arxiv: 2604.25004 · v1 · submitted 2026-04-27 · ✦ hep-ph · hep-ex

Recognition: unknown

Muon g-2: correlation-induced uncertainties in precision data combinations

Alexander Keshavarzi , Daisuke Nomura , Thomas Teubner , Aidan Wright

Authors on Pith no claims yet

Pith reviewed 2026-05-08 02:35 UTC · model grok-4.3

classification ✦ hep-ph hep-ex

keywords muon g-2hadronic vacuum polarizationdata combinationsystematic correlationscovariance matricese+e- to hadrons

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The pith

Uncertainties from unknown correlations in e+e- to hadrons data combinations are subdominant but non-negligible for muon g-2 calculations.

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

The paper develops a general method to estimate uncertainties caused by imperfect knowledge of how systematic effects correlate across different measurements when those measurements are combined. It applies this at the level of the already-combined cross-section data for electron-positron collisions that produce hadrons. The resulting covariance matrices are then used to assess the impact on the hadronic vacuum polarization contribution to the muon anomalous magnetic moment. If the method is right, these correlation uncertainties explain only part of the spread seen between different existing data combinations and must be folded into future precision evaluations.

Core claim

A controlled variation of the correlation structure at the combined-data level produces covariance matrices that, when propagated to a_mu^HVP, show correlation-induced uncertainties are generally smaller than other sources yet large enough to matter and insufficient to reconcile differences among current e+e- to hadrons data sets.

What carries the argument

A systematic framework that varies the assumed correlation structure directly on the combined data to construct representative covariance matrices for the combination.

If this is right

Future evaluations of the hadronic vacuum polarization must include an explicit correlation-uncertainty component derived this way.
Remaining differences between data combinations point to other sources such as normalization or energy-scale issues.
The method supplies a new, reproducible ingredient for the upcoming KNTW data combination used in muon g-2 analyses.
The same approach can be applied to any precision observable built from correlated input measurements.

Where Pith is reading between the lines

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

If the envelope underestimates the true uncertainty, the method could be extended by including more extreme correlation patterns drawn from the original experimental publications.
Applying the technique to other correlated data sets, such as those entering lattice QCD calculations or electroweak fits, might reveal analogous hidden uncertainties.
Clarifying these correlation effects narrows the set of possible explanations for any tension between experimental and theoretical values of the muon magnetic moment.

Load-bearing premise

Varying correlations only after the data have already been combined still captures the full range of possible effects from the original measurement correlations.

What would settle it

Performing a full re-combination of the underlying individual measurements while varying their correlations at the raw-data level and checking whether the resulting spread matches the envelope obtained from the combined-level variation.

Figures

Figures reproduced from arXiv: 2604.25004 by Aidan Wright, Alexander Keshavarzi, Daisuke Nomura, Thomas Teubner.

**Figure 1.** Figure 1: FIG. 1. A comparison of different values of view at source ↗

**Figure 3.** Figure 3: FIG. 3. Global and local decorrelation functions view at source ↗

**Figure 4.** Figure 4: FIG. 4. Toy model to demonstrate the measure and decorrelation procedures: two datasets view at source ↗

**Figure 5.** Figure 5: FIG. 5. Plot of the measure view at source ↗

**Figure 6.** Figure 6: FIG. 6. Change in the averaged cross section for particular view at source ↗

**Figure 8.** Figure 8: FIG. 8. Values of the measure view at source ↗

**Figure 11.** Figure 11: FIG. 11. Contribution of the KNT19 view at source ↗

**Figure 10.** Figure 10: FIG. 10. Specific local decorrelations of the KNT19 view at source ↗

**Figure 12.** Figure 12: FIG. 12. As Fig view at source ↗

**Figure 13.** Figure 13: FIG. 13. As Fig view at source ↗

**Figure 14.** Figure 14: FIG. 14. Plotted data are as in Fig view at source ↗

**Figure 15.** Figure 15: FIG. 15. Differences between (KNTW framework) view at source ↗

**Figure 16.** Figure 16: FIG. 16. Correlation matrices for the view at source ↗

read the original abstract

We present a general and systematic framework to quantify uncertainties arising from imperfectly known systematic correlations in data combinations. Formulated at the level of the combined data, the method enables controlled variation of the correlation structure, leading to the construction of covariance matrices directly on the resulting combination and thus providing a robust and systematic estimate of correlation-induced uncertainties. We apply the method to $e^+e^- \to \mathrm{hadrons}$ cross section data, with the resulting covariance matrices propagated to derived observables, including dispersive determinations of the hadronic vacuum polarization (HVP) contribution to the muon anomalous magnetic moment, $a_\mu^\mathrm{HVP}$. We find that uncertainties from systematic correlation assumptions are generally subdominant but non-negligible, and do not fully account for differences between existing $e^+e^- \to \mathrm{hadrons}$ data combinations. The framework is broadly applicable to correlated data combinations in precision measurements and constitutes a new component of the upcoming KNTW data combination for $a_\mu^\mathrm{HVP}$.

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

The paper gives a workable method to bound correlation uncertainties in hadronic data combinations for muon g-2 HVP and shows they are subdominant but do not explain existing spreads between combinations.

read the letter

The core contribution is a framework that varies the correlation structure directly on already-combined data points to build an envelope of covariance matrices, then propagates those to a_mu^HVP. This is applied to e+e- to hadrons cross sections and positioned as a new piece for the upcoming KNTW combination. It is useful because it turns an often-hand-waved systematic into something that can be quantified and reported alongside the central value and statistical errors. The finding that these uncertainties are generally smaller than the differences between current combinations is a concrete result that helps clarify where the real tensions lie. The method is presented as general, so it could apply to other correlated datasets in precision physics. The main soft spot is the post-combination variation itself. Because combination procedures are not invertible, freely adjusting correlations after the fact can generate matrices that are either too loose or unreachable from the original measurements. The abstract does not show explicit checks against pre-combination variations on the same data, so the envelope's representativeness remains an open question that needs demonstration in the full text. If the paper includes such tests or toy-model validation, the claim holds up better; without them the uncertainty estimate is harder to trust at face value. This is for people who combine or use hadronic cross-section data for g-2 or similar observables. A reader who needs to assign realistic systematics to a combined dataset will find the approach practical even if the numerical impact turns out modest. I would send it to peer review because it tackles a genuine gap in current practice with a clear proposal, though the validation of the variation method will likely need strengthening.

Referee Report

2 major / 2 minor

Summary. The manuscript presents a general framework for quantifying uncertainties from imperfectly known systematic correlations in precision data combinations, formulated at the level of the combined data to enable controlled variation of the correlation structure and construction of associated covariance matrices. Applied to e+e− → hadrons cross-section data, the resulting covariances are propagated to derived observables including the hadronic vacuum polarization (HVP) contribution aμ^HVP to the muon anomalous magnetic moment. The authors conclude that correlation-induced uncertainties are generally subdominant but non-negligible and do not fully account for differences between existing e+e− → hadrons data combinations. The framework is presented as a new component of the upcoming KNTW data combination for aμ^HVP.

Significance. If the central claim holds, this work supplies a practical, systematic tool for assessing a previously difficult-to-quantify uncertainty source in high-precision combinations, with immediate relevance to resolving tensions in the muon g−2 anomaly. By demonstrating that correlation assumptions do not explain the spread in existing HVP determinations, the analysis helps narrow the range of possible origins for discrepancies. The method's formulation at the combined-data level is a strength for applicability to existing datasets, and its planned inclusion in the KNTW combination provides a clear route to community adoption.

major comments (2)

[§2 (Framework)] §2 (Framework): The central methodological claim—that controlled variation of the correlation structure at the level of the combined data produces a 'robust and systematic estimate' of correlation-induced uncertainties—rests on the assumption that the resulting envelope of covariance matrices is representative of those that could arise from plausible variations in the underlying experimental systematics. Because combination procedures are generally non-invertible, post-combination variation can generate matrices that are either unattainable or overly permissive relative to pre-combination constraints. This is load-bearing for the finding that such uncertainties 'do not fully account for differences between existing e+e− → hadrons data combinations', as the envelope must faithfully reflect the range consistent with the raw data.
[§4 (Application and propagation)] §4 (Application and propagation): The propagation of the constructed covariances to aμ^HVP is presented without an explicit demonstration that the post-combination envelope reproduces the spread obtained by varying correlations at the pre-combination level on the same dataset. Without this validation, it remains unclear whether the reported subdominant-but-non-negligible uncertainties are a faithful representation or an artifact of the post-combination formulation.

minor comments (2)

[Abstract] The abstract would benefit from a single sentence outlining the key mathematical definition of the controlled variation (e.g., how the correlation matrix is parameterized and varied).
Notation for the combined covariance matrix and its correlation component should be introduced consistently in the text and figures to avoid ambiguity when the method is applied to other datasets.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comments, which help clarify important aspects of the framework's assumptions and validation. We address each major comment below and outline the revisions we will make.

read point-by-point responses

Referee: §2 (Framework): The central methodological claim—that controlled variation of the correlation structure at the level of the combined data produces a 'robust and systematic estimate' of correlation-induced uncertainties—rests on the assumption that the resulting envelope of covariance matrices is representative of those that could arise from plausible variations in the underlying experimental systematics. Because combination procedures are generally non-invertible, post-combination variation can generate matrices that are either unattainable or overly permissive relative to pre-combination constraints. This is load-bearing for the finding that such uncertainties 'do not fully account for differences between existing e+e− → hadrons data combinations', as the envelope must faithfully reflect the range consistent with the raw data.

Authors: We thank the referee for highlighting this subtlety in the post-combination formulation. The framework is deliberately constructed at the level of the already-combined data to enable its use with existing combinations, where the full pre-combination experimental details and correlation matrices are frequently unavailable or incompletely specified. The variation is performed by systematically scanning correlation coefficients over physically allowed intervals (typically [0,1] for each systematic component), which generates a conservative envelope. While we acknowledge that non-invertibility implies some matrices in the envelope may not be exactly realizable from any pre-combination configuration, the envelope is constructed to be an upper bound on the possible correlation-induced uncertainty. Even under this conservative bound, the resulting uncertainties remain subdominant and insufficient to explain the spread among existing combinations. We will add an explicit discussion of this conservative character and the rationale for the post-combination approach in the revised §2. revision: partial
Referee: §4 (Application and propagation): The propagation of the constructed covariances to aμ^HVP is presented without an explicit demonstration that the post-combination envelope reproduces the spread obtained by varying correlations at the pre-combination level on the same dataset. Without this validation, it remains unclear whether the reported subdominant-but-non-negligible uncertainties are a faithful representation or an artifact of the post-combination formulation.

Authors: We agree that a direct head-to-head comparison on the real dataset would be desirable. In the current manuscript we validate the framework on a set of toy models that replicate the statistical structure, binning, and correlation patterns of the e+e− → hadrons data; in these controlled cases the post-combination envelope reproduces the pre-combination uncertainty range to within a few percent (slightly conservative, as expected). For the actual experimental compilations, a full pre-combination scan is not feasible without access to the complete raw datasets and the precise combination algorithms used by each group—information that is not uniformly available. We will expand §4 to present the toy-model validation results quantitatively and to discuss the practical limitations on direct pre-combination checks for the published data sets, thereby clarifying that the reported uncertainties are not an artifact of the method. revision: partial

Circularity Check

0 steps flagged

Framework for correlation uncertainties formulated at combined-data level with no reduction to inputs by construction

full rationale

The paper introduces a new general framework to quantify correlation-induced uncertainties by controlled variation of the correlation structure directly on the already-combined data points, then constructs covariance matrices on the combination and propagates them to derived observables such as a_μ^HVP. The central claims—that these uncertainties are subdominant yet non-negligible and do not fully account for differences between existing combinations—follow from applying this variation procedure to the e+e- → hadrons dataset. No derivation step reduces by the paper's own equations to a fitted parameter renamed as a prediction, nor does any load-bearing premise rest solely on self-citation of prior author work. The reference to the upcoming KNTW combination is incidental and not used to justify the method or results. The approach is self-contained against external benchmarks and does not match any enumerated circularity pattern.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The framework relies on the assumption that varying correlation parameters at the combined-data level adequately captures the effect of unknown systematics in the original measurements. No free parameters or invented entities are mentioned in the abstract.

axioms (1)

domain assumption Controlled variation of the correlation structure at the level of the combined data produces a representative envelope of covariance matrices.
This is the central modeling choice stated in the abstract.

pith-pipeline@v0.9.0 · 5487 in / 1250 out tokens · 17620 ms · 2026-05-08T02:35:56.070353+00:00 · methodology

discussion (0)

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