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arxiv: 2407.10913 · v2 · submitted 2024-07-15 · ✦ hep-lat · hep-ph· hep-th

Hybrid calculation of hadronic vacuum polarization in muon g-2 to 0.48\%

A.Boccaletti , Sz.Borsanyi , A.Cotellucci , M.Davier , Z.Fodor , F.Frech , A.Gerardin , D.Giusti
show 14 more authors
A.Yu.Kotov L.Lellouch Th.Lippert A.Lupo B.Malaescu S.Mutzel A.Portelli A.Risch M.Sjo F.Stokes K.K.Szabo B.C.Toth G.Wang Z.Zhang
This is my paper

Pith reviewed 2026-05-23 23:07 UTC · model grok-4.3

classification ✦ hep-lat hep-phhep-th
keywords hadronic vacuum polarizationmuon anomalous magnetic momentlattice QCDmuon g-2standard model test
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The pith

Lattice calculation of hadronic vacuum polarization produces a muon g-2 prediction that differs from experiment by only 0.5 standard deviations.

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

The paper computes the leading-order hadronic vacuum polarization contribution to the muon anomalous magnetic moment using lattice QCD on finer lattices than in prior work. It augments the lattice results at short and intermediate distances with a small long-distance piece taken from experiment in the energy regime where different data sets agree. The resulting value is 715.1(2.5)(2.3)[3.4] × 10^{-10}. When this number is added to all other standard-model contributions, the full prediction for a_μ lies only 0.5 sigma from the latest experimental measurement. The agreement constitutes a test of the standard model to eleven significant figures.

Core claim

We obtain a_μ^{LO-HVP} = 715.1(2.5)(2.3)[3.4] × 10^{-10} from lattice simulations on finer lattices combined with a small long-distance contribution from experiment; this result, when added to the rest of the standard model, produces a prediction for the muon anomalous magnetic moment that differs from the measured value by only 0.5 standard deviations.

What carries the argument

The hybrid lattice-plus-experiment method that evaluates the hadronic vacuum polarization by combining short- and intermediate-distance lattice data with a long-distance tail taken from experiment where measurements agree.

If this is right

  • The uncertainty on the leading hadronic contribution drops by a factor of 1.6 relative to the earlier lattice result.
  • The complete standard-model prediction for a_μ now lies 0.5 sigma from the experimental central value.
  • The test of the standard model reaches eleven significant figures.
  • Finer lattices improve the accuracy of the continuum extrapolation.

Where Pith is reading between the lines

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

  • If the experimental long-distance input remains stable, future lattice effort can focus on further reduction of short-distance errors.
  • The same hybrid strategy may be useful for other precision observables limited by long-distance effects.
  • A future shift in either the lattice central value or the experimental measurement larger than the quoted error would reopen the possibility of physics beyond the standard model.

Load-bearing premise

The long-distance contribution can be taken from experiment in the regime where all measurements agree and the continuum extrapolation from the new finer lattices introduces no undetected systematic bias that would shift the central value outside the quoted total uncertainty.

What would settle it

A new lattice simulation on still finer lattices that moves the short-distance contribution by more than 3.4 × 10^{-10}, or a re-analysis of the long-distance regime that shifts the hybrid central value outside the present error band.

Figures

Figures reproduced from arXiv: 2407.10913 by A.Boccaletti, A.Cotellucci, A.Gerardin, A.Lupo, A.Portelli, A.Risch, A.Yu.Kotov, B.C.Toth, B.Malaescu, D.Giusti, F.Frech, F.Stokes, G.Wang, K.K.Szabo, L.Lellouch, M.Davier, M.Sjo, S.Mutzel, Sz.Borsanyi, Th.Lippert, Z.Fodor, Z.Zhang.

Figure 1
Figure 1. Figure 1: Main uncertainties and their reduction in our successive lattice calculations of [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Left panel: comparison of our result for the light contribution of the intermediate-distance window, a LO-HVP,light µ,04−10 , with other results in the literature. Our result is the red square, the purple squares correspond to other lattice computations, the blue circle [31] and triangle [3] to data-driven approaches. Right panel: comparison of determinations of the full a LO-HVP µ,04−10. Here, in the data… view at source ↗
Figure 3
Figure 3. Figure 3: Comparison of standard-model predictions of the muon anomalous magnetic moment with its [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 1
Figure 1. Figure 1: Landscape of our ensembles. The horizontal and vertical axes are the squared pseudo-scalar [PITH_FULL_IMAGE:figures/full_fig_p013_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Left panel: normalized autocorrelation function of energy density [PITH_FULL_IMAGE:figures/full_fig_p015_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Taste violation as a function of lattice spacing, for axial-vector [PITH_FULL_IMAGE:figures/full_fig_p016_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Ω baryon effective masses extracted from the GEVP for five excited states (upper panel) and for the ground state (lower panel) on an ensemble at β = 4.1479. In the lower panel the blue band is obtained from a single exponential fit to the ground state propagator. In the upper panel the gray horizontal line corresponds to the mass of the recent observation of an excited Ω baryon from the Belle experiment [1… view at source ↗
Figure 5
Figure 5. Figure 5: Left panel: cumulative distribution function (CDF) of [PITH_FULL_IMAGE:figures/full_fig_p019_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Results for the ground state Ω baryon mass with fit range [0.9 fm, 2.0 fm] on different ensembles. Each ensemble has six data points with the same color, which correspond to correlated fits to the ΩVI, ΩXI and ΩBa propagators followed by the same propagators in uncorrelated fits. The plot shows the relative deviation from the ensemble average, ie. the average over the six points with the same color. The up… view at source ↗
Figure 7
Figure 7. Figure 7: Decomposition of the neutral and charged kaon masses in three different isospin schemes. Red [PITH_FULL_IMAGE:figures/full_fig_p024_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Strong-isospin-breaking (SIB) contribution to [PITH_FULL_IMAGE:figures/full_fig_p042_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: The valence QED contribution [a light µ ] ′′ 20 on a selected a = 0.0787 fm configuration, as the function of the upper limit of the time integration tc. The green squares show the results obtained through a chiral extrapolation from measurements performed at valence quark masses which are κ = 3, 5, 7 times larger than the physical light quark mass ml . The red circles correspond to the measurements perfor… view at source ↗
Figure 10
Figure 10. Figure 10: Strong-isospin-breaking (SIB) contribution to [PITH_FULL_IMAGE:figures/full_fig_p044_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Results for data-driven determination of finite-volume effects in the [PITH_FULL_IMAGE:figures/full_fig_p045_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Comparison of results for the I = 1 finite-volume correction in various windows. The red points correspond to the 4hex lattice results. The other points correspond to the data-driven determinations from individual data sets. Their averages are also displayed (inner two bands), as described in [PITH_FULL_IMAGE:figures/full_fig_p046_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Results for aµ,28−∞ obtained using the π +π − spectra measured by BaBar, KLOE, CMD-3 and in τ decays. The results are normalized by their weighted average, which is shown by a red diamond in the bottom. Above that, the red circle shows the weighted average without the τ data. Neither of these needed a PDG rescaling of the error. The red band represents the total uncertainty, which is obtained by adding li… view at source ↗
Figure 14
Figure 14. Figure 14: Results for aµ,28−35. Figure description is the same as in [PITH_FULL_IMAGE:figures/full_fig_p050_14.png] view at source ↗
read the original abstract

We present a new lattice QCD calculation of the leading order hadronic vacuum polarization (LO-HVP) contribution to the muon anomalous magnetic moment $a_\mu$. We reduce uncertainties compared to our earlier computation arXiv:2002.12347 by a factor of 1.6. We perform simulations on finer lattices allowing for an even more accurate continuum extrapolation. We also include a small, long-distance contribution obtained using input from experiments in a low-energy regime where they all agree. Combined with other standard model contributions our result, $a_\mu^{LO-HVP}=715.1(2.5)(2.3)[3.4] \times 10^{-10}$, leads to a prediction that differs from the recent measurement of $a_\mu$ by only 0.5 standard deviations. This provides a remarkable validation of the standard model to 11 digits.

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

0 major / 2 minor

Summary. The manuscript presents a hybrid lattice QCD plus experimental determination of the leading-order hadronic vacuum polarization (LO-HVP) contribution to the muon anomalous magnetic moment. Simulations on finer lattices improve the continuum extrapolation relative to the authors' prior work (arXiv:2002.12347), and a small long-distance piece is taken from experiment in the regime where all measurements agree. The central result is a_μ^{LO-HVP} = 715.1(2.5)(2.3)[3.4] × 10^{-10} (0.48 % total uncertainty). Combined with other Standard Model contributions, this yields a prediction differing from the recent experimental a_μ measurement by only 0.5 standard deviations.

Significance. If the quoted total uncertainty of 3.4 × 10^{-10} is reliable, the result constitutes a substantial advance, reducing the uncertainty by a factor of 1.6 and supplying an independent lattice evaluation of the dominant intermediate-distance contribution. The use of finer lattices for a more controlled continuum extrapolation and the explicit separation of the long-distance piece (taken where experimental data converge) are clear strengths. The 0.5-σ agreement supplies a high-precision test of the Standard Model at the level of eleven digits.

minor comments (2)
  1. [Abstract] The notation (2.5)(2.3)[3.4] for the error budget is compact but would benefit from an explicit one-sentence statement of which components are statistical, systematic, and the total in quadrature, preferably repeated in the abstract and in the final results table.
  2. [Section on long-distance contribution] The description of the long-distance matching window would be clearer if the precise energy or distance cut-off used to separate the lattice and experimental regimes were stated numerically in the text rather than only by reference to prior work.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of the manuscript and for recommending acceptance. The referee's summary accurately reflects the key advances: the use of finer lattices for a more controlled continuum extrapolation and the hybrid treatment of the long-distance contribution taken from experiment in the regime of agreement among measurements.

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained

full rationale

The paper computes the dominant LO-HVP contribution via independent lattice QCD simulations on finer lattices with continuum extrapolation, citing prior work only for methodological context and uncertainty reduction. The small long-distance piece is taken directly from external experimental data in a regime of agreement across measurements, providing an external benchmark rather than an internal fit. No step reduces by construction to a fitted parameter renamed as prediction, no self-citation chain bears the central claim, and no ansatz or uniqueness theorem is imported from overlapping authors to force the result. The final comparison to the a_μ measurement is a post-computation validation against an independent datum, leaving the derivation self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review; specific free parameters, axioms, and invented entities are not enumerated in the provided text. Standard lattice QCD assumptions (continuum limit, chiral extrapolation, etc.) are implicitly required but not detailed.

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discussion (0)

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Forward citations

Cited by 15 Pith papers

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

  1. Higher-order hadronic vacuum polarization contribution to the muon $g-2$ from lattice QCD

    hep-lat 2026-03 conditional novelty 9.0

    Lattice QCD yields the NLO HVP contribution to muon g-2 as -101.57(26)stat(54)syst ×10^{-11}, 1.4σ below the 2025 White Paper estimate and twice as precise.

  2. Lattice determination of the higher-order hadronic vacuum polarization contribution to the muon $g-2$

    hep-lat 2026-04 unverdicted novelty 8.0

    Lattice QCD gives a_μ^{hvp,nlo} = (-101.57 ± 0.60) × 10^{-11} at 0.6% precision, 1.4σ below the 2025 White Paper estimate and in 4.6σ tension with pre-CMD-3 data-driven results.

  3. Light new physics and the $\tau$ lepton dipole moments: prospects at Belle II

    hep-ph 2025-10 unverdicted novelty 7.0

    Light new particles generate asymmetries in e+e- to tau+tau- that allow model-dependent constraints on tau dipole moments, including non-zero effects without electron polarization via imaginary parts.

  4. Normalizing flows for all-orders QED corrections in lattice field theory

    hep-lat 2026-05 unverdicted novelty 6.0

    Normalizing flows enable all-order QED corrections in lattice scalar QED in 2-4 dimensions with reduced variance and transferability from small to large lattices.

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

    hep-ph 2026-04 unverdicted novelty 6.0

    A general framework quantifies correlation-induced uncertainties in precision data combinations and applies it to e+e- to hadrons cross sections for muon g-2 HVP determinations.

  6. Light new physics and the $\tau$ lepton dipole moments

    hep-ph 2025-11 unverdicted novelty 6.0

    This work provides a comprehensive analysis of light new physics contributions to tau lepton dipole moments, detailing interpretations of asymmetry measurements for spin-0 and spin-1 bosons, their decoupling to the EF...

  7. Field-theoretic versus data-driven evaluations of electromagnetic corrections to hadronic vacuum polarization in $(g-2)_\mu$

    hep-ph 2025-09 conditional novelty 6.0

    Virtual electromagnetic corrections largely cancel radiative-channel contributions in data-driven HVP evaluations for muon g-2, reconciling timelike and spacelike methods via a VMD model.

  8. Aspects of a Five-Dimensional $U(1)_{L_\mu - L_\tau}$ Model at Future Muon-Based Colliders

    hep-ph 2026-04 unverdicted novelty 5.0

    Future muon colliders can probe Kaluza-Klein excitations of a 5D U(1)_{Lμ-Lτ} gauge boson across MeV to TeV masses with couplings down to 10^{-5}.

  9. The anomalous magnetic moment of the muon in the Standard Model: an update

    hep-ph 2025-05 accept novelty 5.0

    The updated SM prediction for the muon anomalous magnetic moment is 116592033(62)×10^{-11}, showing no tension with the experimental average of 38(63)×10^{-11}.

  10. Comparison of the hadronic vacuum polarization between hadronic $\tau$-decay data and lattice QCD

    hep-ph 2026-05 unverdicted novelty 4.0

    Lattice QCD and tau-decay dispersive calculations of isospin-one HVP generally agree, except for a significant difference in the 2π−π+π0 four-pion mode contribution to window quantities.

  11. Prospects of five-dimensional $L_\mu-L_\tau$ gauge interactions in the light of elastic neutrino-electron scatterings: The scope of the DUNE near detector

    hep-ph 2024-07 unverdicted novelty 4.0

    Five-dimensional U(1)_{Lμ-Lτ} model predicts multiple gauge bosons whose contributions to elastic neutrino-electron scattering can be probed at DUNE, covering much of the muon (g-2) consistent parameter space.

  12. Variance reduction strategies for lattice QCD

    hep-lat 2026-05 unverdicted novelty 2.0

    Variance reduction schemes based on decompositions of quark propagators have proven useful for precision lattice QCD observables and may help reduce the computational cost of reaching large volumes.

  13. An Update on the Isospin-Breaking Effects in the Pion Decay Constant with Staggered Quarks

    hep-lat 2026-04 unverdicted novelty 2.0

    Preliminary update on isospin-breaking corrections to the pion decay constant in staggered N_f=2+1+1 QCD with QED_L, including correlator data for scale setting.

  14. Lepton anomalous magnetic moments: Theory

    hep-ph 2025-12 unverdicted novelty 2.0

    The paper provides an overview of theoretical calculations for lepton anomalous magnetic moments arising from quantum corrections in the Standard Model.

  15. FLAG Review 2024

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    The FLAG 2024 review provides updated averages of lattice QCD determinations for quark masses, decay constants, form factors, mixing parameters, and nucleon matrix elements.

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