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Run 2/3 measurement of the muon anomalous magnetic moment by the Muon g-2 experiment at Fermilab

T0 review · 0 major / 3 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Analyzing 2019-2020 data, the Muon g-2 experiment measures the muon's anomalous magnetic moment to 215 parts per billion, a factor 2.2 improvement over its first result, and sets a world average of 116592059(22) x 10^-11.

desk verdict A faithful conference summary of the already-published Run 2/3 muon g-2 result, with no new science and only minor proofing errors. read the letter →

arxiv 2506.21219 v1 pith:SWDDCFTU submitted 2025-06-26 hep-ex physics.ins-det

Estifa'a Zaid (1) (the g-2 collaboration) ((1) University of Liverpool , Oliver Lodge , Liverpool , United Kingdom) This is my paper · ORCID
classification hep-exphysics.ins-det
keywords muonanomalousmagneticmomentg-2precisionmeasurementstorageringcoherentbetatronoscillationsstandardmodelhadronicvacuumpolarizationwiggleplot
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper reports the Muon g-2 experiment's second measurement of the muon's anomalous magnetic moment, a_mu = (g-2)/2, from data collected in 2019-2020. The result reaches a precision of 215 parts per billion (0.20 ppm), a factor 2.2 improvement over the 2021 Run 1 result, with both statistical and systematic uncertainties roughly halved. The new value agrees with the Run 1 and Brookhaven measurements, and the combined experimental world average is a_mu = 116592059(22) x $10^{-11}$. The paper further compares this value with the latest Standard Model predictions, where a persistent tension remains, and sketches the outlook for a final result using all data through 2023.

What carries the argument

The central object is the ratio omega_a / omega_p, the muon spin anomalous precession frequency divided by the proton Larmor frequency measured by NMR probes. The precession frequency omega_a is extracted from a multi-parameter fit to the 'wiggle plot' – the time spectrum of high-energy decay positrons – and the fit must account for beam dynamics such as coherent betatron oscillations (CBO), muon losses, and detector effects. Five corrections (electric field, pitch, muon loss, phase acceptance, differential decay) are applied to omega_a, and two (quad and kicker transients) to omega_p, before well-known constants convert the ratio into a_mu. The CBO model is the dominant source of systematic uncertainty in the Run 2/3 result.

What would settle it

Re-fit the Run 2/3 positron time spectra with an independent coherent betatron oscillation model, allowing a different time dependence for the CBO frequency drift, and compare the extracted omega_a; a shift larger than the quoted systematic error would show the result is model-dependent. Alternatively, compare the 2023 value with the experiment's final analysis of all data: if the 2025 result moves outside the 2023 uncertainty, the earlier analysis was likely limited by an unmodeled systematic.

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Extended reading notes

Core claim

The central claim is that the Run 2/3 dataset, containing 4.7 times more positron data than Run 1, yields a_mu = 116592059(22) x $10^{-11}$ with a total precision of 215 ppb. The uncertainty breaks down into a statistical component of 201 ppb and a systematic component of 70 ppb, the latter more than a factor of two smaller than Run 1's 157 ppb and now below the experiment's design goal of 100 ppb. The paper attributes the improvement to hardware fixes (repaired quad resistors, upgraded kicker cables, better magnetometry) and to refined analysis of pileup and coherent betatron oscillations. The Run 2/3 value is in excellent agreement with the Run 1 result and with Brookhaven's measurement, and the combination of the three experiments gives a world average of 116592059(22) x $10^{-11}$.

Load-bearing premise

The measurement's central value depends on how accurately the coherent betatron oscillation of the beam is modeled in the fit; a wrong model could shift the extracted frequency by more than the quoted 21 ppb systematic uncertainty.

Editorial extensions

If this is right

  • The experimental world average for a_mu becomes 116592059(22) x 10^-11, sharpening the discrepancy with the Standard Model to a level that calls for an explanation.
  • The systematic uncertainty of 70 ppb is below the experiment's 100 ppb design goal, demonstrating that the storage-ring technique can reach the target precision.
  • The agreement among Run 1, Run 2/3, and Brookhaven rules out a statistical fluctuation as the source of the g-2 anomaly.
  • The improved kicker and quad hardware reduced coherent betatron oscillations, which is the main reason the systematic errors shrank; a final analysis with all data is expected in 2025.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the 2025 final result keeps the same central value, the combined uncertainty could approach 100 ppb, and the tension with the Standard Model would become decisive enough to shape the search for new physics (editorial extrapolation).
  • A dedicated tracker-based measurement of the beam's betatron motion could cross-check the CBO model and possibly reduce the 21 ppb systematic; the paper notes trackers are part of the detector suite, but this use is not discussed (editorial suggestion).
  • The comparison with theory is complicated by the split between dispersive and lattice calculations of hadronic vacuum polarization; an independent data-driven measurement of that contribution, such as the proposed muon-electron scattering experiment mentioned in the paper, could decide whether the anomaly is new physics or a theory artifact.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

0 major / 3 minor

Summary. This proceedings contribution from PIC 2024, written on behalf of the Fermilab Muon g-2 collaboration, reports the published Run 2/3 measurement of the muon anomalous magnetic moment. It states that the Run 2/3 result, announced in August 2023, has a total precision of 215 ppb with a 70 ppb systematic uncertainty, a factor 2.2 improvement over the Run 1 result, and yields a world average of a_mu = 116592059(22) x 10^-11. The paper reviews the experimental method, the systematic improvements in Run 2/3, and the current Standard Model comparison. It contains no new data or analysis; the central numbers and references match the cited PRL publications.

Significance. The manuscript is a clear, concise summary that accurately transcribes the published Run 2/3 muon g-2 result, its quoted uncertainties, and the world average. Its strength lies in faithful reporting: the central value, total precision, and systematic budget agree with PRL 131,161802, and the comparison with the Run 1 result and Brookhaven is stated correctly. As a proceedings for a broad physics audience, it provides a useful and readable overview of the measurement and its context. It does not claim new physics results, and it explicitly relies on the collaboration's peer-reviewed papers for the final numbers. The only issues are typographical inaccuracies in two quoted values, which do not affect the main conclusion.

minor comments (3)
  1. [Section 3] The text quotes the Run 1 statistical error as 460 ppb, but the published Run 1 result (PRL 126, 141801) quotes a statistical uncertainty of 434 ppb. Furthermore, 460 ppb and the quoted 157 ppb systematic uncertainty do not combine in quadrature to the stated total of +/-54 x 10^-11 (about 463 ppb). Please correct the statistical uncertainty to the published value and check the resulting consistency.
  2. [Section 2.1] The storage ring radius is given as 3.56 m, but the central orbit radius of the BNL/FNAL muon g-2 storage ring is 7.112 m. Please correct this value, as it is a specific factual claim about the apparatus.
  3. [Abstract and Section 1] The abstract and Section 1 describe the Run 2/3 precision as 0.20 ppm, while Section 4 quotes 215 ppb (0.215 ppm). Please make the rounding explicit or use a single consistent value so that the quoted precision is unambiguous.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the paper is a conference summary that transcribes the already-published Fermilab Run 2/3 result, with no new derivation or fitted prediction.

full rationale

This is a proceedings article, not an original derivation. Its central claims—the 215 ppb precision, the 70 ppb systematic uncertainty, and the world average a_mu = 116592059(22) x 10^-11—are quoted from the collaboration's own published PRL papers (Refs. [3] and [4]) and from the experimental world-average compilation. That is reporting, not circular reasoning: the cited publications are peer-reviewed, externally validated measurements, and the auxiliary constants (muon-to-electron mass ratio, shielded proton-to-electron magnetic moment ratio, g_e) are taken from independent CODATA and spectroscopy sources. The paper performs no fit, no parameter extraction, and no 'prediction' that is constructed from its own inputs. The dominant systematic (CBO modeling) is a property of the underlying published measurement, not a circular input to this summary; the paper explicitly notes that the uncertainty was reduced from 38 ppb to 21 ppb using increased statistics and improved running conditions, which is a statement about the published error budget rather than a self-referential derivation. Two minor proofreading-level inconsistencies (Run 1 statistical error of 460 ppb versus the quoted total of 54 x 10^-11, and a 3.56 m ring radius rather than the ~7.11 m central orbit radius) are not load-bearing to the reported result. No step in the paper's logical chain reduces by definition to its own conclusion, and no unverified self-citation is used to justify the central numbers. Therefore the appropriate circularity score is 0.

Assumptions & free parameters 0 free parameters · 2 assumptions · 0 invented entities

This proceedings introduces no fitted parameters and no new entities. Its claims rest on the correctness of the cited experimental publications and on externally measured physical constants used in Eq. (4).

assumptions (2)
  • domain assumption The published Run 1 and Run 2/3 experimental results (Refs [3], [4]) are correct.
    The paper is a review that relies on these results as established facts, without re-deriving them.
  • domain assumption The external constants in Eq. (4) (muon-to-electron mass ratio, shielded proton moment ratio) are accurately known from independent measurements.
    The paper invokes these constants to translate the measured frequency ratio into a_mu, citing CODATA and muonium spectroscopy.

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Cite this review

Pith. "Pith review of Run 2/3 measurement of the muon anomalous magnetic moment by the Muon g-2 experiment at Fermilab." pith.science (2026). https://pith.science/paper/SWDDCFTU

@misc{pith2026250621219,
  author       = {Pith},
  title        = {Pith review of: Run 2/3 measurement of the muon anomalous magnetic moment by the Muon g-2 experiment at Fermilab},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SWDDCFTU}},
  note         = {Machine review of arXiv:2506.21219}
}
abstract

The Muon g-2 experiment at Fermilab seeks to measure the muon magnetic moment anomaly, $a_\mu =(g-2)/2$, with a final target precision of 0.14 parts-per-million (ppm). The experiment's initial result, published in 2021 using Run 1 data from 2018, confirmed the previous measurement at Brookhaven National Laboratory with a comparable sensitivity of 0.46 ppm. In 2023, a new result based on Run 2 and Run 3 data, collected in 2019 and 2020, was released. These datasets contain four times the data from Run 1, significantly enhancing sensitivity and achieving an unprecedented uncertainty of 0.20 ppm. This advancement resulted in a two-fold improvement in both statistical and systematic uncertainties. Here, we will discuss the muon $g-2$ measurement, the increased precision relative to the Run 1 result, and provide an outlook on future measurements which will incorporate datasets from 2021 to 2023. Additionally, we will explore the implications of comparing the new measurements with the latest Standard Model predictions for muon g-2.

Figures

Figures reproduced from arXiv: 2506.21219 by the authors.

Figure 1
Figure 1. View of the muon g-2 experimental setup at Fermilab. The most notable feature is the storage ring covered in a white insulating blanket [7]. circumference of the steel yoke providing a uniform magnetic field throughout [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Fourier transform of the residuals from a time-series fit. The red dashed curve shows the result when betatron motion and muon losses are neglected, while the black curve corresponds to the full fit, including these effects. The inset shows 𝑒 + time spectrum (black) from the Run 1c dataset, overlaid with the full fit function (red) [3]. 𝜔𝑎 = 𝜔𝑠 − 𝜔𝑐 = 𝑎𝜇 𝑒 𝑚𝜇𝑐 𝐵. (2) The frequency of precession 𝜔𝑠 and the strength o… view at source ↗
Figure 3
Figure 3. Left, Overview of the experimental results for 𝑎𝜇, the plot shows the Run 1 [3] and Run 2/3 result [4] as well as the FNAL average of the two. The Brookhaven result [2] is also shown and the combination of all the above is shown as the world average [4]. Right, Error budget of the Run 1 analysis compared to the Run 2/3 analysis. As shown in [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Left: The dominant 2𝜋 contribution to the HVP provided by different 𝑒 + 𝑒 − experiments [7]. Right: Summary of the muon 𝑔 − 2 landscape comparing theoretical predictions with the experimental measurement of 𝑎𝜇 [17]. 2.1𝜎 tension with the dispersive approach. Further co…

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