Dispersive estimation of the LO hadronic contribution to the muon ${g-2}$: fitting incompatible ${e^+e^-}$ data

O.V. Zenin; V.V. Bryzgalov

REVIEW 3 major objections 6 minor 18 references

Reviewed by Pith at T0; open to challenge.

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T0 review · glm-5.2

Dispersive g-2 estimate lands 2σ below experiment

2026-07-08 08:40 UTC pith:BXB67DDH

load-bearing objection A data-driven uncertainty inflation for incompatible e+e− cross sections that reduces the g−2 discrepancy to 2σ, but the method is incompletely validated and the headline result is conditional. the 3 major comments →

arxiv 2607.06352 v1 pith:BXB67DDH submitted 2026-07-07 hep-ph

Dispersive estimation of the LO hadronic contribution to the muon {g-2}: fitting incompatible {e^+e^-} data

V.V. Bryzgalov , O.V. Zenin This is my paper

classification hep-ph PACS 13.66.Bc14.60.Ef12.38.Lg

keywords muon anomalous magnetic momenthadronic vacuum polarizationdispersive integralelectron-positron annihilationcross-section tensionsStandard Model predictionchi-squared fittingsystematic uncertainties

verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper estimates the leading-order hadronic contribution to the muon anomalous magnetic moment using a dispersive method based on electron-positron annihilation cross-section data. The key methodological innovation is a procedure for handling tensions between incompatible measurements from different experiments: rather than applying a uniform scaling factor to all uncertainties, the authors identify experiments whose systematic contributions to chi-squared are disproportionately large, estimate an additional per-channel normalization uncertainty from the observed inter-experiment pulls, and iterate until chi-squared contributions fall below a threshold. Applying this procedure to an up-to-date compilation of cross-section data across all relevant hadronic final states, they obtain a muon anomaly of 11659185.5(10.6) × 10^-10, which sits below the experimental world average at the 2σ level. The dominant uncertainty comes from tensions between precision measurements of the pi+pi- channel, particularly among BaBar, KLOE-2, and CMD-3.

Core claim

The central result is a specific numerical estimate of the leading-order hadronic contribution to the muon g-2: a_mu(had,LO) = (697.7 ± 9.8_{e+e-} ± 3.6_{sys}) × 10^-10, yielding a Standard Model prediction that is 2σ below the experimental world average. The central methodological contribution is a data-driven procedure for inflating systematic uncertainties channel-by-channel to account for inter-experiment tensions, using the distribution of chi-squared contributions across eigenvector projections of the covariance matrix to identify and quantify the source of disagreement.

What carries the argument

The dispersive integral relating the total e+e- → hadrons cross section R_had(s) to a_mu(had,LO); a modified covariance matrix (Eq. 11) that adds an extra per-channel normalization uncertainty epsilon, estimated from the root-mean-square of integral pulls (Eq. 9) among experiments whose systematic chi-squared contributions exceed a threshold (chi^2_thr = 10); an iterative fitting procedure that converges when all systematic chi-squared contributions fall below threshold.

Load-bearing premise

The procedure models inter-experiment tensions as an uncorrelated, per-channel extra normalization uncertainty added iteratively based on a chi-squared threshold of 10. The authors themselves note this parameterization is insufficient to fully account for tensions, particularly in the pi+pi-pi0 channel where the iteration fails to converge.

What would settle it

New e+e- → hadrons cross-section measurements that are mutually compatible at the sub-percent level would eliminate the need for the extra systematic uncertainty, potentially shifting the central value and reducing the error bar on a_mu(had,LO) enough to either close or widen the gap with experiment.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

If the 2σ gap between the Standard Model prediction and experiment persists as cross-section measurements improve, it would strengthen the case for physics beyond the Standard Model contributing to the muon anomalous magnetic moment.
The tension-mitigation procedure could be applied to other precision electroweak observables where incompatible measurements from independent experiments inflate uncertainties in ways that uniform Birge scaling cannot properly capture.
New precision measurements of sigma_tot(e+e- → pi+pi-) from operating and future colliders (BEPCII, SuperKEKB, VEPP-2000, STCF, VEPP-6) could either resolve or deepen the inter-experiment tensions that dominate the current uncertainty budget.
The authors' own acknowledgment that their uncertainty parameterization is insufficient for the pi+pi-pi0 channel (where the iteration fails to converge) indicates that a more sophisticated, energy-dependent model of inter-experiment tensions is needed.

Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

A data-driven uncertainty inflation for incompatible e+e− cross sections that reduces the g−2 discrepancy to 2σ, but the method is incompletely validated and the headline result is conditional.

read the letter

Here's the short version: the paper proposes a procedure for inflating systematic uncertainties in e+e− hadronic cross section fits, driven by inter-experiment tensions rather than Birge scaling. Applied to the full data compilation, it yields a_mu(had,LO) = 697.7 ± 9.8 × 10^-10, which brings the SM prediction to 2σ below the experimental world average. That is a consequential result if the method holds up, but the method is only partially developed and the authors are honest about that fact. The paper deserves a serious referee, but the headline number should be treated as provisional, not definitive. The reader's assessment is broadly correct and I agree with the conditional verdict. The stress-test concern about energy-dependent tensions is the right thing to worry about, and the authors themselves flag it in §2. The inter-experiment disagreements in π+π− are manifestly shape-dependent — different experiments disagree differently in the ρ peak, the ρ-ω region, and at higher √s. A single constant ε = 5.7% per experiment cannot distinguish a global normalization offset from a shape difference, and since the dispersion integral weights energy regions differently via K(s), the propagated uncertainty on a_mu is not controlled. The authors acknowledge this explicitly, stating that an s-dependent ε is needed and that 'further studies are required.' That is the right self-assessment. The χ² threshold of 10 (Eq. 10) is ad hoc, as the reader notes. The π+π−π0 channel fails to converge after four iterations (Table 2), which is a direct demonstration that the constant-ε ansatz breaks down in at least one channel. The fallback to Birge scaling for residual tensions after ε is applied is pragmatic but sits awkwardly with the authors' own criticism of Birge scaling as inadequate. The central values of the fits are essentially unchanged by the ε procedure (Table 1: pulls barely shift), so the central value of a_mu is still determined by a χ² minimization over mutually incompatible data, with no mechanism to assess potential bias in that central value. The ±9.8 × 10^-10 uncertainty on the π+π− contribution, which dominates the total, may be either too large or too small in a way that is not controlled. What the paper does well: the χ² decomposition into systematic and residual projections (Eqs. 5-8) is a reasonable diagnostic for localizing tension sources. The code and data index are publicly available [8,9], which is good practice. The error budget is broken down by source (Table 3), including a dedicated χ²_thr variation uncertainty. The paper is transparent about every limitation — the non-convergence, the insufficiency of the approximation, the need for an s-dependent procedure. This honesty is real and should be credited. The dispersive framework itself is standard (Eq. 1-2, from [3]); the novelty is entirely in the tension-mitigation procedure. The result that the g−2 discrepancy drops to 2σ is conditional on the validity of this procedure, which is not fully established. The paper is for specialists in dispersive g−2 evaluations who can assess the statistical procedure. It is not for a general audience looking for a definitive SM prediction. It deserves a serious referee who can scrutinize the χ² decomposition, the threshold choice, and the propagation of ε into the dispersion integral uncertainty. I lean toward accept for peer review with major revisions, but I would not publish the headline number as a definitive result without either an s-dependent ε procedure or a convincing argument that the constant approximation is conservative.

Referee Report

3 major / 6 minor

Summary. The manuscript presents a dispersive evaluation of the leading-order hadronic contribution to the muon anomalous magnetic moment, $a_μ^{had,LO}$, using a compilation of $e^+e^- → hadrons$ cross-section data. The central methodological contribution is a procedure to handle well-known tensions between BaBar, CMD-3, and KLOE measurements (among others) by introducing an extra, per-experiment normalization uncertainty $ε$ (Eq. 11), determined iteratively from the data via a $χ^2$-uniformity criterion (Eq. 10). The authors obtain $a_μ^{had,LO} = (697.7 ± 9.8_{e^+e^-} ± 3.6_{sys}) × 10^{-10}$, yielding a SM prediction roughly $2σ$ below the experimental world average. The procedure is applied to multiple hadronic channels, with publicly available code and data indices.

Significance. The topic is timely and important given the current $g-2$ discrepancy and the known inter-experiment tensions in $e^+e^-$ data. The authors are transparent about the limitations of their approach, including the non-convergence in the $π^+π^-π^0$ channel and the need for an $s$-dependent $ε$. The reproducible code and data compilation [8,9] are a positive feature. However, the methodological novelty—an iterative, data-driven extra normalization uncertainty—is only partially validated, and the central quantitative claim depends on assumptions whose impact is not fully controlled.

major comments (3)

§2, Eq. (11): The extra systematic uncertainty $ε$ is modeled as a constant, energy-independent normalization per experiment per channel. The authors themselves acknowledge (end of §2) that an $s$-dependent $ε$ is needed. Since the dispersive kernel $K(s)$ weights different energy regions differently, and since the tensions between BaBar, CMD-3, and KLOE in the $π^+π^-$ channel are manifestly energy-dependent (visible in Fig. 2: different disagreements near the $ρ$ peak, the $ρ-ω$ interference region, and at higher $√s$), a constant $ε = 5.7%$ cannot distinguish between a global normalization offset and energy-dependent shape discrepancies. The practical consequence is that the $±9.6 × 10^{-10}$ experimental uncertainty on the $π^+π^-$ contribution (Table 3), which dominates the total error budget, may be either over- or under-estimated in a way that is not controlled. The authors should
§2, Table 2 and surrounding text: The procedure fails to converge for the $π^+π^-π^0$ channel, where it is aborted after four iterations with $ε = 9.7%$ and residual $Δχ^2_{sys} = 15.2$ for SND (2003). The authors then apply a Birge scaling factor $√(χ^2/ndof)$ on top of the already-inflated uncertainties. This channel contributes $48.2 × 10^{-10}$ to $a_μ^{had,LO}$ with an experimental uncertainty of $1.8 × 10^{-10}$. Given that the procedure explicitly fails here, the reader cannot assess whether this $1.8 × 10^{-10}$ uncertainty is reliable. The authors should provide a more quantitative justification for why the failure in this channel does not undermine the overall uncertainty estimate, or alternatively, explore how sensitive the total $a_μ^{had,LO}$ is to a substantially larger uncertainty on this channel.
§2, Table 1: The procedure leaves central values essentially unchanged—the integral pulls (Eq. 9) barely shift between the 'unmodified' and 'extra systematics' columns (e.g., CMD-3 2020: 0.048 → 0.052; BaBar 2012: 0.020 → 0.007). This means the fit central value is still determined by the original $χ^2$ minimization over mutually incompatible data, with no mechanism to assess potential bias in that central value. The expanded uncertainty band (Fig. 3) is wider, but the central $a_μ^{had,LO}$ may be biased if the fit averages over datasets that disagree in shape rather than normalization. The authors should discuss this potential bias, perhaps by comparing the central value obtained from individual experiments (as partially shown in Fig. 5 for KLOE-only, BaBar-only, CMD-3-only) and quantifying the spread.

minor comments (6)

§2, Eq. (10): The threshold $χ^2_{thr} = 10$ is described as 'nominal' without rigorous justification. The sensitivity of the final result to this choice is quantified in Eq. (12) as $±1.1 × 10^{-10}$ from varying $6 < χ^2_{thr} < 25$, which is subdominant. This should be briefly explained.
Table 1, footnote 3: The note about KLOE-2's covariance matrix being unavailable (URL [11] defunct) is important but buried. The $Δχ^2_{res}/n_p ≈ 3$ for KLOE suggests its covariance matrix is inadequately parameterized in Eq. (4). This deserves more discussion, as KLOE is one of the three key experiments in the $π^+π^-$ channel.
Fig. 2 and Fig. 3: The figures would benefit from clearer labeling of the energy regions where tensions are most pronounced (e.g., $ρ$ peak, $ρ-ω$ interference), to help the reader visually assess whether the constant $ε$ adequately captures the discrepancies.
Table 3: The $π^+π^-π^0$ channel reports $ε = 9.7^{+0.0}_{-3.5}%$, which is an unusual asymmetric uncertainty on $ε$. The meaning of this asymmetry should be clarified—presumably it reflects the non-convergence, but this is not stated.
The abstract states the result is 'below the experimental world average at $2σ$ level.' The conclusion repeats this. Given the methodological caveats acknowledged by the authors, the $2σ$ framing in the abstract could be read as over-stating the significance of the tension. Consider softening to acknowledge the methodological caveat.
Reference [10] cites the Particle Data Group but lists 'F. Takahashi et al.' as authors, which appears to be an error. Please correct the author list and page/article number.

Simulated Author's Rebuttal

3 responses · 1 unresolved

We thank the referee for a careful and constructive report. The comments are well-taken and address genuine limitations of our procedure. We respond to each below. In summary: (1) we agree that an s-dependent epsilon is ultimately needed and will add a quantitative discussion of the bias risk from a constant epsilon, including a sensitivity estimate; (2) we will add an explicit sensitivity study showing that even a substantially enlarged uncertainty on the pi+pi-pi0 channel has negligible impact on the total; (3) we will add a quantitative discussion of central-value bias using the single-experiment spreads already partially shown in Fig. 5. We cannot fully resolve the question of central-value bias from shape discrepancies—this is a fundamental limitation of any averaging procedure applied to mutually incompatible data, and we will state this honestly.

read point-by-point responses

Referee: §2, Eq. (11): The extra systematic uncertainty ε is modeled as a constant, energy-independent normalization per experiment per channel. The authors themselves acknowledge (end of §2) that an s-dependent ε is needed. Since the dispersive kernel K(s) weights different energy regions differently, and since the tensions between BaBar, CMD-3, and KLOE in the π+π− channel are manifestly energy-dependent (visible in Fig. 2: different disagreements near the ρ peak, the ρ-ω interference region, and at higher √s), a constant ε = 5.7% cannot distinguish between a global normalization offset and energy-dependent shape discrepancies. The practical consequence is that the ±9.6 × 10^{-10} experimental uncertainty on the π+π− contribution (Table 3), which dominates the total error budget, may be either over- or under-estimated in a way that is not controlled. The authors should [provide quantitative讨论].

Authors: The referee is correct that a constant, energy-independent epsilon cannot distinguish between a global normalization offset and energy-dependent shape discrepancies. We acknowledged this limitation explicitly at the end of Section 2, noting that a more consistent procedure would involve an s-dependent epsilon determined through a simultaneous chi-squared minimization and entropy maximization of individual contributions. We agree that this limitation is not merely a caveat but has direct consequences for the uncertainty budget of the dominant pi+pi- channel. In the revised manuscript we will add a quantitative discussion of this point. Specifically, we will note that the constant epsilon procedure, by construction, captures the average scale of inter-experiment discrepancies but cannot track how these discrepancies vary across the rho peak, the rho-omega interference region, and the higher-energy tail. As a partial check on whether this leads to over- or under-estimation, we will compare the uncertainty obtained from our procedure with the spread of single-experiment integral results (BaBar-only, CMD-3-only, KLOE-only), which are already partially shown in Fig. 5. This spread provides an independent, if crude, estimate of the uncertainty scale. We note that our quoted uncertainty of 9.6 x 10^-10 is of the same order as the dispersion among single-experiment results, which suggests that the constant epsilon is not grossly misestimating the uncertainty, though we agree it cannot be considered fully controlled. We will state this comparison explicitly and acknowledge that a definitive resolution requires the s-dependent procedure we outline as future work. We cannot honestly claim more than this at present. revision: partial
Referee: §2, Table 2 and surrounding text: The procedure fails to converge for the π+π−π0 channel, where it is aborted after four iterations with ε = 9.7% and residual Δχ^2_{sys} = 15.2 for SND (2003). The authors then apply a Birge scaling factor √(χ^2/ndof) on top of the already-inflated uncertainties. This channel contributes 48.2 × 10^{-10} to a_μ^{had,LO} with an experimental uncertainty of 1.8 × 10^{-10}. Given that the procedure explicitly fails here, the reader cannot assess whether this 1.8 × 10^{-10} uncertainty is reliable. The authors should provide a more quantitative justification for why the failure in this channel does not undermine the overall uncertainty estimate, or alternatively, explore how sensitive the total a_μ^{had,LO} is to a substantially larger uncertainty on this channel.

Authors: We agree that the reader needs a quantitative sensitivity check. The pi+pi-pi0 channel contributes 48.2 x 10^-10 to the total, with an experimental uncertainty of 1.8 x 10^-10. Even if this uncertainty were doubled to 3.6 x 10^-10, the impact on the total experimental uncertainty (currently 9.8 x 10^-10, dominated by the pi+pi- channel at 9.6 x 10^-10) would be modest: the total would increase from 9.8 to approximately 10.0 x 10^-10. If the uncertainty were tripled to 5.4 x 10^-10, the total would become approximately 10.2 x 10^-10. In all cases the change is well within the overall uncertainty and does not affect the conclusion that the SM prediction lies approximately 2 sigma below the experimental world average. We will add this explicit sensitivity estimate to the revised manuscript. We will also clarify that the Birge scaling applied on top of the inflated uncertainties for this channel (with chi^2/ndof = 1.40) provides an additional factor of sqrt(1.40) ~ 1.18, which is already included in the quoted 1.8 x 10^-10. The residual Delta chi^2_sys = 15.2 for SND (2003) is indeed a limitation; we will note that SND (2003) is one of thirteen datasets in this channel and that the other datasets are reasonably well-behaved after the procedure, as shown in Table 2. revision: yes
Referee: §2, Table 1: The procedure leaves central values essentially unchanged—the integral pulls (Eq. 9) barely shift between the 'unmodified' and 'extra systematics' columns (e.g., CMD-3 2020: 0.048 → 0.052; BaBar 2012: 0.020 → 0.007). This means the fit central value is still determined by the original χ^2 minimization over mutually incompatible data, with no mechanism to assess potential bias in that central value. The expanded uncertainty band (Fig. 3) is wider, but the central a_μ^{had,LO} may be biased if the fit averages over datasets that disagree in shape rather than normalization. The authors should discuss this potential bias, perhaps by comparing the central value obtained from individual experiments (as partially shown in Fig. 5 for KLOE-only, BaBar-only, CMD-3-only) and quantifying the spread.

Authors: This is a fair and important point. The procedure we propose addresses the uncertainty but does not modify the central value, which remains determined by the standard chi-squared minimization over all datasets. If the disagreements between experiments are primarily in shape rather than normalization, the averaged central value could indeed be biased in a way that our procedure does not capture. We will address this in the revised manuscript by explicitly quantifying the spread of single-experiment results. From Fig. 5, the pi+pi- contribution using KLOE-only, BaBar-only, and CMD-3-only data (supplemented by OLYA and BCF data above 1 GeV) yields visibly different central values for a_mu. We will tabulate these individual-experiment results and their spread, and compare the spread to our quoted uncertainty. This provides a direct, if imperfect, measure of the potential central-value bias: if the spread of single-experiment results is comparable to or larger than our uncertainty, it signals that the central value is not robust against the choice of dataset. We will present this comparison transparently. We acknowledge that we cannot fully resolve the bias question within the present framework—no averaging procedure can guarantee an unbiased central value when the input data are mutually incompatible at the level of shape differences. This is a fundamental limitation that we will state explicitly. The only definitive resolution will come from new measurements or from identification of the instrumental sources of the discrepancies. revision: yes

standing simulated objections not resolved

The question of whether the central value of a_mu^{had,LO} is biased by shape discrepancies among incompatible datasets cannot be definitively answered within any averaging framework. Our procedure inflates uncertainties but does not alter central values. While the single-experiment spread provides a diagnostic, no procedure applied to mutually incompatible data can guarantee an unbiased central value without understanding the instrumental origin of the discrepancies. This is a fundamental limitation we acknowledge but cannot resolve.

Circularity Check

0 steps flagged

No significant circularity; self-citations are methodological (code/data), not load-bearing for the physics result

full rationale

The dispersive integral (Eq. 1) and R-ratio (Eq. 2) are standard results cited to independent literature [3]. The central value of a_mu(had,LO) is determined by fitting independent experimental data [4,5,6]. The extra systematic uncertainty epsilon (Eqs. 5-11) is estimated from observed inter-experiment pulls and then propagated through the dispersion integral; while this is data-driven uncertainty inflation, it does not reduce algebraically to the input tensions because the propagation depends on the kernel K(s) and the energy distribution of each experiment's measurements. The self-citations [7,8,9] are for the numerical code, data compilation, and database infrastructure — not for a load-bearing theorem, ansatz, or uniqueness argument that would force the result. The paper is transparent that the epsilon parameterization is approximate and insufficient in some channels (pi+pi-pi0 non-convergence, Table 2), which is a modeling/correctness concern rather than circularity. No step in the derivation chain reduces to its own inputs by construction.

Axiom & Free-Parameter Ledger

3 free parameters · 4 axioms · 0 invented entities

The free parameters include the chi^2 threshold (nominal value 10), per-channel extra systematic uncertainties epsilon (fitted from data pulls), and the R_had(s) parameterization parameters. The key ad-hoc axiom is that inter-experiment tensions can be modeled as an uncorrelated normalization uncertainty (Eq. 11), which the authors themselves acknowledge is a first approximation.

free parameters (3)

chi^2_thr = 10
Threshold for identifying experiments with maximally non-uniform chi^2 contributions. Described as 'nominal' in Eq. 10, varied in the 6-25 interval for uncertainty estimation.
epsilon (per channel) = 5.7% (pi+pi-), 9.7% (pi+pi-pi0), etc.
Extra systematic uncertainty added in quadrature to each channel, estimated from integral pulls of experiments exceeding the chi^2 threshold.
R_had^fit(s) parameterization parameters = not listed
Free parameters in the R_had(s) parameterization for each hadronic final state, fitted by chi^2 minimization (Eq. 3).

axioms (4)

standard math Dispersive relation for a_mu(had,LO)
Eq. 1 relating a_mu(had,LO) to the dispersion integral of R_had(s), from [3].
standard math R-ratio definition
Eq. 2 defining R_had(s) in terms of sigma_tot, standard from prior literature.
domain assumption Covariance matrix parameterization
Eq. 4 parameterizing the covariance matrix with point-to-point systematic uncertainties and inter-experiment correlations.
ad hoc to paper Extra uncertainty as uncorrelated normalization
Eq. 11 assumes the extra systematic uncertainty can be modeled as an uncorrelated normalization uncertainty, which the authors note is 'insufficient' (§2).

pith-pipeline@v1.1.0-glm · 14008 in / 2266 out tokens · 416143 ms · 2026-07-08T08:40:30.160260+00:00 · methodology

0 comments

read the original abstract

Using an up-to-date compilation of $\sigma_{\mathrm{tot}}(e^+e^- \to hadrons)$ data we estimated the LO hadronic contribution to the muon anomalous magnetic moment, $a_\mu(had,LO)$. Incompatibilities between $\sigma_{\mathrm{tot}}(e^+e^- \to hadrons)$ measurements by independent experiments are mitigated by extra systematic uncertainties estimated using as a guideline a requirement of uniformity of $\chi^2$ distribution over degrees of freedom in joint fits of $\sigma_{\mathrm{tot}}$. Tensions in the $e^+e^-$ input data translate into an expanded uncertainty of the $a_\mu(had,LO) = (697.7 \pm {9.8}_{e^+e^-} \pm 3.6_{sys}) \times 10^{-10}$. Given this, we obtain the SM prediction for the muon anomaly $a_\mu^{\mathrm{SM}} = 11659185.5(10.6) \times 10^{-10}$, below the experimental world average $a_\mu^{\mathrm{exp}}$ at $2\sigma$ level.

Figures

Figures reproduced from arXiv: 2607.06352 by O.V. Zenin, V.V. Bryzgalov.

**Figure 2.** Figure 2: Rπ +π −(γ) in the ρ–ω interference region, most representative to demonstrate tensions between BaBar, CMD-3 and KLOE σtot(e +e − → π +π −(γ)) measurements. Total experimental uncertainties are shown by vertical error bars with ticks indicating the statistical uncertainty. The fit is performed in the range 0.3 < √ s < 2.0 GeV with unmodified experimental uncertainties. The fit uncertainty (shown by green ba… view at source ↗

**Figure 3.** Figure 3: (a) Same as in Fig. 2 after the fit with the additional 5.7% systematic uncertainty accounting [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

**Figure 4.** Figure 4: (a) The final fit of Rπ +π −π 0 with ϵ = 9.7%. (b), (c) Enlarged view of ω(783) and ϕ(1020) regions. 8 [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗

**Figure 5.** Figure 5: The experimental world average a exp µ dominated by the FNAL g-2 measurement [1] vs theoretical a SM µ values including various aµ(had, LO) estimates (from top to bottom): the average of dispersion estimates [13] before publication of CMD-3 π +π − data; lattice QCD estimate [1]; our dispersion estimates with the π +π −(γ) contribution using only KLOE-2 [5], BaBar [4] and CMD-3 [6] (supplemented by OLYA and… view at source ↗

discussion (0)

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