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arxiv: 2506.21145 · v2 · pith:H7ULDZBNnew · submitted 2025-06-26 · ✦ hep-ph · hep-th

Imaginary scaling invariance of the one-loop effective potential

P.M. Ferreira , B. Grzadkowski , O.M. Ogreid This is my paper

Pith reviewed 2026-05-22 00:32 UTC · model grok-4.3

classification ✦ hep-ph hep-th
keywords r0 symmetryGOOFy symmetryone-loop effective potentialtwo-Higgs doublet modelUV cutoffbosonic field theoriesrenormalization group
0
0 comments X

The pith

The r0 symmetry persists at one loop if the UV cutoff squared transforms non-trivially under it.

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

The paper examines the one-loop properties of r0 symmetries, also known as GOOFy symmetries, which provide renormalization-group stable relations among parameters in bosonic field theories. It focuses on the two-Higgs doublet model that respects this symmetry and on a minimal symmetric model. The key result is that the symmetry survives in the one-loop effective potential only when the square of the ultraviolet cutoff is allowed to transform non-trivially under r0. The minimal model further requires two real scalar fields to realize the symmetry at this order. This construction preserves the relations among parameters while incorporating quantum corrections.

Core claim

It is concluded that the symmetry is present at the one-loop provided the UV cutoff squared transforms non-trivially under r0. The minimal model requires the presence of two real fields.

What carries the argument

The non-trivial transformation property assigned to the ultraviolet cutoff squared under the r0 symmetry, which keeps the one-loop effective potential invariant.

Load-bearing premise

The ultraviolet cutoff squared can be assigned a non-trivial transformation property under the r0 symmetry without violating other consistency requirements of the quantum field theory.

What would settle it

A direct computation of the one-loop effective potential in the r0-invariant two-Higgs doublet model that fails to remain invariant when the UV cutoff squared is transformed according to the required rule.

read the original abstract

Recently, a hitherto unknown class of renormalization group stable relations between parameters of bosonic field theories have been identified and dubbed as the r0 or 'GOOFy' symmetries. Here, one-loop properties of the r0 invariant two-Higgs Doublet Model and a minimal symmetric model are discussed. It is concluded that the symmetry is present at the one-loop provided the UV cutoff squared transforms non-trivially under r0. The minimal model requires the presence of two real fields.

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 manuscript examines the one-loop effective potential in r0-symmetric bosonic theories, focusing on the two-Higgs-doublet model and a minimal model. It concludes that r0 invariance holds at one loop provided the UV cutoff squared transforms non-trivially under the r0 symmetry; the minimal model is stated to require two real scalar fields.

Significance. If the central claim is correct, the result would extend the recently identified r0 symmetries to the quantum level within a hard-cutoff regularization. This could offer new parameter relations in Higgs-sector models, but the non-trivial transformation assigned to the regulator raises questions about whether the invariance is intrinsic to the renormalized theory or an artifact of the chosen scheme.

major comments (2)
  1. [One-loop effective potential (section discussing the Coleman-Weinberg formula)] The central claim requires that quadratic and logarithmic cutoff terms in the Coleman-Weinberg potential compensate exactly under r0 when Λ² transforms non-trivially. The explicit one-loop integral expressions and the transformation rules for Λ² must be shown to achieve this cancellation without residual cutoff dependence after renormalization.
  2. [Discussion of regularization and renormalization] Physical observables must be regulator-independent after renormalization. Assigning a non-trivial r0 transformation to Λ² appears to tie the symmetry to the hard-cutoff scheme; the manuscript should demonstrate that the same invariance emerges in a scheme-independent manner (e.g., via dimensional regularization or after subtracting divergences).
minor comments (2)
  1. [Model definitions] Define the action of r0 on all fields and parameters explicitly, including how it acts on the two real scalars in the minimal model.
  2. [Results section] Clarify whether the reported one-loop results are obtained before or after renormalization-group improvement.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major comment below and indicate the revisions we will make.

read point-by-point responses

  1. Referee: [One-loop effective potential (section discussing the Coleman-Weinberg formula)] The central claim requires that quadratic and logarithmic cutoff terms in the Coleman-Weinberg potential compensate exactly under r0 when Λ² transforms non-trivially. The explicit one-loop integral expressions and the transformation rules for Λ² must be shown to achieve this cancellation without residual cutoff dependence after renormalization.

    Authors: We thank the referee for highlighting the need for explicit demonstration. The manuscript derives the one-loop effective potential in the hard-cutoff regularization and shows that the r0 symmetry is preserved when Λ² transforms non-trivially under the symmetry. In the revision we will expand the relevant section to display the explicit one-loop integral expressions for the quadratic and logarithmic terms together with the precise transformation rule assigned to Λ². This will make the exact cancellation manifest and confirm that no residual cutoff dependence survives in the renormalized potential. revision: yes

  2. Referee: [Discussion of regularization and renormalization] Physical observables must be regulator-independent after renormalization. Assigning a non-trivial r0 transformation to Λ² appears to tie the symmetry to the hard-cutoff scheme; the manuscript should demonstrate that the same invariance emerges in a scheme-independent manner (e.g., via dimensional regularization or after subtracting divergences).

    Authors: We agree that physical observables must ultimately be regulator-independent. Our construction extends the r0 symmetry to act on the regulator itself, thereby preserving the symmetry at one loop within the hard-cutoff scheme. In the revised manuscript we will add a clarifying paragraph stating that the symmetry-induced relations among renormalized parameters remain intact once divergences are subtracted consistently with the symmetry. A full verification in dimensional regularization would require a separate definition of how the symmetry acts on the regulator in that scheme; such an extension lies beyond the scope of the present work, which focuses on the cutoff regularization where the symmetry is most directly realized. revision: partial

Circularity Check

0 steps flagged

Minor reference to prior r0 symmetry identification; one-loop extension adds independent content

full rationale

The paper takes the r0 symmetries as given from recent external identification and performs explicit one-loop calculations in the effective potential for the 2HDM and minimal model. The conclusion that invariance holds when the UV cutoff squared is assigned a non-trivial r0 transformation is presented as a conditional result of those calculations rather than a re-expression or fit of the input symmetry. No load-bearing step reduces by construction to a self-fit, self-citation chain, or ansatz smuggled from prior work by the same authors. The derivation remains self-contained against the stated assumptions and the explicit cutoff dependence in the Coleman-Weinberg potential.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the prior existence of r0 symmetries and on the modeling choice that the UV cutoff may transform non-trivially; no free parameters or new entities are mentioned in the abstract.

axioms (1)
  • domain assumption r0 symmetries constitute a class of renormalization-group-stable relations between parameters of bosonic field theories
    Invoked in the opening sentence of the abstract as the foundation for the subsequent one-loop analysis.

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. GOOFy fermions

    hep-ph 2026-04 unverdicted novelty 6.0

    New fermion transformations and all-order renormalization-invariant parameter regions are identified for two-Higgs-doublet models including scalar-fermion interactions.

Reference graph

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40 extracted references · 40 canonical work pages · cited by 1 Pith paper · 11 internal anchors

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