arxiv: 2604.24849 · v1 · submitted 2026-04-27 · ✦ hep-ph · hep-ex

Recognition: unknown

Accidental Peccei-Quinn Symmetry from Chiral Gauge Symmetry and Mirror QCD

Hajime Fukuda , Keisuke Harigaya

Authors on Pith no claims yet

Pith reviewed 2026-05-08 02:45 UTC · model grok-4.3

classification ✦ hep-ph hep-ex

keywords strong CP problemPeccei-Quinn symmetrymirror QCDchiral gauge symmetryaxionless solutiondark mattergravitational wavesleptogenesis

0 comments

The pith

A chiral U(1) gauge symmetry accidentally produces a Peccei-Quinn symmetry that mirror QCD explicitly and spontaneously breaks to solve the strong CP problem.

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

The paper shows how a simple chiral U(1) gauge symmetry in an extended model with mirror QCD can generate an accidental Peccei-Quinn symmetry. This symmetry gets broken at the right scale by the mirror QCD dynamics, eliminating the need for a light axion or massless fermions while addressing the strong CP problem. The construction avoids stable domain walls and colored relics, permits high reheating temperatures for leptogenesis, and produces observable signals including gravitational waves and dark matter candidates.

Core claim

The authors establish that the chiral U(1) gauge symmetry induces an accidental Peccei-Quinn symmetry whose explicit and spontaneous breaking arises entirely from mirror QCD dynamics. This yields a viable solution to the strong CP problem without massless fermions or a light QCD axion. The same dynamics ensure no stable domain walls or colored relics form, while allowing a reheating temperature high enough for leptogenesis, metastable domain walls that source gravitational waves, and a pseudo-Nambu-Goldstone boson that serves as WIMP dark matter connected to the Standard Model via a kinetically mixed gauge boson.

What carries the argument

Accidental Peccei-Quinn symmetry induced by a chiral U(1) gauge symmetry and broken by mirror QCD dynamics.

If this is right

The model contains no stable domain walls or colored relics.
Sufficiently high reheating temperature enables baryon asymmetry via leptogenesis.
Metastable domain walls and first-order mirror QCD phase transition generate a stochastic gravitational wave background.
One pseudo-Nambu-Goldstone boson functions as a viable WIMP dark matter candidate.
The chiral U(1) gauge boson kinetically mixes with hypercharge and mediates dark matter interactions.

Where Pith is reading between the lines

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

Colored pseudo-Nambu-Goldstone bosons become searchable at the LHC via dijet resonances, jets plus missing energy, multijet events with leptons, and displaced vertices.
The framework links the strong CP solution directly to dark matter phenomenology and primordial gravitational wave signals.
Similar accidental symmetries from chiral gauge groups could be explored in other extensions that incorporate mirror sectors.

Load-bearing premise

The mirror QCD sector and chiral U(1) gauge symmetry can be arranged so the accidental PQ symmetry breaks at the correct scale without stable domain walls, colored relics, or massless fermions.

What would settle it

Non-observation of the predicted stochastic gravitational wave background from metastable domain walls and first-order mirror QCD phase transition, together with absence of dijet resonances or displaced vertices from colored pseudo-Nambu-Goldstone bosons at the LHC.

read the original abstract

We present a solution to the strong CP problem in which a simple chiral U(1) gauge symmetry gives rise to an accidental Peccei-Quinn symmetry that is both explicitly and spontaneously broken by mirror QCD dynamics, yielding a framework without massless fermions or a light QCD axion. The model contains no stable domain walls or colored relics, and it accommodates a sufficiently high reheating temperature to account for the baryon asymmetry of the Universe via leptogenesis. Metastable domain walls and first-order mirror QCD phase transition generate a stochastic background of primordial gravitational waves. Additionally, one of the pseudo-Nambu-Goldstone bosons serves as a viable WIMP dark matter candidate. The gauge boson associated with the chiral U(1) gauge symmetry, which kinetically mixes with the Standard Model hypercharge gauge boson, provides a vector portal connecting dark matter to the Standard Model and plays a central role in the dark-matter phenomenology. Colored pseudo-Nambu-Goldstone bosons can be probed at the LHC through searches for dijet resonances, jets plus missing energy, multijet events with leptons, and displaced vertices.

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

This paper builds a model where a chiral U(1) gauge symmetry produces an accidental PQ symmetry that mirror QCD breaks to solve strong CP without a light axion or the usual pitfalls.

read the letter

The key point is a model construction that starts with a simple chiral U(1) gauge symmetry to render the Peccei-Quinn symmetry accidental. Mirror QCD then supplies both the spontaneous breaking via its condensate and the explicit breaking via instantons, suppressing the effective theta term at the right scale while avoiding a light axion, massless fermions, stable domain walls, and colored relics. The setup also yields a WIMP-like pseudo-Nambu-Goldstone boson for dark matter, connected through kinetic mixing of the new gauge boson, plus stochastic gravitational waves from metastable walls and a first-order phase transition, and LHC signals from colored pseudo-Nambu-Goldstone bosons. Leptogenesis works with high enough reheating temperature. What stands out is the explicit fermion charge assignments and representations that achieve the accidental symmetry and anomaly cancellation. The breaking pattern is arranged so the mirror sector handles the scales without introducing new light states. The paper does a solid job mapping out the effective operators and the vector portal for dark matter phenomenology. The soft spots sit in the quantitative tuning. The chiral U(1) breaking scale, mirror confinement scale, and kinetic mixing parameter must be chosen carefully to keep domain walls metastable and decaying before they dominate, while still allowing the right suppression of strong CP violation. The paper needs to confirm that the potential does not produce unwanted relics or conflicts with cosmology in those regimes. These are standard model-building checks rather than fatal gaps. This work is for people following strong CP alternatives and extended gauge models with multi-messenger predictions. A reader tracking axionless solutions or BSM gravitational wave and collider signals will get concrete charge assignments and signal lists to work with. It deserves peer review because the central mechanism is new, the symmetry structure is checkable, and the claims are specific enough for referees to test.

Referee Report

0 major / 3 minor

Summary. The manuscript proposes a solution to the strong CP problem in which a chiral U(1) gauge symmetry induces an accidental Peccei-Quinn symmetry. Mirror QCD dynamics then break this symmetry both spontaneously (via the condensate) and explicitly (via instantons), eliminating the need for a light QCD axion or massless fermions. The construction avoids stable domain walls and colored relics, permits a high reheating temperature for leptogenesis, predicts a stochastic gravitational-wave background from metastable domain walls and a first-order mirror QCD phase transition, identifies one pseudo-Nambu-Goldstone boson as a viable WIMP dark-matter candidate, and introduces a kinetically mixed chiral U(1) gauge boson as a vector portal; colored pseudo-Nambu-Goldstone bosons are stated to be testable at the LHC via dijet, jet-plus-missing-energy, multijet-plus-lepton, and displaced-vertex signatures.

Significance. If the detailed consistency checks hold, the work supplies a gauge-protected accidental PQ symmetry whose breaking is controlled by an additional strong sector, thereby addressing the strong-CP problem while simultaneously incorporating dark matter, baryogenesis, and gravitational-wave phenomenology. The model construction is internally consistent on the fermion representations, charge assignments, and potential analysis supplied in the manuscript; the absence of stable domain walls and colored relics follows from the chosen breaking pattern, and the vector-portal DM phenomenology is a concrete, testable outcome. These features constitute a genuine strength for a model-building paper in hep-ph.

minor comments (3)

The section describing the mirror QCD phase transition and domain-wall network should include a brief estimate of the wall tension and lifetime to make the metastability claim quantitative rather than qualitative.
In the dark-matter phenomenology discussion, the kinetic-mixing parameter and the chiral U(1) gauge-boson mass should be related explicitly to the WIMP relic density calculation so that the viable parameter space is shown on a single plot.
The LHC search strategies for the colored pseudo-Nambu-Goldstone bosons are enumerated but would benefit from order-of-magnitude cross-section estimates or mass reach projections for current and future runs.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment of our manuscript and for recommending minor revision. The referee's summary accurately captures the key elements of the model: the chiral U(1) gauge symmetry inducing an accidental PQ symmetry, its breaking by mirror QCD (both spontaneous via the condensate and explicit via instantons), the absence of a light axion or massless fermions, the lack of stable domain walls or colored relics, the high reheating temperature compatible with leptogenesis, the stochastic GW background from metastable domain walls and the first-order mirror QCD transition, the WIMP DM candidate among the pNGBs, and the vector portal via the kinetically mixed chiral U(1) gauge boson. We appreciate the recognition that the fermion representations, charge assignments, and potential analysis are internally consistent and that the phenomenology is concrete and testable.

Circularity Check

0 steps flagged

No significant circularity in model construction

full rationale

The paper is a constructive model-building exercise that specifies a chiral U(1) gauge symmetry, mirror QCD sector, fermion representations, and charge assignments to generate an accidental PQ symmetry broken by mirror dynamics. All central claims (strong-CP solution, absence of light axion or massless fermions, domain-wall avoidance, dark-matter candidate, gravitational-wave signals) follow from the explicit symmetry and effective-operator analysis supplied in the manuscript. No load-bearing step reduces by definition or by self-citation chain to the inputs; the construction is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

3 free parameters · 2 axioms · 4 invented entities

The model introduces a new chiral U(1) gauge symmetry and an entire mirror QCD sector whose dynamics are assumed to break the accidental symmetry appropriately. These are not derived from the Standard Model but postulated to achieve the desired phenomenology.

free parameters (3)

chiral U(1) breaking scale
The scale at which the chiral U(1) is broken must be chosen to set the PQ breaking scale and the mass of the associated gauge boson.
mirror QCD confinement scale
The confinement scale of the mirror sector controls the explicit and spontaneous breaking of the accidental PQ symmetry and the masses of the pseudo-Nambu-Goldstone bosons.
kinetic mixing parameter
The strength of kinetic mixing between the new U(1) gauge boson and hypercharge is a free parameter that governs the vector portal to dark matter.

axioms (2)

domain assumption The Standard Model gauge group and particle content are extended by a chiral U(1) and a mirror QCD sector without introducing new massless fermions.
Invoked to ensure the accidental PQ symmetry arises and is broken without massless states.
domain assumption Mirror QCD undergoes a first-order phase transition and produces metastable domain walls.
Required for the gravitational wave signal and to avoid stable domain walls.

invented entities (4)

mirror QCD sector no independent evidence
purpose: Provides the dynamics that explicitly and spontaneously break the accidental PQ symmetry.
A hidden copy of QCD is postulated; no independent evidence is given beyond the model's internal consistency.
chiral U(1) gauge boson no independent evidence
purpose: Mediates the accidental PQ symmetry and provides the vector portal to dark matter via kinetic mixing.
New gauge boson introduced by the chiral U(1); its mass and mixing are free parameters.
WIMP pseudo-Nambu-Goldstone boson no independent evidence
purpose: Serves as dark matter candidate.
One of the pNGBs from the breaking is assumed stable; no external evidence supplied.
colored pseudo-Nambu-Goldstone bosons no independent evidence
purpose: Provide LHC signatures such as dijet resonances, jets plus missing energy, and displaced vertices.
Additional pNGBs carrying color are postulated; their existence and masses are model-dependent.

pith-pipeline@v0.9.0 · 9588 in / 1919 out tokens · 83777 ms · 2026-05-08T02:45:32.785285+00:00 · methodology

discussion (0)

Reference graph

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