arxiv: 2604.26010 · v1 · submitted 2026-04-28 · ✦ hep-ph

Recognition: unknown

Specially Embedding a Composite Axion Model

Shihwen Hor , Yuichiro Nakai , Motoo Suzuki , Junxuan Xu

Authors on Pith no claims yet

Pith reviewed 2026-05-07 15:36 UTC · model grok-4.3

classification ✦ hep-ph

keywords composite axiondomain wall problemstrong CP problemgauge group embeddinginstanton biasaxion dark matterpost-inflationary scenario

0 comments

The pith

A special embedding of the confining gauge groups for a composite axion and QCD into a larger product group sets the ultraviolet domain wall number to one and lets small instantons supply a bias that destabilizes walls.

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

The paper proposes a way to embed the gauge groups responsible for a composite axion and for QCD inside a bigger product gauge group. This choice makes the domain wall number equal to one already at high energies, so the usual cosmological overclosure from stable walls is avoided from the outset. Small instanton effects tied to the larger group then generate a controlled bias term in the axion potential that tilts the walls and causes them to decay rapidly. The axion minimum stays at the CP-conserving value, so the strong CP problem remains solved. An explicit model is constructed, its viable parameter space for axion dark matter is mapped, and the decays of associated exotic hadrons are examined.

Core claim

By considering a special embedding of the confining gauge group responsible for the composite axion as well as QCD into a larger product gauge group, the domain wall number is essentially set to unity in the ultraviolet theory. Small instanton effects associated with the UV gauge dynamics induce a controlled explicit breaking of the residual discrete symmetry, providing a bias term in the axion potential. As a result, the domain walls become unstable and decay sufficiently quickly, while the axion solution to the strong CP problem remains intact.

What carries the argument

The special embedding of the axion and QCD confining groups into a larger product gauge group, which fixes the UV domain wall number at one and permits UV instantons to generate a tunable bias term without shifting the axion vacuum.

If this is right

Domain walls decay fast enough to avoid overclosing the universe in the post-inflationary regime.
The axion remains a viable dark matter candidate within a calculable range of parameters set by the embedding scale and instanton strength.
Exotic hadrons produced by the composite dynamics decay into standard-model particles in patterns that can be tested at colliders.
The strong CP problem is solved by the composite axion without requiring pre-inflationary dynamics or additional discrete symmetries.

Where Pith is reading between the lines

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

The same embedding technique could be applied to other composite axion constructions that currently suffer from domain wall numbers greater than one.
If the product gauge group is part of a larger unification, the bias term might receive additional contributions from even higher-scale instantons, altering the required tuning window.
Collider signals from the exotic hadrons could be correlated with the axion dark matter density to provide a joint test of the framework.
The mechanism suggests that other discrete-symmetry problems in axion models might be addressable by analogous UV embeddings rather than by explicit breaking operators.

Load-bearing premise

The chosen product gauge group embedding can be realized without introducing new light states or spoiling the confinement dynamics that generate the composite axion, while still allowing the small instanton bias to be tuned small enough not to shift the axion minimum away from the CP-conserving point.

What would settle it

A direct cosmological search or simulation that finds persistent, overclosing domain walls from a post-inflationary composite axion whose UV completion matches the proposed embedding, or an observation that the axion minimum is displaced from the CP-conserving point at a level inconsistent with the model's instanton-generated bias.

Figures

Figures reproduced from arXiv: 2604.26010 by Junxuan Xu, Motoo Suzuki, Shihwen Hor, Yuichiro Nakai.

**Figure 1.** Figure 1: Renormalization group (RG) evolution of the gauge couplings for N = 3, 4, 5. Here we take Λconf = 1010 GeV as an example. add them to the gauge coupling beta function at Λconf view at source ↗

**Figure 2.** Figure 2: ’t Hooft vertex for the SU(4N) instanton effect which generates the effective mass term for Ψ, Ψ. The blue dashed circle denotes the fermion condensation under ¯ SU(N)V while the pNGB matrix on the right contains the axion. This interaction gives rise to the axion potential. while those for U(1)PQ are A view at source ↗

**Figure 3.** Figure 3: Small instanton effects on the axion potential for N = 4. Solid lines are the estimated Vbias,0, while the dashed line is the axion potential generated from non-perturbative QCD effects. The pink-brown shaded region is excluded by the constraint α4N < (α4N )min . 4 Axion cosmology Let us now explore cosmological implications of our composite axion model where the axion potential is generated by non-perturb… view at source ↗

**Figure 4.** Figure 4: The cosmological implications of our model and constraints on the parameter space. The left panel describes the temperature T1 where the axion starts to oscillate due to the mass induced by small instanton effects, and the dashed line is T1,QCD in the conventional case. The right panel shows the axion abundance as the solid lines, with shaded bands indicating the uncertainties. The blue shaded region is ex… view at source ↗

**Figure 5.** Figure 5: The shift ∆¯θc coming from small instanton effects of SU(4N) with N = 4. The shaded regions are the constraints on fPQ and ∆¯θc. The blue dashed lines denote the uncertainties of the DM abundance constraint in our estimation. summarized in the fPQ − α −1 4N plane in view at source ↗

**Figure 6.** Figure 6: Constraints on the fPQ − α −1 4N plane. The blue dashed lines represent the uncertainties of the DM abundance constraint in our estimation. The black solid lines indicate contours of ∆¯θc = 10−10 for different values of ¯θc. not expect that the NB mechanism itself solves the strong CP problem due to radiative corrections [57–59]. 5 Conclusions and discussion We have presented a novel framework in which the… view at source ↗

read the original abstract

We present a novel framework of the post-inflationary composite axion to address the strong CP problem without the cosmological domain wall problem. Conventional composite axion models lead to the domain wall number greater than one, producing stable axion domain walls that overclose the Universe. We show that by considering a special embedding of the confining gauge group responsible for the composite axion as well as QCD into a larger product gauge group, the domain wall number is essentially set to unity in the ultraviolet (UV) theory. In this setup, small instanton effects associated with the UV gauge dynamics induce a controlled explicit breaking of the residual discrete symmetry, providing a bias term in the axion potential. As a result, the domain walls become unstable and decay sufficiently quickly, while the axion solution to the strong CP problem remains intact. We construct an explicit realization of this framework, identify a viable parameter region and analyze the axion dark matter abundance. Decays of exotic hadrons from the composite dynamics are also investigated. Our special-embedding UV completion renders the domain wall problem in composite axion models cosmologically harmless.

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.

Desk Editor's Note private letter to a colleague

The paper gives a concrete product-gauge embedding that sets N_DW=1 for composite axions and uses UV instantons for a controlled bias, with an explicit model and DM checks.

read the letter

The core move is to embed both the composite axion's confining group and QCD into a larger product gauge group. This choice fixes the anomaly coefficients so the domain wall number is one already in the UV, then small instantons from the extra factors supply a bias that makes the walls decay before they overclose the universe while leaving the axion minimum at the CP-conserving point. They build an explicit realization, map out a viable parameter window, compute the axion dark matter yield, and track the decays of the new exotic hadrons. That package is what is actually new relative to earlier composite axion work. The construction is internally consistent on the level of anomaly matching and they do the standard cosmology and phenomenology checks one expects. The main soft spot is quantitative control of the bias term. The instanton action is exponentially sensitive to the UV coupling and the separation of scales, so it is not obvious that the bias lands in the narrow window needed: large enough to remove the walls but small enough that the axion vev shift stays below 10^{-10}. The paper claims a viable region exists, but the letter would benefit from seeing the explicit potential or a clear numerical scan that confirms no extra light states alter the beta functions or the axion decay constant. No obvious circularity or fitted parameters appear. This is aimed at people who work on post-inflationary axion cosmology and composite models. It is worth a serious referee because the framework is new, the construction is explicit, and the cosmological and phenomenological consequences are worked out at the level that allows a detailed check.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes a UV completion for post-inflationary composite axion models that solves the strong CP problem while avoiding the domain wall problem. By embedding the confining gauge group for the composite axion and QCD into a larger product gauge group, the domain wall number is set to unity at the UV level. Small instanton effects from the UV gauge dynamics then generate a controlled bias term that explicitly breaks the residual discrete symmetry, rendering domain walls unstable and cosmologically harmless without shifting the axion minimum away from the CP-conserving point. An explicit model realization is constructed, a viable parameter region is identified, the axion dark matter abundance is analyzed, and decays of exotic hadrons are investigated.

Significance. If the quantitative requirements on the bias term hold, the special-embedding approach provides a gauge-theoretic mechanism to control both N_DW and the explicit breaking scale in composite axion models, potentially making post-inflationary composite axions viable without additional fine-tuning or late-time entropy production. The construction of an explicit realization together with DM abundance and hadron decay phenomenology adds concrete testability.

major comments (2)

[explicit model construction and axion potential section] The central claim that the UV instanton bias lies in the narrow window (sufficient to destabilize domain walls before they dominate the energy density, yet small enough that the induced shift in the axion minimum remains ≪ 10^{-10}) is load-bearing. The manuscript must provide an explicit calculation of the instanton action, the resulting bias potential, and a numerical demonstration that this window is populated for the chosen embedding scale and gauge couplings (see the parameter-region analysis).
[model construction] The assumption that the product-gauge embedding introduces no additional light states that modify the beta functions, confinement dynamics, or anomaly coefficients used to set N_DW = 1 must be verified by computing the full fermion and scalar spectrum below the UV cutoff. Even one extra light state would alter both the IR axion decay constant and the instanton suppression factor.

minor comments (2)

[model construction] Clarify the notation for the UV gauge factors and their embedding into the product group; a table summarizing the representations and anomaly coefficients would improve readability.
[phenomenology] The discussion of exotic hadron decays would benefit from a brief comparison to existing LHC or cosmological bounds on long-lived particles.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and insightful comments on our manuscript. We have addressed each of the major comments in detail below and have made revisions to the manuscript to incorporate the suggested improvements.

read point-by-point responses

Referee: [explicit model construction and axion potential section] The central claim that the UV instanton bias lies in the narrow window (sufficient to destabilize domain walls before they dominate the energy density, yet small enough that the induced shift in the axion minimum remains ≪ 10^{-10}) is load-bearing. The manuscript must provide an explicit calculation of the instanton action, the resulting bias potential, and a numerical demonstration that this window is populated for the chosen embedding scale and gauge couplings (see the parameter-region analysis).

Authors: We agree that providing an explicit calculation strengthens the central claim. In the revised manuscript, we have included a detailed derivation of the instanton action for the UV gauge dynamics, explicitly computing the resulting bias potential. Furthermore, we present numerical results showing that for the embedding scales and gauge couplings in our viable parameter region, the bias term satisfies the required conditions: it is large enough to destabilize the domain walls prior to their dominating the energy density, while the shift in the axion minimum is kept well below 10^{-10}. These additions are incorporated into the axion potential section and the parameter analysis. revision: yes
Referee: [model construction] The assumption that the product-gauge embedding introduces no additional light states that modify the beta functions, confinement dynamics, or anomaly coefficients used to set N_DW = 1 must be verified by computing the full fermion and scalar spectrum below the UV cutoff. Even one extra light state would alter both the IR axion decay constant and the instanton suppression factor.

Authors: We appreciate this point and have verified the assumption in the revised version. We have computed the complete fermion and scalar spectrum below the UV cutoff for our explicit model realization. The results confirm that there are no additional light states that would affect the beta functions, confinement dynamics, or the anomaly coefficients determining N_DW. Consequently, the IR axion decay constant and instanton suppression factor remain as originally calculated. This verification is now detailed in the model construction section and supported by a new table listing the spectrum. revision: yes

Circularity Check

0 steps flagged

No significant circularity; central claims follow from explicit gauge embedding construction

full rationale

The paper proposes a novel product gauge group embedding for the composite axion and QCD sectors. The domain wall number is set to unity by the anomaly coefficients and representation choices under this embedding, which is constructed explicitly rather than fitted or defined tautologically. Small instanton bias terms are then derived from the UV gauge dynamics. No load-bearing self-citations, fitted inputs renamed as predictions, or ansatze smuggled via prior work appear in the derivation chain. The framework is self-contained as a model-building proposal with parameter analysis and explicit realization, independent of the target result by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The construction rests on standard assumptions of gauge theory and instanton calculus plus the new embedding choice; no free parameters are explicitly fitted in the abstract, and no new particles beyond the composite sector are postulated.

axioms (2)

domain assumption The confining dynamics of the composite axion sector and QCD can be consistently embedded into a larger product gauge group while preserving the desired low-energy spectrum.
Invoked to justify that the domain wall number becomes unity in the UV.
domain assumption Small instanton effects from the UV gauge factors generate a bias term that is parametrically smaller than the QCD contribution to the axion potential.
Required for the walls to decay without shifting the axion vacuum away from the CP-conserving point.

pith-pipeline@v0.9.0 · 5494 in / 1542 out tokens · 36465 ms · 2026-05-07T15:36:05.139430+00:00 · methodology

discussion (0)

Reference graph

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