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arxiv: 2607.02026 · v1 · pith:VUQ2H466new · submitted 2026-07-02 · ✦ hep-ph

One-loop proton decay from Peccei-Quinn symmetry

H. B. C\^amara This is my paper

Pith reviewed 2026-07-03 10:54 UTC · model grok-4.3

classification ✦ hep-ph
keywords Peccei-Quinn symmetryproton decayvector-like quarksaxionstrong CP problemZ2 symmetryone-loop processesKSVZ axion
0
0 comments X

The pith

Promoting the Standard Model B+L symmetry to Peccei-Quinn symmetry with vector-like quarks induces one-loop proton decay while a residual Z2 forbids tree-level decay.

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

The paper establishes that vector-like quarks can generate the QCD anomaly for a Kim-Shifman-Vainshtein-Zakharov axion while a residual Z2 symmetry after Peccei-Quinn breaking blocks tree-level proton decay. The same quarks plus Z2-odd scalar mediators produce the effective operator u_R u_R d_R e_R at one loop, allowing radiative proton decay. Different choices of representations yield distinct axion-photon couplings that can be tested in helioscope and haloscope searches. The setup also predicts an extra decay channel containing an axion, suppressed by the Peccei-Quinn scale, and allows axion dark matter in both pre- and post-inflationary cosmologies. A sympathetic reader would care because the construction ties the solution to the strong CP problem directly to a controlled, loop-level proton decay signal.

Core claim

We promote the accidental B+L symmetry of the Standard Model to a Peccei-Quinn symmetry while realizing spontaneous proton decay radiatively. The PQ anomaly sector consists of vector-like quarks providing a KSVZ-type axion solution to the strong CP problem. After spontaneous PQ breaking a residual Z2 symmetry remains which forbids tree-level proton decay. The VLQs required to generate the QCD anomaly, together with scalar mediators odd under the residual Z2, induce one-loop proton decay through the effective operator u_R u_R d_R e_R. The resulting models lead to distinct predictions for the axion-to-photon coupling.

What carries the argument

The residual Z2 symmetry after PQ breaking, together with vector-like quarks and Z2-odd scalars that generate the one-loop effective operator u_R u_R d_R e_R.

If this is right

  • Different ultraviolet completions with distinct vector-like fermion and scalar representations produce different values of the axion-photon coupling testable in helioscope and haloscope experiments.
  • The model predicts the additional decay channel p to e+ pi0 a, suppressed by the PQ-breaking scale.
  • Axion dark matter can be realized consistently in both pre-inflationary and post-inflationary cosmological scenarios.

Where Pith is reading between the lines

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

  • Searches for the axion-accompanied proton decay mode could serve as a distinctive signature that separates this mechanism from conventional GUT-induced decays.
  • The same Z2-odd scalars that mediate the loop may open new channels for axion production in astrophysical environments.
  • The construction suggests that other accidental global symmetries of the Standard Model could be promoted to Peccei-Quinn-like symmetries with similar radiative decay implications.

Load-bearing premise

Vector-like fermion and scalar representations exist that satisfy the PQ anomaly condition, carry the required Z2 charges, and generate a viable one-loop diagram for the u_R u_R d_R e_R operator without introducing other unwanted effects.

What would settle it

Observation of proton decay in the e+ pi0 channel at a rate far above the loop-suppressed expectation, or failure to find the predicted axion-photon coupling in the range fixed by the same representations, would rule out the construction.

Figures

Figures reproduced from arXiv: 2607.02026 by H. B. C\^amara.

Figure 1
Figure 1. Figure 1: FIG. 1: One-loop box diagram generating the proton decay operator [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: One-loop proton (top) and neutron (bottom) two-body decays mediated by Ψ [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Axion-to-photon coupling [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
read the original abstract

We promote the accidental $B+L$ symmetry of the Standard Model to a Peccei-Quinn (PQ) symmetry while realizing spontaneous proton decay radiatively. The PQ anomaly sector consists of vector-like quarks (VLQs), providing a Kim-Shifman-Vainshtein-Zakharov-type axion solution to the strong CP problem. After spontaneous PQ breaking, a residual $\mathcal{Z}_2$ symmetry remains, which forbids tree-level proton decay. The VLQs required to generate the QCD anomaly, together with scalar mediators, odd under the residual $\mathcal{Z}_2$, induce one-loop proton decay through the effective operator $u_R u_R d_R e_R$. We study its ultraviolet completions, featuring distinct vector-like fermion and scalar representations, and show that the resulting models lead to distinct predictions for the axion-to-photon coupling, testable in helioscope and haloscope experiments. In addition to the proton decay channel $p \rightarrow e^+ \pi^0$, this framework predicts proton decay with an axion in the final state, $p \rightarrow e^+ \pi^0 a$, suppressed by the PQ-breaking scale. We also discuss axion dark matter in pre- and post-inflationary cosmology.

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

1 major / 2 minor

Summary. The paper promotes the SM's accidental B+L symmetry to a global PQ symmetry solved by vector-like quarks (VLQs) in a KSVZ-like setup. Spontaneous PQ breaking leaves a residual Z2 that forbids all tree-level ΔB=1 operators. The same VLQs, together with additional Z2-odd scalar mediators, generate a one-loop diagram for the effective operator u_R u_R d_R e_R, inducing proton decay. Explicit UV completions with different fermion and scalar representations are constructed; these yield distinct values of the axion-photon coupling g_aγγ and predict an additional channel p → e⁺ π⁰ a suppressed by the PQ scale. Axion dark-matter cosmology in pre- and post-inflationary scenarios is also discussed.

Significance. If the charge assignments and loop diagrams are viable, the work supplies a concrete mechanism that simultaneously addresses the strong-CP problem and renders proton decay radiative while protecting against tree-level violation. The explicit construction of multiple UV completions that produce distinguishable g_aγγ predictions (testable in helioscopes and haloscopes) and the additional axion-accompanied decay mode constitute clear strengths. The framework is falsifiable and links two otherwise separate phenomenological sectors.

major comments (1)
  1. [UV completions] UV-completion sections: the manuscript states that the chosen VLQ and scalar representations simultaneously satisfy the QCD anomaly condition, carry the required Z2 charges, and permit a one-loop diagram for u_R u_R d_R e_R without generating tree-level ΔB=1 operators. An explicit listing or table of all allowed operators generated by the new fields at dimension 6 and below would make this claim directly verifiable; without it the protection argument remains schematic.
minor comments (2)
  1. [Abstract / Introduction] The abstract and introduction refer to 'distinct predictions for the axion-to-photon coupling' but do not quote the numerical ranges or the functional dependence on the PQ scale; adding a short table or explicit expressions would improve clarity.
  2. [Model setup] Notation for the residual Z2 charges on the scalar mediators is introduced without a dedicated charge table; a compact table listing all new fields, their SM quantum numbers, PQ charges, and Z2 parities would aid the reader.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading and positive assessment of our work. The single major comment is constructive and we address it directly below. We will incorporate the requested addition in the revised manuscript.

read point-by-point responses

  1. Referee: [UV completions] UV-completion sections: the manuscript states that the chosen VLQ and scalar representations simultaneously satisfy the QCD anomaly condition, carry the required Z2 charges, and permit a one-loop diagram for u_R u_R d_R e_R without generating tree-level ΔB=1 operators. An explicit listing or table of all allowed operators generated by the new fields at dimension 6 and below would make this claim directly verifiable; without it the protection argument remains schematic.

    Authors: We agree that an explicit operator table would make the Z2 protection argument immediately verifiable. In the revised version we will add a new table (or subsection) that enumerates all gauge- and Z2-invariant operators involving the VLQs and Z2-odd scalars up to dimension 6. The table will explicitly show (i) the absence of any tree-level ΔB=1 operators, (ii) the presence of the required one-loop diagram for u_R u_R d_R e_R, and (iii) consistency with the QCD anomaly condition. This addition will be placed in the UV-completion sections and will not alter any numerical results or conclusions. revision: yes

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper constructs explicit UV completions by choosing vector-like fermion and scalar representations that simultaneously satisfy the PQ anomaly condition, residual Z2 charge assignments, and permit a one-loop diagram for the u_R u_R d_R e_R operator. The resulting axion-photon coupling predictions follow directly from the anomaly coefficients of those chosen representations rather than from any fitted parameter or self-citation chain. No load-bearing step reduces by construction to an input; the central claims remain independent of the target observables once the representations are fixed.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 1 invented entities

The construction rests on the existence of suitable VLQ representations for the anomaly and Z2-odd scalars for the loop; these are postulated without independent evidence beyond satisfying the stated conditions.

free parameters (1)
  • PQ breaking scale
    Suppresses the p -> e+ pi0 a channel; value not fixed by the abstract.
axioms (1)
  • domain assumption Vector-like quarks can be chosen to generate the required QCD anomaly while preserving a residual Z2 after PQ breaking.
    Invoked to enable both the axion and the one-loop decay.
invented entities (1)
  • Z2-odd scalar mediators no independent evidence
    purpose: To mediate the one-loop proton decay diagram together with VLQs.
    Introduced to realize the effective operator while respecting the residual symmetry.

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discussion (0)

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