,

    M. Reece, “Extra-Dimensional Axion Expectations,” arXiv:2406.08543 [hep-ph]

    arXiv

  40. [48]

    High-Quality Axions from Higher-Form Symmetries in Extra Dimensions,

    N. Craig and M. Kongsore, “High-Quality Axions from Higher-Form Symmetries in Extra Dimensions,” arXiv:2408.10295 [hep-ph]

    arXiv

  41. [49]

    Axions In String Theory,

    P. Svrcek and E. Witten, “Axions In String Theory,” JHEP 06 (2006) 051, arXiv:hep-th/0605206

    2006 arXiv

  42. [50]

    A Visible QCD Axion from an Enlarged Color Group,

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

    2016 arXiv

  43. [51]

    Chiral Dynamics in the Large n Limit,

    P. Di Vecchia and G. Veneziano, “Chiral Dynamics in the Large n Limit,” Nucl. Phys. B171 (1980) 253–272

    1980

  44. [52]

    Axion Predictions in SO(10) × U (1)PQ Models,

    A. Ernst, A. Ringwald, and C. Tamarit, “Axion Predictions in SO(10) × U (1)PQ Models,” JHEP 02 (2018) 103, arXiv:1801.04906 [hep-ph]

    2018 arXiv

  45. [53]

    Axion dark matter from topological defects,

    M. Kawasaki, K. Saikawa, and T. Sekiguchi, “Axion dark matter from topological defects,” Phys. Rev. D91 no. 6, (2015) 065014, arXiv:1412.0789 [hep-ph]. – 37 –

    2015 arXiv

  46. [54]

    Axion mass prediction from adaptive mesh refinement cosmological lattice simulations,

    J. N. Benabou, M. Buschmann, J. W. Foster, and B. R. Safdi, “Axion mass prediction from adaptive mesh refinement cosmological lattice simulations,” arXiv:2412.08699 [hep-ph]

    arXiv

  47. [55]

    Axions from Strings: the Attractive Solution,

    M. Gorghetto, E. Hardy, and G. Villadoro, “Axions from Strings: the Attractive Solution,” JHEP 07 (2018) 151, arXiv:1806.04677 [hep-ph]

    2018 arXiv

  48. [56]

    The Superlight Axion and Neutrino Masses,

    R. N. Mohapatra and G. Senjanovic, “The Superlight Axion and Neutrino Masses,” Z. Phys. C 17 (1983) 53–56

    1983

  49. [57]

    Minimal nonsupersymmetric SO(10) model: Gauge coupling unification, proton decay, and fermion masses,

    K. S. Babu and S. Khan, “Minimal nonsupersymmetric SO(10) model: Gauge coupling unification, proton decay, and fermion masses,” Phys. Rev. D92 no. 7, (2015) 075018, arXiv:1507.06712 [hep-ph]

    2015 arXiv

  50. [58]

    Massive neutrinos and invisible axion minimally connected,

    S. Bertolini, L. Di Luzio, H. Koleˇ sov´ a, and M. Malinsk´ y, “Massive neutrinos and invisible axion minimally connected,” Phys. Rev. D91 no. 5, (2015) 055014, arXiv:1412.7105 [hep-ph]

    2015 arXiv

  51. [59]

    Peccei-Quinn Symmetry and Nucleon Decay in Renormalizable SUSY SO(10),

    K. S. Babu, T. Fukuyama, S. Khan, and S. Saad, “Peccei-Quinn Symmetry and Nucleon Decay in Renormalizable SUSY SO(10),” JHEP 06 (2019) 045, arXiv:1812.11695 [hep-ph]

    2019 arXiv

  52. [60]

    Axion mass prediction from minimal grand unification,

    L. Di Luzio, A. Ringwald, and C. Tamarit, “Axion mass prediction from minimal grand unification,” Phys. Rev. D98 no. 9, (2018) 095011, arXiv:1807.09769 [hep-ph]

    2018 arXiv

  53. [61]

    Several Problems in Particle Physics and Cosmology Solved in One SMASH,

    G. Ballesteros, J. Redondo, A. Ringwald, and C. Tamarit, “Several Problems in Particle Physics and Cosmology Solved in One SMASH,” Front. Astron. Space Sci.6 (2019) 55, arXiv:1904.05594 [hep-ph]

    2019 arXiv

  54. [62]

    A minimal non-supersymmetric SO(10) model with Peccei–Quinn symmetry,

    S. M. Boucenna, T. Ohlsson, and M. Pernow, “A minimal non-supersymmetric SO(10) model with Peccei–Quinn symmetry,” Phys. Lett. B792 (2019) 251–257, arXiv:1812.10548 [hep-ph]. [Erratum: Phys.Lett.B 797, 134902 (2019)]

    2019 arXiv

  55. [63]

    Natural Alignment of Quark Flavors and Radiatively Induced Quark Mixings,

    A. Dev and R. N. Mohapatra, “Natural Alignment of Quark Flavors and Radiatively Induced Quark Mixings,” Phys. Rev. D98 no. 7, (2018) 073002, arXiv:1804.01598 [hep-ph]

    2018 arXiv

  56. [64]

    Axion-mediated forces, CP violation and left-right interactions,

    S. Bertolini, L. Di Luzio, and F. Nesti, “Axion-mediated forces, CP violation and left-right interactions,” Phys. Rev. Lett.126 no. 8, (2021) 081801, arXiv:2006.12508 [hep-ph]

    2021 arXiv

  57. [65]

    A predictive SO(10) model,

    G. Lazarides, R. Maji, R. Roshan, and Q. Shafi, “A predictive SO(10) model,” JCAP 12 (2022) 009, arXiv:2210.03710 [hep-ph]

    2022 arXiv

  58. [66]

    Predictive neutrino spectrum in minimal SO(10) grand unification,

    K. S. Babu and R. N. Mohapatra, “Predictive neutrino spectrum in minimal SO(10) grand unification,” Phys. Rev. Lett.70 (1993) 2845–2848, arXiv:hep-ph/9209215

    1993 arXiv

  59. [67]

    How neutrino and charged fermion masses are connected within minimal supersymmetric SO(10),

    B. Bajc, G. Senjanovic, and F. Vissani, “How neutrino and charged fermion masses are connected within minimal supersymmetric SO(10),” PoS HEP2001 (2001) 198, arXiv:hep-ph/0110310

    2001 arXiv

  60. [68]

    Neutrino oscillation data versus minimal supersymmetric SO(10) model,

    T. Fukuyama and N. Okada, “Neutrino oscillation data versus minimal supersymmetric SO(10) model,” JHEP 11 (2002) 011, arXiv:hep-ph/0205066

    2002 arXiv

  61. [69]

    b - tau unification and large atmospheric mixing: A Case for noncanonical seesaw,

    B. Bajc, G. Senjanovic, and F. Vissani, “b - tau unification and large atmospheric mixing: A Case for noncanonical seesaw,” Phys. Rev. Lett.90 (2003) 051802, arXiv:hep-ph/0210207

    2003 arXiv

  62. [70]

    Minimal SUSY SO(10), b tau unification and large neutrino mixings,

    H. S. Goh, R. N. Mohapatra, and S.-P. Ng, “Minimal SUSY SO(10), b tau unification and large neutrino mixings,” Phys. Lett. B570 (2003) 215–221, arXiv:hep-ph/0303055

    2003 arXiv

  63. [71]

    Minimal SUSY SO(10) model and predictions – 38 – for neutrino mixings and leptonic CP violation,

    H. S. Goh, R. N. Mohapatra, and S.-P. Ng, “Minimal SUSY SO(10) model and predictions – 38 – for neutrino mixings and leptonic CP violation,” Phys. Rev. D68 (2003) 115008, arXiv:hep-ph/0308197

    2003 arXiv

  64. [72]

    Neutrino masses and mixings in a minimal SO(10) model,

    K. S. Babu and C. Macesanu, “Neutrino masses and mixings in a minimal SO(10) model,” Phys. Rev. D72 (2005) 115003, arXiv:hep-ph/0505200

    2005 arXiv

  65. [73]

    Fermion masses in SUSY SO(10) with type II seesaw: A Non-minimal predictive scenario,

    S. Bertolini, M. Frigerio, and M. Malinsky, “Fermion masses in SUSY SO(10) with type II seesaw: A Non-minimal predictive scenario,” Phys. Rev. D70 (2004) 095002, arXiv:hep-ph/0406117

    2004 arXiv

  66. [74]

    On CP violation in minimal renormalizable SUSY SO(10) and beyond,

    S. Bertolini and M. Malinsky, “On CP violation in minimal renormalizable SUSY SO(10) and beyond,” Phys. Rev. D72 (2005) 055021, arXiv:hep-ph/0504241

    2005 arXiv

  67. [75]

    Fermion masses and mixings in SO(10) models and the neutrino challenge to SUSY GUTs,

    S. Bertolini, T. Schwetz, and M. Malinsky, “Fermion masses and mixings in SO(10) models and the neutrino challenge to SUSY GUTs,” Phys. Rev. D73 (2006) 115012, arXiv:hep-ph/0605006

    2006 arXiv

  68. [76]

    Minimal SO(10) splits supersymmetry,

    B. Bajc, I. Dorsner, and M. Nemevsek, “Minimal SO(10) splits supersymmetry,” JHEP 11 (2008) 007, arXiv:0809.1069 [hep-ph]

    2008 arXiv

  69. [77]

    Fermion Masses in SO(10) Models,

    A. S. Joshipura and K. M. Patel, “Fermion Masses in SO(10) Models,” Phys. Rev. D83 (2011) 095002, arXiv:1102.5148 [hep-ph]

    2011 arXiv

  70. [78]

    Fits to SO(10) Grand Unified Models,

    A. Dueck and W. Rodejohann, “Fits to SO(10) Grand Unified Models,” JHEP 09 (2013) 024, arXiv:1306.4468 [hep-ph]

    2013 arXiv

  71. [79]

    A non supersymmetric SO(10) grand unified model for all the physics below MGU T,

    G. Altarelli and D. Meloni, “A non supersymmetric SO(10) grand unified model for all the physics below MGU T,” JHEP 08 (2013) 021, arXiv:1305.1001 [hep-ph]

    2013 arXiv

  72. [80]

    Revisiting fermion mass and mixing fits in the minimal SUSY SO(10) GUT,

    T. Fukuyama, K. Ichikawa, and Y. Mimura, “Revisiting fermion mass and mixing fits in the minimal SUSY SO(10) GUT,” Phys. Rev. D94 no. 7, (2016) 075018, arXiv:1508.07078 [hep-ph]

    2016 arXiv

  73. [81]

    Resurrecting Minimal Yukawa Sector of SUSY SO(10),

    K. S. Babu, B. Bajc, and S. Saad, “Resurrecting Minimal Yukawa Sector of SUSY SO(10),” JHEP 10 (2018) 135, arXiv:1805.10631 [hep-ph]

    2018 arXiv

  74. [82]

    Fits to Non-Supersymmetric SO(10) Models with Type I and II Seesaw Mechanisms Using Renormalization Group Evolution,

    T. Ohlsson and M. Pernow, “Fits to Non-Supersymmetric SO(10) Models with Type I and II Seesaw Mechanisms Using Renormalization Group Evolution,” JHEP 06 (2019) 085, arXiv:1903.08241 [hep-ph]

    2019 arXiv

  75. [83]

    Flavor Hierarchies from Clockwork in SO(10) GUT,

    K. S. Babu and S. Saad, “Flavor Hierarchies from Clockwork in SO(10) GUT,” Phys. Rev. D 103 no. 1, (2021) 015009, arXiv:2007.16085 [hep-ph]

    2021 arXiv

  76. [84]

    Axion Couplings to Matter. 1. CP Conserving Parts,

    M. Srednicki, “Axion Couplings to Matter. 1. CP Conserving Parts,” Nucl. Phys. B260 (1985) 689–700

    1985

  77. [85]

    Manifesting the Invisible Axion at Low-energies,

    H. Georgi, D. B. Kaplan, and L. Randall, “Manifesting the Invisible Axion at Low-energies,” Phys. Lett. B169 (1986) 73–78

    1986

  78. [86]

    An even lighter QCD axion,

    L. Di Luzio, B. Gavela, P. Quilez, and A. Ringwald, “An even lighter QCD axion,” JHEP 05 (2021) 184, arXiv:2102.00012 [hep-ph]

    2021 arXiv

  79. [87]

    Axion couplings in grand unified theories,

    P. Agrawal, M. Nee, and M. Reig, “Axion couplings in grand unified theories,” JHEP 10 (2022) 141, arXiv:2206.07053 [hep-ph]

    2022 arXiv

  80. [88]

    Catalogues of Cosmologically Self-Consistent Hadronic QCD Axion Models,

    L. Di Luzio, S. Hoof, C. Marinissen, and V. Plakkot, “Catalogues of Cosmologically Self-Consistent Hadronic QCD Axion Models,” arXiv:2412.17896 [hep-ph]. – 39 –

    arXiv

  81. [89]

    Axion dark matter in the post-inflationary Peccei-Quinn symmetry breaking scenario,

    A. Ringwald and K. Saikawa, “Axion dark matter in the post-inflationary Peccei-Quinn symmetry breaking scenario,” Phys. Rev. D93 no. 8, (2016) 085031, arXiv:1512.06436 [hep-ph]. [Addendum: Phys.Rev.D 94, 049908 (2016)]

    2016 arXiv

  82. [90]

    Intermediate mass scales in the non-supersymmetric SO(10) grand unification: A Reappraisal,

    S. Bertolini, L. Di Luzio, and M. Malinsky, “Intermediate mass scales in the non-supersymmetric SO(10) grand unification: A Reappraisal,” Phys. Rev. D80 (2009) 015013, arXiv:0903.4049 [hep-ph]

    2009 arXiv

  83. [91]

    Quantum nature of the minimal potentially realistic SO(10) Higgs model,

    K. Jarkovsk´ a, M. Malinsk´ y, T. Mede, and V. Susiˇ c, “Quantum nature of the minimal potentially realistic SO(10) Higgs model,” Phys. Rev. D105 no. 9, (2022) 095003, arXiv:2109.06784 [hep-ph]

    2022 arXiv

  84. [92]

    Yukawa Sector of Minimal SO(10) Unification,

    K. S. Babu, B. Bajc, and S. Saad, “Yukawa Sector of Minimal SO(10) Unification,” JHEP 02 (2017) 136, arXiv:1612.04329 [hep-ph]

    2017 arXiv

  85. [93]

    Implications of LEP results for SO(10) grand unification,

    N. G. Deshpande, E. Keith, and P. B. Pal, “Implications of LEP results for SO(10) grand unification,” Phys. Rev. D46 (1993) 2261–2264

    1993

  86. [94]

    Ultraviolet Completion of a Two-loop Neutrino Mass Model,

    K. S. Babu and S. Saad, “Ultraviolet Completion of a Two-loop Neutrino Mass Model,” arXiv:2412.14562 [hep-ph]

    arXiv

  87. [95]

    Search for proton decay via p → e+π0 and p → µ+π0 with an enlarged fiducial volume in Super-Kamiokande I-IV,

    Super-Kamiokande Collaboration, A. Takenaka et al., “Search for proton decay via p → e+π0 and p → µ+π0 with an enlarged fiducial volume in Super-Kamiokande I-IV,” Phys. Rev. D102 no. 11, (2020) 112011, arXiv:2010.16098 [hep-ex]

    2020

  88. [96]

    On the estimation of gravitational wave spectrum from cosmic domain walls,

    T. Hiramatsu, M. Kawasaki, and K. Saikawa, “On the estimation of gravitational wave spectrum from cosmic domain walls,” JCAP 02 (2014) 031, arXiv:1309.5001 [astro-ph.CO]

    2014 arXiv

  89. [97]

    Axion cosmology with long-lived domain walls,

    T. Hiramatsu, M. Kawasaki, K. Saikawa, and T. Sekiguchi, “Axion cosmology with long-lived domain walls,” JCAP 01 (2013) 001, arXiv:1207.3166 [hep-ph]

    2013 arXiv

  90. [98]

    Imperfect Axion Precludes the Domain Wall Problem,

    Y. Zhang, “Imperfect Axion Precludes the Domain Wall Problem,” Phys. Rev. Lett.132 no. 8, (2024) 081003, arXiv:2305.15495 [hep-ph]

    2024 arXiv

  91. [99]

    Ruling out light axions: The writing is on the wall,

    K. A. Beyer and S. Sarkar, “Ruling out light axions: The writing is on the wall,” SciPost Phys. 15 no. 1, (2023) 003, arXiv:2211.14635 [hep-ph]. – 40 –

    2023 arXiv

Pith tools

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