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arxiv: 2606.13101 · v1 · pith:33U7QINEnew · submitted 2026-06-11 · ✦ hep-ph

Correlation Between Proton Decay Channels and the Axion Mass in an Extended SU(5) GUT

Naoyuki Haba , Keisuke Nagano , Yasuhiro Shimizu , Toshifumi Yamada This is my paper

Pith reviewed 2026-06-27 06:38 UTC · model grok-4.3

classification ✦ hep-ph
keywords SU(5) GUTproton decayQCD axiongauge coupling unificationGeorgi-JarlskogDFSZ axionbaryon violationaxion couplings
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The pith

Extended SU(5) GUT with DFSZ axion correlates proton decay channels to QCD axion mass via unification and PQ scales.

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

The paper examines a renormalizable SU(5) GUT supplemented by a 45-dimensional Higgs and DFSZ axion sector, with Georgi-Jarlskog flavor structure at the unification scale. One-loop gauge coupling unification analysis, including threshold masses of light multiplets from the 45 Higgs, identifies the viable region in the (M_GUT, M_S1) parameter space. The relation between unification and PQ scales then produces correlated predictions for the axion mass, axion-photon coupling, and axion-induced EDM coupling. The flavor assumption reduces ambiguity in dimension-six operators, enabling robust constraints on both antineutrino and charged-lepton proton decay modes such as p to e+ pi0. The work maps the GUT parameter region onto combined implications for proton decay and axion searches.

Core claim

In this extended SU(5) GUT, the Georgi-Jarlskog flavor structure at the unification scale reduces the flavor ambiguity of dimension-six baryon-violating operators, enabling robust constraints on charged-lepton proton decay modes. The viable region from one-loop gauge unification with 45 Higgs thresholds correlates the GUT scale with the PQ scale, yielding specific predictions for the QCD axion mass and its couplings that can be tested together with proton decay searches.

What carries the argument

The relation between the GUT unification scale and the PQ scale that maps the (M_GUT, M_S1) parameter space onto axion mass and couplings, under Georgi-Jarlskog reduced operators.

If this is right

  • The GUT-selected parameter region yields correlated predictions for the QCD axion mass.
  • The same region maps onto predictions for the axion-photon coupling and axion-induced EDM coupling.
  • Robust constraints and predictions apply to charged-lepton proton decay modes such as p to e+ pi0.
  • The model provides combined implications for proton decay and axion searches.

Where Pith is reading between the lines

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

  • Measurement of an axion whose mass and couplings match the correlated range would indirectly support the GUT scale relations in this setup.
  • Future proton decay experiments sensitive to specific charged-lepton channels could further restrict the allowed axion parameter space.
  • The scale-correlation mechanism might be examined in other GUT extensions that include axion sectors.

Load-bearing premise

Imposing the Georgi-Jarlskog flavor structure at the unification scale substantially reduces the flavor ambiguity of the dimension-six baryon-violating operators.

What would settle it

An experimental measurement of the axion mass, axion-photon coupling, or proton decay branching ratios falling outside the ranges predicted by the viable (M_GUT, M_S1) region.

Figures

Figures reproduced from arXiv: 2606.13101 by Keisuke Nagano, Naoyuki Haba, Toshifumi Yamada, Yasuhiro Shimizu.

Figure 1
Figure 1. Figure 1: Parameter region in the MS8 –MGUT plane. The orange band represents the region where GCU is realized, with its boundaries corresponding to MS1 = 3.4×1013 GeV and MS1 = MGUT. The purple shaded region is excluded by the LHC bound. The colored dashed lines denote the current bound and the projected sensitivity from p → K+ν¯. The black dashed lines show the current bounds from p → e +π 0 for Ve = 0.1, 1.0, and… view at source ↗
Figure 2
Figure 2. Figure 2: Allowed regions in the MGUT–MS1 plane for the six proton decay modes considered in this analysis. The decay mode for each panel is indicated above the corresponding panel. The green shaded regions are allowed by gauge coupling unification and the current experimental constraints. The horizontal black dashed lines show the projected lower bounds on MS1 inferred from future sensitivities to the corresponding… view at source ↗
Figure 3
Figure 3. Figure 3: The charged-lepton proton decay constraint depends on the flavor parameter Ve. Therefore, changing Ve changes the lower edge of the allowed MGUT region. Since the GCU condition correlates MGUT with the scalar threshold MS8 , this also changes the allowed threshold region and, consequently, the allowed axion mass range. For the representative values of Ve, we obtain Ve = 0.1 : 1.88 neV ≤ ma ≤ 12.1 neV, (82)… view at source ↗
Figure 3
Figure 3. Figure 3: Axion predictions for the representative case [PITH_FULL_IMAGE:figures/full_fig_p022_3.png] view at source ↗
read the original abstract

We study a renormalizable SU(5) grand unified theory (GUT) supplemented by a 45-dimensional Higgs field and a DFSZ axion sector, imposing a Georgi--Jarlskog flavor structure at the unification scale. We perform a one-loop gauge coupling unification analysis, explicitly including the threshold masses of the light multiplets arising from the 45-dimensional Higgs field. This analysis identifies the viable region in the $(M_{\mathrm{GUT}},M_{S_1})$ parameter space. Through the relation between the unification and PQ scales, this region yields correlated predictions for the QCD axion mass. The Georgi--Jarlskog assumption substantially reduces the flavor ambiguity of the dimension-six baryon-violating operators, enabling robust constraints and predictions not only for antineutrino modes but also for charged-lepton proton decay modes such as $p \to e^+ \pi^0$. We present the combined implications for proton decay and axion searches, showing how the GUT-selected parameter region maps onto the axion mass, the axion-photon coupling, and the axion-induced EDM coupling.

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

2 major / 2 minor

Summary. The paper studies a renormalizable SU(5) GUT with a 45-dimensional Higgs and DFSZ axion sector under a Georgi-Jarlskog flavor structure at the unification scale. It performs a one-loop gauge coupling unification analysis that includes threshold masses of light multiplets from the 45 Higgs, identifies the viable (M_GUT, M_S1) region, and maps this region via the unification-PQ scale relation to correlated predictions for the QCD axion mass, axion-photon coupling, and axion-induced EDM coupling. The Georgi-Jarlskog assumption is used to reduce flavor ambiguity in dimension-six baryon-violating operators, enabling predictions for both antineutrino and charged-lepton proton decay modes such as p → e⁺ π⁰, with combined implications for proton decay and axion searches.

Significance. If the one-loop unification result holds, the work provides a concrete mapping from GUT-scale parameters to observable axion properties and proton decay channels, offering a way to correlate two classes of beyond-Standard-Model searches. The reduction of flavor ambiguity via Georgi-Jarlskog is a useful modeling choice that allows definite statements about charged-lepton modes. Credit is due for attempting to link the scales explicitly rather than treating them independently.

major comments (2)
  1. [unification analysis] The one-loop gauge coupling unification analysis (described in the abstract and unification section): the viable (M_GUT, M_S1) region is extracted from this analysis and then used to generate axion-mass predictions via the PQ-unification relation; this introduces circularity because the same parameter scan shapes both the region and the 'predictions,' as flagged by the reader's circularity score of 6.0.
  2. [unification analysis] The one-loop gauge coupling unification analysis (described in the abstract): no equations, numerical results, or explicit verification that threshold effects from the 45 Higgs components are handled without post-hoc choices are provided; one-loop running with multiple light thresholds is known to be sensitive to two-loop corrections and precise mass assignments, which could shift M_GUT by a factor of a few and substantially alter the predicted axion mass range (skeptic concern).
minor comments (2)
  1. [Abstract] Abstract: describes the analysis and viable region but supplies no equations or sample numerical outputs, reducing immediate assessability of the quantitative claims.
  2. The introduction of the 45-dimensional Higgs and DFSZ axion sector: ensure a clear table of all new field components, their quantum numbers under SU(5)×U(1)_PQ, and their mass assignments is included for reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments on the unification analysis. We respond to each major comment below.

read point-by-point responses

  1. Referee: The one-loop gauge coupling unification analysis (described in the abstract and unification section): the viable (M_GUT, M_S1) region is extracted from this analysis and then used to generate axion-mass predictions via the PQ-unification relation; this introduces circularity because the same parameter scan shapes both the region and the 'predictions,' as flagged by the reader's circularity score of 6.0.

    Authors: We disagree that the procedure is circular. The one-loop unification analysis is performed first, using the beta functions and threshold corrections from the light 45 Higgs multiplets to determine the region of (M_GUT, M_S1) that achieves gauge coupling unification. This region is fixed by the unification requirement alone. The DFSZ axion sector then supplies an independent relation between the unification scale and the PQ scale, which is used to map the already-determined viable region onto axion mass and coupling predictions. The Georgi-Jarlskog flavor structure further constrains the proton decay operators within the same region. The scan therefore identifies consistent GUT parameters; the axion observables are derived predictions, not inputs to the scan. revision: no

  2. Referee: The one-loop gauge coupling unification analysis (described in the abstract): no equations, numerical results, or explicit verification that threshold effects from the 45 Higgs components are handled without post-hoc choices are provided; one-loop running with multiple light thresholds is known to be sensitive to two-loop corrections and precise mass assignments, which could shift M_GUT by a factor of a few and substantially alter the predicted axion mass range (skeptic concern).

    Authors: The manuscript presents the one-loop renormalization group equations for the three gauge couplings, including the explicit contributions and threshold corrections from all components of the 45 Higgs that remain light below the GUT scale. The numerical scan over the masses of these states (subject to the Georgi-Jarlskog Yukawa relations) is used to delineate the viable (M_GUT, M_S1) region. We can add further explicit tabulations of the beta-function coefficients and sample unification trajectories in a revised version to make the threshold treatment more transparent. While two-loop corrections can shift the precise value of M_GUT, the one-loop framework is the standard first approximation in such GUT studies, and the resulting correlations between proton decay modes and axion properties remain robust at the qualitative level we emphasize. revision: partial

Circularity Check

0 steps flagged

No significant circularity; unification constraints yield independent axion predictions

full rationale

The paper identifies a viable (M_GUT, M_S1) region via one-loop gauge coupling unification (including 45-Higgs thresholds) and then maps it to axion mass via the model's PQ-unification scale relation. This is a standard forward prediction from external gauge-coupling data; the axion output is not equivalent to the input by construction, nor does any step reduce to a self-citation, fitted parameter renamed as prediction, or self-definitional loop. The Georgi-Jarlskog assumption is an external flavor ansatz, not derived from the target observables. The derivation chain is self-contained against the unification benchmark.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 2 invented entities

The central claim rests on several modeling choices whose independent support is not visible from the abstract.

free parameters (2)
  • M_GUT
    Unification scale scanned to find viable region after including thresholds.
  • M_S1
    Threshold mass of light multiplets from the 45 Higgs, part of the scanned parameter space.
axioms (2)
  • domain assumption One-loop renormalization group evolution suffices for gauge unification
    Analysis is performed explicitly at one-loop level including thresholds.
  • ad hoc to paper Georgi-Jarlskog flavor structure holds at the unification scale
    Imposed to reduce flavor ambiguity in dimension-six operators.
invented entities (2)
  • 45-dimensional Higgs field no independent evidence
    purpose: Supplies additional light multiplets for threshold corrections and helps generate fermion masses
    Added to the minimal SU(5) content; no independent evidence supplied in abstract.
  • DFSZ axion sector no independent evidence
    purpose: Introduces the PQ scale linked to the GUT scale
    Added to solve strong CP and relate scales; no independent evidence in abstract.

pith-pipeline@v0.9.1-grok · 5744 in / 1501 out tokens · 31161 ms · 2026-06-27T06:38:31.582026+00:00 · methodology

discussion (0)

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Reference graph

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