REVIEW
The strong CP problem versus Planck scale physics
High Energy Physics - Phenomenology · Submitted 2 Sep 1996 · 36 references
Pith's verdict: A useful constraint paper: the relaxed PQ criterion and the one-loop SUSY regeneration result are real, but the Landau-pole claim is soft and the paper knows it.
T0 · AI review
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Referee report
The paper
The paper claims
The paper argues that the usual rule for protecting the axion from Planck-scale symmetry breaking is too strict, and that once the rule is relaxed, supersymmetric axion models still fail while the composite models that get the Peccei-Quinn
The reading
What carries the argument
Three pieces of machinery carry the argument. The first is the relaxed naturalness criterion itself: gauge symmetries need only forbid PQ-breaking operators of dimension below 10 that are built exclusively from fields with vacuum expectation values, so that operators such as $(¥varphi_i¥psi)^2(¥chi_j¥omega_k)$ in Randall's model are harmless because they contain no vev-carrying field. The second is the one-loop interference between a soft supersymmetry-breaking trilinear scalar term and a Planck-suppressed superpotential operator, which reintroduces a PQ-breaking scalar potential that holomorphy alone had suppressed. The third is a renormalization-group estimate of $¥alpha_s^{-1}(M_P)$ in the composite models, combining the perturbative running with estimated non-perturbative contributions $¥delta_{PGB}$ and $¥delta_{axicolor}$ from colored pseudo-Goldstone bosons and axihadrons.
Extended reading notes
Core claim
The central claim is that the standard dimension-10 prohibition on Planck-induced Peccei-Quinn breaking can be relaxed to a narrower one: only operators formed purely of fields with vacuum expectation values of order $f_{PQ}$ are dangerous, since an operator containing vev-less fields merely induces a suppressed axion coupling. Applying this relaxed criterion, the paper shows that supersymmetric axion models do not pass. In the $E_6 ¥times U(1)_X$ model whose renormalizable superpotential is $¥kappa ¥Phi ¥Psi_+ ¥Psi_-$, the soft trilinear term $¥kappa' m_s ¥Phi ¥Psi_+ ¥Psi_-$ interferes at one loop with the Planck-suppressed $¥Phi^6$ term to generate a six-scalar operator with coefficient of order $¥kappa^*¥kappa_1¥kappa' m_s/(4¥pi)^2 M_P^3 ¥log(M_P/m_s)$, and the requirement that $¥bar¥theta$ stay below $10^{-9}$ forces $|¥kappa ¥kappa_1 ¥kappa'| < O(10^{-18})$. A five-scalar term $¥Phi^4¥Phi^¥dagger$ is induced independently of the soft trilinear coupling, and the proposed repair with an extra real $E_6$ representation fails because gauge-anomaly cancellation forces the two $¥Psi$ charges to be opposite, leaving the dangerous operator intact.
Load-bearing premise
The claim that Randall's composite axion model hits a Landau pole below the Planck scale depends on estimated non-perturbative contributions to the running of the strong coupling being positive and large, and the paper itself says those contributions are hard to compute.
Editorial extensions
If this is right
- Any axion model that relies on the holomorphy of a supersymmetric superpotential to protect the Peccei-Quinn symmetry must be re-examined once soft supersymmetry breaking is included, because the protection does not survive to the scalar potential.
- Composite axion models without fundamental scalars satisfy the naturalness requirement on $f_{PQ}$ easily, but the only one that also evades Planck-induced PQ-breaking operators is driven to a Landau pole for QCD below the Planck scale.
- The heavy stable axibaryons and color-triplet pseudo-Goldstone bosons of composite axion models are cosmologically excluded unless there is a period of inflation with reheating temperature below their masses.
- Unifying color with the axicolor gauge group would simultaneously make the heavy stable particles decay and remove the Landau pole, so the viability of composite axions reduces to whether such a unification can be constructed.
- Models that tie the Peccei-Quinn scale to the scale of dynamical supersymmetry breaking are especially exposed, because the products of fields needed to generate the $Â¥mu$ and $B$ terms are themselves gauge-invariant and can be accompanied by Planck-suppressed PQ-breaking operators.
Reading between the lines
- The argument generalizes past axions: any global symmetry whose protection rests on the holomorphic structure of a supersymmetric theory should be checked against the soft terms, since a Planck-suppressed operator plus a soft trilinear coupling is enough to regenerate the forbidden term at one loop.
- If the Landau-pole conclusion holds, it converts a model-building preference into a constraint: composite axion models are only viable inside a unified group large enough to contain both color and axicolor, which makes the search for such embeddings the natural next calculation.
- The relaxed vev-only criterion suggests a practical checklist for future axion model building: list the fields that condense or acquire expectation values, and check PQ-breaking operators built from those alone, rather than cataloguing every gauge-invariant contraction.
- A controlled lattice or large-$N$ estimate of the axicolor contribution to the running of the strong coupling would settle the paper's most fragile quantitative claim without requiring new data.
Original abstract
We discuss conditions that should be satisfied by axion models for solving the strong CP problem. It has been observed that Planck scale effects may render the axion models ineffective if there are gauge invariant operators of dimension less than 10 which break explicitly the Peccei-Quinn (PQ) symmetry. We argue that only those operators formed of fields which have vacuum expectation values are dangerous. Supersymmetric axion models fail to prevent even this restricted class of operators. Furthermore, the models that relate the PQ scale and the supersymmetry breaking scale are particularly sensitive to gauge invariant PQ-breaking operators. By contrast, in non-supersymmetric composite axion models the PQ scale arises naturally, and the dangerous operators can be avoided. However, the composite axion models contain heavy stable particles which are cosmologically ruled out. Another problem is a Landau pole for the QCD coupling constant. Both these problems may be solved if the unification of color with the gauge interactions which bind the axion could be achieved.
The compiled record
The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
The abstract, sentence by sentence
We discuss conditions that should be satisfied by axion models for solving the strong CP problem. It has been observed that Planck scale effects may render the axion models ineffective if there are gauge invariant operators of dimension less than 10 which break explicitly the Peccei-Quinn (PQ) symmetry. We argue that only those operators formed of fields which have vacuum expectation values are dangerous. Supersymmetric axion models fail to prevent even this restricted class of operators. Furthermore, the models that relate the PQ scale and the supersymmetry breaking scale are particularly sensitive to gauge invariant PQ-breaking operators. By contrast, in non-supersymmetric composite axion models the PQ scale arises naturally, and the dangerous operators can be avoided. However, the composite axion models contain heavy stable particles which are cosmologically ruled out. Another problem is a Landau pole for the QCD coupling constant. Both these problems may be solved if the unification of color with the gauge interactions which bind the axion could be achieved.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We discuss conditions that should be satisfied by axion models for solving the strong CP problem. | contribution 0.75 | 0.77 | 0.05 | asserted 0.53 |
| s1 | It has been observed that Planck scale effects may render the axion models ineffective if there are gauge invariant operators of dimension less than 10 which break explicitly the Peccei-Quinn (PQ) symmetry. | background 0.99 | 0.09 | 0.09 | hedged possibility 0.97 |
| s2 | We argue that only those operators formed of fields which have vacuum expectation values are dangerous. | contribution 0.60 | 0.68 | 0.17 | asserted 0.97 |
| s3 | Supersymmetric axion models fail to prevent even this restricted class of operators. | result 0.92 | 0.53 | 0.14 | asserted 1.00 |
| s4 | Furthermore, the models that relate the PQ scale and the supersymmetry breaking scale are particularly sensitive to gauge invariant PQ-breaking operators. | result 0.83 | 0.45 | 0.07 | asserted 0.98 |
| s5 | By contrast, in non-supersymmetric composite axion models the PQ scale arises naturally, and the dangerous operators can be avoided. | result 0.87 | 0.39 | 0.23 | asserted 1.00 |
| s6 | However, the composite axion models contain heavy stable particles which are cosmologically ruled out. | limitation 0.64 | 0.19 | 0.06 | asserted 1.00 |
| s7 | Another problem is a Landau pole for the QCD coupling constant. | limitation 0.61 | 0.20 | 0.03 | asserted 0.99 |
| s8 | Both these problems may be solved if the unification of color with the gauge interactions which bind the axion could be achieved. | interpretation 0.40 | 0.28 | 0.45 | hedged possibility 1.00 |
What was examined, and what was not
- arXiv listing abstract v2
- full text
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- references and citing sentences
- relations to other papers
- P abstract
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- T body sentences
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- R cross-paper relations
References
How the literature uses it
32 arXiv papers cite this in 51 sentences
Papers citing it · 41 sentences without a confident label
Builds on it 1 paper
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The original work of Ref. [ref] and the analysis of Dobrescu of Ref. [ref] considered the pure QCD case where $=(3)_c$, but the model can be straightforwardly generalized to a GUT scenario by replacing the fundamental representation of $(3)_c$ with that of $(5)$.
Chiral models of composite axions and accidental Peccei-Quinn symmetry · Randall's model · 0.94
Uses its method or tool 1 paper
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The squared masses of the triplet and octet pNG bosons are estimated as [equation] Radiative corrections from QCD [ref] are [equation] where the gauge couplings are evaluated at their respective dynamical scales, $m_π^0$ and $m_π^±$ are the neutral and charged pion masses and we have used $Λ_S / Λ_QCD ∼√(3/N)f_S / f_π$ from NDA.
Footprints of New Strong Dynamics via Anomaly and the 750 GeV Diphoton · The masses of the pNG bosons · 0.86
Cites it as support 2 papers
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However, as is argued in Ref. [ref] , since these operators do not acquire a VEV, their modification to the axion potential is at least as suppressed as the lowest dimensional operator that involves only fields with VEVs from spontaneous $_PQ$ breaking.
The Quality/Cosmology Tension for a Post-Inflation QCD Axion · Cosmology/quality tension · 0.98
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The Planck-scale operators which dominantly cause $θ̅$ to deviate from zero are those involving only scalars with high scale VEVs, while operators involving fields that do not obtain VEVs are expected to be subdominant [ref] .
Protecting the Axion with Local Baryon Number · PQ Protection from U1B · 0.97
Cites it as background 6 papers
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Indeed, such a bias in the axion potential is a new contribution, in addition to those from QCD strong dynamics, and hence can potentially spoil the Peccei-Quinn mechanism [ref] in which the QCD axion as a solution to the strong CP problem [ref] .
Axion Domain Walls, Small Instantons, and Non-Invertible Symmetry Breaking · Introduction · 0.90
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The PQ symmetry is realized as an accidental symmetry from discrete gauge symmetries [ref] , abelian gauge symmetries [ref] , and non-abelian gauge symmetries [ref] .
A natural and simple UV completion of the QCD axion model · Introduction · 0.92
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The bias is in principle a free parameter that should be added to the model, and the phenomenology of the DW network can change drastically depending on its size, In general, one can expect this to come from quantum gravity effects that make the starting $U(1)$ global symmetry only approximate [ref] .
Axionic domain walls at Pulsar Timing Arrays: QCD bias and particle friction · ALP domain walls · 0.80
Discussion
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