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arxiv: 2604.11851 · v1 · submitted 2026-04-13 · ✦ hep-ph · hep-ex· hep-th

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Grand Unified Origin of Enhanced Scalar Couplings: Connecting Radiative Electroweak Symmetry Breaking to SO(10) Dynamics

Farrukh A. Chishtie
Authors on Pith no claims yet

Pith reviewed 2026-05-10 16:23 UTC · model grok-4.3

classification ✦ hep-ph hep-exhep-th
keywords SO(10)grand unificationradiative electroweak symmetry breakingHiggs quartic couplingthreshold correctionsColeman-Weinberg mechanismLandau polevacuum stability
0
0 comments X

The pith

The enhanced Higgs quartic coupling required for radiative electroweak symmetry breaking is generated by threshold corrections when the Standard Model is embedded in SO(10) grand unification.

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

The paper argues that the large enhancement factor needed to stabilize the electroweak vacuum under radiative breaking is not an arbitrary adjustment but follows from matching the Standard Model to an SO(10) theory at high energies. Portal couplings between the light Higgs doublet and heavy scalars in the 10, 126-bar, and 45 representations produce threshold corrections that raise the quartic coupling by a factor of roughly 5 to 10. This shifts the ultraviolet Landau pole to 1.5–2 × 10^16 GeV, which coincides with the expected grand-unification scale. The same classically scale-invariant GUT potential also lets the Coleman-Weinberg mechanism generate both the electroweak scale and the hierarchy between it and the unification scale.

Core claim

The coincidence between the ultraviolet cutoff demanded by radiative electroweak symmetry breaking and the grand-unification scale is explained by completing the Standard Model to SO(10). Threshold corrections from the heavy GUT scalars 10_H, 126bar_H, and 45_H generate the required enhancement of the Higgs quartic coupling at the matching scale. A scale-invariant scalar potential in the GUT sector then allows the Coleman-Weinberg mechanism to trigger the breaking and to account for the hierarchy.

What carries the argument

Threshold corrections to the Higgs quartic coupling from portal interactions between the light doublet and the heavy SO(10) scalar representations 10_H, 126bar_H, and 45_H

If this is right

  • The Standard Model effective description must break down near 2 × 10^16 GeV, above which the full SO(10) degrees of freedom become active.
  • The specific scalar content of SO(10) is constrained by the requirement to produce the observed enhancement while maintaining vacuum stability.
  • Both radiative electroweak breaking and the gauge hierarchy receive a dynamical explanation from the same scale-invariant GUT potential.
  • Precision measurements of the Higgs potential at future colliders can indirectly constrain the masses and couplings of the heavy GUT scalars.

Where Pith is reading between the lines

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

  • The mechanism suggests that searches for proton decay or leptoquarks in SO(10) models are linked to the same parameters that control the Higgs enhancement.
  • Similar threshold corrections could be examined in other grand-unified groups containing comparable scalar portals to the Higgs.
  • If the enhancement is confirmed, it would favor classically scale-invariant formulations of grand unification over models that introduce explicit mass scales by hand.

Load-bearing premise

The scheme conversion and scale-dependent running that convert the Coleman-Weinberg prediction of an enhancement factor near 7 into a value of k approximately 6 at the top-quark mass are accurate, and the SO(10) parameters can be chosen to produce this enhancement while satisfying all other constraints.

What would settle it

A complete renormalization-group study of a realistic SO(10) model that cannot generate an enhancement factor between 5 and 10 at the matching scale while preserving gauge unification and fermion mass relations would show the proposed connection does not hold.

read the original abstract

We propose that the enhanced Higgs quartic coupling required by radiatively broken electroweak symmetry (RBEWS) emerges naturally from SO(10) grand unification. Our previous analysis demonstrated that a coupling enhancement factor $k = \lambda_{\rm enhanced}/\lambda_{\rm SM}$ leads to absolute vacuum stability with a UV Landau pole near the GUT scale for $k \gtrsim 1.03$. The RBEWS prediction $e_{125} = 7.2$ of Steele and Wang, when properly translated from the Coleman-Weinberg scheme at the electroweak VEV to the $\overline{\rm MS}$ scheme at $M_t$ via scheme conversion and scale-dependent ratio evolution, yields $k(M_t) \approx 6.0$--$6.4$, corresponding to a UV pole at $\Lambda_{\rm UV} \sim {1.5\text{--}2} \times 10^{16}$~GeV -- remarkably close to the GUT scale $M_{\rm GUT} \sim 2 \times 10^{16}$~GeV. We argue this coincidence is not accidental: the UV pole signals the scale where the Standard Model effective description must be embedded into the full SO(10) structure. We derive threshold corrections from SO(10) scalar sectors containing $\mathbf{10}_H$, $\mathbf{\overline{126}}_H$, and $\mathbf{45}_H$ representations, showing that portal couplings between the light Higgs doublet and heavy GUT scalars can generate enhancement factors of order $k \sim 5$--$10$ at the matching scale. The Coleman-Weinberg mechanism operating within a classically scale-invariant GUT scalar potential provides a dynamical origin for both RBEWS and the hierarchy between $M_{\rm GUT}$ and the electroweak scale.

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 claims that the enhanced Higgs quartic coupling required by radiatively broken electroweak symmetry breaking (RBEWS) arises naturally from SO(10) grand unification. It translates the Coleman-Weinberg prediction e_125=7.2 to an MSbar enhancement factor k(M_t)≈6.0-6.4 via scheme conversion and scale-dependent evolution, yielding a UV Landau pole at 1.5-2×10^16 GeV near the GUT scale. Threshold corrections from portal couplings involving the 10_H, 126bar_H, and 45_H scalars are derived to generate k~5-10 at the matching scale, and the Coleman-Weinberg mechanism in a scale-invariant GUT potential is invoked to provide a dynamical origin for both RBEWS and the electroweak hierarchy.

Significance. If the scheme translation and explicit threshold calculations hold, the work supplies a concrete dynamical link between electroweak vacuum stability and SO(10) unification, interpreting the Landau-pole coincidence as evidence for GUT embedding rather than accident. Deriving the required enhancement from standard SO(10) representations is a positive feature that grounds the claim in explicit model building.

major comments (2)
  1. [Abstract] Abstract: the central claim that the RBEWS prediction e_125=7.2 translates to k(M_t)≈6.0-6.4 (and thus places the UV pole near M_GUT) rests on scheme conversion plus scale-dependent ratio evolution that are asserted to 'yield' this range but are not re-derived. The manuscript does not exhibit the conversion factors, the modified beta functions for the enhanced quartic, or the numerical integration of dk/dlogμ; if two-loop terms or the precise definition of the enhanced λ shift the target outside the 5-10 window, the matching to SO(10) thresholds fails.
  2. [Abstract] Abstract (threshold corrections paragraph): while portal couplings from 10_H, 126bar_H, and 45_H are stated to generate k~5-10, the manuscript must demonstrate that the same parameter choices simultaneously preserve gauge unification, keep all GUT-sector couplings perturbative up to M_GUT, and do not reintroduce fine-tuning in the hierarchy. Without explicit constraints or scans, it remains unclear whether the required enhancement is achieved without violating other phenomenological bounds.
minor comments (2)
  1. [Abstract] Notation for the 126 representation should be standardized (e.g., consistent use of 126bar_H throughout) to avoid reader confusion.
  2. [Abstract] The manuscript should cite the prior Steele-Wang work on the Coleman-Weinberg RBEWS prediction explicitly when stating the e_125=7.2 value.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments. We appreciate the opportunity to clarify the technical details underlying our claims and will revise the manuscript to make the derivations fully explicit and self-contained.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that the RBEWS prediction e_125=7.2 translates to k(M_t)≈6.0-6.4 (and thus places the UV pole near M_GUT) rests on scheme conversion plus scale-dependent ratio evolution that are asserted to 'yield' this range but are not re-derived. The manuscript does not exhibit the conversion factors, the modified beta functions for the enhanced quartic, or the numerical integration of dk/dlogμ; if two-loop terms or the precise definition of the enhanced λ shift the target outside the 5-10 window, the matching to SO(10) thresholds fails.

    Authors: We agree that the explicit intermediate steps were not displayed in the manuscript. These conversions and the running of k were performed in our earlier RBEWS analysis, but to address the concern we will add a dedicated appendix that (i) tabulates the scheme-conversion factors between the Coleman-Weinberg scheme at the electroweak VEV and the MSbar scheme at M_t, (ii) writes the modified one- and two-loop beta functions for the enhanced quartic, and (iii) shows the numerical integration of dk/dlogμ. The resulting plots confirm that k(M_t) remains inside 6.0–6.4 even after inclusion of two-loop terms and that the target window for SO(10) threshold matching is robust. revision: yes

  2. Referee: [Abstract] Abstract (threshold corrections paragraph): while portal couplings from 10_H, 126bar_H, and 45_H are stated to generate k~5-10, the manuscript must demonstrate that the same parameter choices simultaneously preserve gauge unification, keep all GUT-sector couplings perturbative up to M_GUT, and do not reintroduce fine-tuning in the hierarchy. Without explicit constraints or scans, it remains unclear whether the required enhancement is achieved without violating other phenomenological bounds.

    Authors: We concur that explicit verification is required. In the revision we will insert a new subsection containing benchmark values of the portal couplings that produce k≈5–10 at the matching scale. For each benchmark we will (a) recompute the gauge beta functions including the threshold corrections and confirm that unification still occurs near 2×10^16 GeV, (b) verify that all GUT-sector couplings (including the new portals) remain perturbative up to M_GUT, and (c) show that the classically scale-invariant potential continues to protect the hierarchy without additional fine-tuning. A limited parameter scan will be included to delineate the viable region. revision: yes

Circularity Check

1 steps flagged

Self-cited prior analysis supplies the k-to-Landau-pole mapping that makes the GUT-scale coincidence load-bearing

specific steps
  1. self citation load bearing [Abstract]
    "Our previous analysis demonstrated that a coupling enhancement factor $k = λ_{enhanced}/λ_{SM}$ leads to absolute vacuum stability with a UV Landau pole near the GUT scale for $k ≳ 1.03$. The RBEWS prediction $e_{125} = 7.2$ of Steele and Wang, when properly translated from the Coleman-Weinberg scheme at the electroweak VEV to the MSbar scheme at $M_t$ via scheme conversion and scale-dependent ratio evolution, yields $k(M_t) ≈ 6.0$--$6.4$, corresponding to a UV pole at Λ_UV ∼ 1.5--2 × 10^16 GeV -- remarkably close to the GUT scale $M_{GUT} ∼ 2 × 10^16$ GeV."

    The specific numerical translation from e_125=7.2 to k(M_t)≈6.0-6.4 (and the resulting pole scale) is stated as 'yields' without exhibiting the conversion factors, beta-function modifications, or integration steps inside this manuscript. The general claim that k ≳ 1.03 produces a pole near the GUT scale is explicitly attributed to the author's prior work, so the 'not accidental' coincidence that places the pole at M_GUT reduces to a self-citation rather than an independent derivation performed here.

full rationale

The paper's central argument—that the UV Landau pole at ~1.5-2×10^16 GeV is not accidental and signals SO(10) embedding—rests on translating the external Steele-Wang e_125=7.2 into k(M_t)≈6.0-6.4 and then linking that k to a pole position matching M_GUT. This mapping is asserted via the author's previous analysis (quoted in the abstract) without re-deriving the scheme conversion, modified beta functions, or numerical running in the present work. The SO(10) threshold corrections from 10_H, 126bar_H, and 45_H are independently derived and can produce k~5-10, supplying genuine content. Because the coincidence claim reduces to the self-cited result rather than a fully self-contained derivation, the circularity is partial (one load-bearing self-citation) but not total; the overall structure remains mostly independent of its own inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the RBEWS prediction taken from prior work, the assumption that SO(10) is realized with the listed scalar representations, and the applicability of the Coleman-Weinberg mechanism in a classically scale-invariant GUT potential; no new free parameters are explicitly introduced in the abstract.

axioms (2)
  • domain assumption Coleman-Weinberg mechanism generates masses and the electroweak scale from a classically scale-invariant GUT scalar potential
    Invoked to provide dynamical origin for both RBEWS and the hierarchy between M_GUT and the electroweak scale.
  • domain assumption SO(10) grand unification is realized with scalar representations 10_H, 126bar_H, and 45_H
    Standard GUT assumption used to compute portal couplings and threshold corrections to the Higgs quartic.

pith-pipeline@v0.9.0 · 5656 in / 1626 out tokens · 108882 ms · 2026-05-10T16:23:15.729534+00:00 · methodology

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