CPT- and Lorentz-Violation Tests with Muon g-2

B. Quinn

arxiv: 1907.00162 · v1 · pith:QGYSFBELnew · submitted 2019-06-29 · ✦ hep-ex · hep-ph

CPT- and Lorentz-Violation Tests with Muon g-2

B. Quinn This is my paper

Pith reviewed 2026-05-25 13:25 UTC · model grok-4.3

classification ✦ hep-ex hep-ph

keywords muon g-2Lorentz violationCPT violationStandard-Model Extensionanomalous magnetic momentFermilab experiment

0 comments

The pith

Muon g-2 experiments set the strongest limits on Lorentz and CPT violation for muons in the Standard-Model Extension.

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

The paper reviews how measurements of the muon's anomalous magnetic moment test for Lorentz symmetry and CPT invariance violations. Existing g-2 data from muon experiments provide most of the tightest bounds on the relevant Standard-Model Extension coefficients in the muon sector. These bounds reach the magnitude of effects that could resolve the observed 3.7 sigma discrepancy between measured and predicted muon g-2 values. The review also outlines how the new Fermilab Muon g-2 experiment can strengthen these tests.

Core claim

Results from muon g-2 experiments have set the majority of the most stringent limits on Standard-Model Extension Lorentz and CPT violation in the muon sector. These limits are consistent with calculations of the level of Standard-Model Extension effects required to account for the current 3.7 sigma experiment-theory discrepancy in the muon's g-2.

What carries the argument

The Standard-Model Extension coefficients that parameterize possible Lorentz and CPT violations in the muon magnetic moment, constrained directly by g-2 precession data.

If this is right

The current bounds restrict the range of SME parameters that could explain the g-2 anomaly.
The Fermilab experiment will produce tighter constraints on the same SME coefficients.
Absence of detected violation so far remains compatible with exact Lorentz invariance at the achieved precision.
The approach links the g-2 anomaly directly to possible symmetry-breaking terms rather than unrelated new physics.

Where Pith is reading between the lines

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

If the anomaly persists without corresponding SME signals in other observables, it would favor alternative explanations outside the muon sector.
The same g-2 technique could be adapted to test SME effects in other charged leptons once their magnetic moments are measured to similar precision.

Load-bearing premise

Any Lorentz or CPT violation that could affect the muon magnetic moment is appropriately described by the Standard-Model Extension parameterization.

What would settle it

A new g-2 measurement whose deviation from the Standard Model prediction shows no match to the expected pattern or magnitude of SME Lorentz-violating signals would undermine the claimed consistency.

Figures

Figures reproduced from arXiv: 1907.00162 by B. Quinn.

**Figure 1.** Figure 1: Comparison of SM evaluations of aµ with the most recent experimental result and prospect. 3 of two frequencies: ~ωa = ~ωc − ~ωs, which is the rate at which the muon’s spin (ωs) advances relative to its momentum (ωc), and the proton Larmorprecession frequency ωp, which is a measure of the ring magnetic field.4 These frequencies are related to the anomaly by aµ = ωa ωp µp µe mµ me ge 2 . (2) The Standard-Mo… view at source ↗

read the original abstract

The status of Lorentz- and CPT-violation searches using measurements of the anomalous magnetic moment of the muon is reviewed. Results from muon g-2 experiments have set the majority of the most stringent limits on Standard- Model Extension Lorentz and CPT violation in the muon sector. These limits are consistent with calculations of the level of Standard-Model Extension effects required to account for the current 3.7{\sigma} experiment-theory discrepancy in the muon's g-2. The prospects for the new Muon g-2 Experiment at Fermilab to improve upon these searches is presented.

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 is a review that compiles existing muon g-2 limits on SME coefficients but adds no new data or calculations.

read the letter

This paper is a review of Lorentz and CPT violation searches that use muon g-2 measurements. It states that those experiments have set most of the tightest bounds in the muon sector under the SME and that the bounds sit at the scale needed to address the current 3.7 sigma discrepancy. The text also flags the upcoming Fermilab run as a chance to tighten the same limits further. No new results appear anywhere in the manuscript. The central statements rest entirely on earlier published work that is cited but not re-derived or re-checked here. The mapping from g-2 observables to specific SME coefficients, the error budgets, and the numerical consistency with the anomaly are all taken from the references. That is not a flaw for a review, but it does mean the paper offers no independent verification. The prospects section is short and does not contain fresh sensitivity estimates or updated projections. A reader already working on muon g-2 or SME phenomenology will find a convenient one-stop summary of the muon-sector bounds. Someone outside that niche will not learn much that is not already in the cited papers. The compilation itself looks accurate and the claims track the literature without internal contradictions. I would send it to peer review for a proceedings or short-review venue because the organization is clear and the scope is modest.

Referee Report

0 major / 2 minor

Summary. The manuscript reviews the status of Lorentz- and CPT-violation searches using measurements of the anomalous magnetic moment of the muon. It asserts that muon g-2 experiments have provided the majority of the most stringent limits on Standard-Model Extension (SME) coefficients in the muon sector. These limits are stated to be consistent with the magnitude of SME effects needed to explain the current 3.7σ discrepancy between experiment and theory in a_μ. The paper also discusses the potential of the upcoming Muon g-2 Experiment at Fermilab to improve these constraints.

Significance. If the compiled limits and referenced calculations are accurate, this review provides a valuable synthesis of how g-2 data constrain SME parameters and their relevance to the muon anomaly. It highlights the experimental reach in a specific sector of Lorentz violation searches. The paper does not introduce new data or derivations but serves as a useful reference by connecting existing results to the anomaly.

minor comments (2)

[Abstract] Abstract: the statement that the limits 'are consistent with calculations of the level of Standard-Model Extension effects required to account for the current 3.7σ discrepancy' would be strengthened by an explicit citation to the referenced calculation of the required SME coefficients.
The manuscript would benefit from a concise summary table (or section) listing the principal SME coefficients constrained by g-2 data together with the numerical limits obtained, to make the claim that these are 'the majority of the most stringent limits' immediately verifiable.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment of our review manuscript and the recommendation for minor revision. The report accurately summarizes the content and notes its value as a synthesis of existing constraints. No specific major comments were raised in the provided report.

Circularity Check

0 steps flagged

No circularity: review compiles external limits without internal derivation

full rationale

This is a review paper whose central claims consist of summarizing published experimental bounds on SME coefficients from muon g-2 data and noting consistency with prior calculations of the size needed to explain the reported anomaly. No equations, fits, or predictions are derived inside the manuscript; the text references external results and does not reduce any quantity to a parameter defined or fitted within the paper itself. The weakest assumption (SME as the appropriate EFT) is an external modeling choice, not a self-referential step. Consequently the derivation chain contains no self-definitional, fitted-input, or self-citation-load-bearing reductions.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Review paper; no new free parameters, axioms, or invented entities are introduced by the present work.

pith-pipeline@v0.9.0 · 5610 in / 1075 out tokens · 27020 ms · 2026-05-25T13:25:41.761184+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/AlexanderDuality.lean alexander_duality_circle_linking unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

Results from muon g-2 experiments have set the majority of the most stringent limits on Standard-Model Extension Lorentz and CPT violation in the muon sector.
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

The Standard-Model Extension (SME) is a general framework that describes CPT- and Lorentz-invariance violation by adding new terms to the SM lagrangian.

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

12 extracted references · 12 canonical work pages · 1 internal anchor

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A. Keshavarzi, D. Nomura, and T. Teubner, Phys. Rev. D 97, 114025 (2018)

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Muon (g-2) Technical Design Report

Muon g − 2 Collaboration, J. Grange et al. , arXiv:1501.06858

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R. Bluhm, V.A. Kosteleck´ y, and C.D. Lane, Phys. Rev. Lett . 84, 1098 (2000)

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Bennett et al

Muon g −2 Collaboration, G.W. Bennett et al. , Phys. Rev. Lett. 100, 091602 (2008)

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Passera, J

M. Passera, J. Phys. G 31, R75 (2005)

work page 2005

[2] [2]

Bennett et al

Muon g − 2 Collaboration, G.W. Bennett et al. , Phys. Rev. Lett. 92, 161802 (2004)

work page 2004

[3] [3]

Keshavarzi, D

A. Keshavarzi, D. Nomura, and T. Teubner, Phys. Rev. D 97, 114025 (2018)

work page 2018

[4] [4]

Muon (g-2) Technical Design Report

Muon g − 2 Collaboration, J. Grange et al. , arXiv:1501.06858

work page internal anchor Pith review Pith/arXiv arXiv

[5] [5]

Colladay and V.A

D. Colladay and V.A. Kosteleck´ y, Phys. Rev. D 58, 116002 (1998)

work page 1998

[6] [6]

Bluhm, V.A

R. Bluhm, V.A. Kosteleck´ y, and C.D. Lane, Phys. Rev. Lett . 84, 1098 (2000)

work page 2000

[7] [7]

Bennett et al

Muon g −2 Collaboration, G.W. Bennett et al. , Phys. Rev. Lett. 100, 091602 (2008)

work page 2008

[8] [8]

Bailey et al

CERN–Mainz–Daresbury Collaboration, J. Bailey et al. , Nucl. Phys. B 150, 1 (1979)

work page 1979

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Lomb, Astrophys

N.R. Lomb, Astrophys. Space Sci. 39, 447 (1976); J.D. Scargle, Astrophys. J. 263, 835 (1982)

work page 1976

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Kosteleck´ y and N

Data Tables for Lorentz and CPT Violation, V.A. Kosteleck´ y and N. Russell, 2019 edition, arXiv:0801.0287v12

work page arXiv 2019

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Otani, JPS Conf

E34 Collaboration, M. Otani, JPS Conf. Proc. 8, 025008 (2015)

work page 2015

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Gomes, A

A.H. Gomes, A. Kosteleck´ y, and A.J. Vargas, Phys. Rev. D 90, 076009 (2014)

work page 2014