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arxiv: 2505.21476 · v3 · pith:6LFHRPHKnew · submitted 2025-05-27 · ✦ hep-ph · hep-ex· hep-lat· nucl-ex· nucl-th

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

R. Aliberti , T. Aoyama , E. Balzani , A. Bashir , G. Benton , J. Bijnens , V. Biloshytskyi , T. Blum
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D. Boito M. Bruno E. Budassi S. Burri L. Cappiello C. M. Carloni Calame M. C\`e V. Cirigliano D. A. Clarke G. Colangelo L. Cotrozzi M. Cottini I. Danilkin M. Davier M. Della Morte A. Denig C. DeTar V. Druzhinin G. Eichmann A. X. El-Khadra E. Estrada X. Feng C. S. Fischer R. Frezzotti G. Gagliardi A. G\'erardin M. Ghilardi D. Giusti M. Golterman S. Gonz\`alez-Sol\'is S. Gottlieb R. Gruber A. Guevara V. G\"ulpers A. Gurgone F. Hagelstein M. Hayakawa N. Hermansson-Truedsson A. Hoecker M. Hoferichter B.-L. Hoid S. Holz R. J. Hudspith F. Ignatov L. Jin N. Kalntis G. Kanwar A. Keshavarzi J. Komijani J. Koponen S. Kuberski B. Kubis A. Kupich A. Kup\'s\'c S. Lahert S. Laporta C. Lehner M. Lellmann L. Lellouch T. Leplumey J. Leutgeb T. Lin Q. Liu I. Logashenko C. Y. London G. L\'opez Castro J. L\"udtke A. Lusiani A. Lutz J. Mager B. Malaescu K. Maltman M. K. Marinkovi\'c J. M\'arquez P. Masjuan H. B. Meyer T. Mibe N. Miller A. Miramontes A. Miranda G. Montagna S. E. M\"uller E. T. Neil A. V. Nesterenko O. Nicrosini M. Nio D. Nomura J. Paltrinieri L. Parato J. Parrino V. Pascalutsa M. Passera S. Peris P. Petit Ros\`as F. Piccinini R. N. Pilato L. Polat A. Portelli D. Portillo-S\'anchez M. Procura L. Punzi K. Raya A. Rebhan C. F. Redmer B. L. Roberts A. Rodr\'iguez-S\'anchez P. Roig J. Ruiz de Elvira P. S\'anchez-Puertas A. Signer J. W. Sitison D. Stamen D. St\"ockinger H. St\"ockinger-Kim P. Stoffer Y. Sue P. Tavella T. Teubner J.-N. Toelstede G. Toledo W. J. Torres Bobadilla J. T. Tsang F. P. Ucci Y. Ulrich R. S. Van de Water G. Venanzoni S. Volkov G. von Hippel G. Wang U. Wenger H. Wittig A. Wright E. Zaid M. Zanke Z. Zhang M. Zillinger C. Alexandrou A. Altherr M. Anderson C. Aubin S. Bacchio P. Beltrame A. Beltran P. Boyle I. Campos Plasencia I. Caprini B. Chakraborty G. Chanturia A. Crivellin A. Czarnecki L.-Y. Dai T. Dave L. Del Debbio K. Demory D. Djukanovic T. Draper A. Driutti M. Endo F. Erben K. Ferraby J. Finkenrath L. Flower A. Francis E. G\'amiz J. Gogniat A. V. Grebe S. G\"undogdu M. T. Hansen S. Hashimoto H. Hayashii D. W. Hertzog L. A. Heuser L. Hostetler X. T. Hou G. S. Huang T. Iijima K. Inami A. J\"uttner R. Kitano M. Knecht S. Kollatzsch A. S. Kronfeld T. Lenz G. Levati Q. M. Li Y. P. Liao J. Libby K. F. Liu V. Lubicz M. T. Lynch A. T. Lytle J. L. Ma K. Miura K. M\"ohling J. Muskalla F. No\"el K. Ottnad P. Paradisi C. T. Peterson A. Pich S. Pitelis S. Plura A. Price D. Radic A. Radzhabov A. Risch S. Romiti S. Sahoo F. Sannino H. Sch\"afer Y. Schelhaas S. I. Serednyakov O. Shekhovtsova J. N. Simone S. Simula E. P. Solodov F. M. Stokes M. Vanderhaeghen A. Vaquero N. Vestergaard W.P. Wang Z. W\k{a}s K. Yamashita Y. B. Yang T. Yoshioka C. Z. Yuan A. S. Zhevlakov
This is my paper

Pith reviewed 2026-05-15 13:14 UTC · model grok-4.3

classification ✦ hep-ph hep-exhep-latnucl-exnucl-th
keywords muon anomalous magnetic momenthadronic vacuum polarizationlattice QCDStandard Model predictiong-2CMD-3
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The pith

Adopting the lattice-QCD average for leading hadronic vacuum polarization shifts the Standard Model prediction for the muon anomalous magnetic moment upward, removing tension with experiment.

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

This paper updates the Standard Model prediction for the muon anomalous magnetic moment a_mu by consolidating pure QED and electroweak pieces while addressing the dominant hadronic uncertainties. Tensions among data-driven evaluations of the leading-order hadronic vacuum polarization have grown after the new CMD-3 measurement of the e+e- to pi+pi- cross section, preventing their combination. The authors instead adopt a consolidated lattice-QCD average for this contribution at 0.9 percent precision. The resulting total prediction is a_mu^SM = 116592033(62) x 10^{-11}. Comparison to the current experimental average yields a difference of only 38(63) x 10^{-11}, consistent within uncertainties.

Core claim

The Standard Model prediction for the muon anomalous magnetic moment is now a_mu^SM = 116592033(62) x 10^{-11} (530 ppb). This value is obtained by using the lattice-QCD average for the leading-order hadronic vacuum polarization contribution rather than data-driven estimates, producing an upward shift that brings theory into agreement with the experimental average of a_mu^exp - a_mu^SM = 38(63) x 10^{-11}.

What carries the argument

The consolidated lattice-QCD average for the leading-order hadronic vacuum polarization (LO HVP) contribution, which replaces conflicting data-driven values and produces the upward shift in the total prediction.

If this is right

  • The muon g-2 anomaly disappears at the present experimental precision of about 500 ppb.
  • Future theory work must reach the 127 ppb target to confront the final E989 experimental precision.
  • Resolution of the remaining tensions among e+e- cross-section data sets will be required for any data-driven approach to regain viability.
  • The hadronic light-by-light contribution has already seen its uncertainty halved through combined dispersive and lattice methods.

Where Pith is reading between the lines

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

  • If the lattice average is correct, systematic biases in dispersive analyses of hadronic data may affect other precision observables that rely on the same inputs.
  • Cross-checks between lattice results and independent experimental channels for the same hadronic quantities could test whether the upward shift is robust.
  • The shift may alter the interpretation of related electroweak precision tests that share hadronic vacuum polarization inputs.

Load-bearing premise

The lattice-QCD calculations supply a more reliable value for the leading-order hadronic vacuum polarization than any combination of the conflicting experimental cross-section data.

What would settle it

A new high-precision lattice-QCD result for the LO HVP contribution that falls significantly below the current consolidated average, or a future data-driven evaluation that reconciles the e+e- cross-section measurements at the old lower value.

read the original abstract

We present the current Standard Model (SM) prediction for the muon anomalous magnetic moment, $a_\mu$, updating the first White Paper (WP20) [1]. The pure QED and electroweak contributions have been further consolidated, while hadronic contributions continue to be responsible for the bulk of the uncertainty of the SM prediction. Significant progress has been achieved in the hadronic light-by-light scattering contribution using both the data-driven dispersive approach as well as lattice-QCD calculations, leading to a reduction of the uncertainty by almost a factor of two. The most important development since WP20 is the change in the estimate of the leading-order hadronic-vacuum-polarization (LO HVP) contribution. A new measurement of the $e^+e^-\to\pi^+\pi^-$ cross section by CMD-3 has increased the tensions among data-driven dispersive evaluations of the LO HVP contribution to a level that makes it impossible to combine the results in a meaningful way. At the same time, the attainable precision of lattice-QCD calculations has increased substantially and allows for a consolidated lattice-QCD average of the LO HVP contribution with a precision of about 0.9%. Adopting the latter in this update has resulted in a major upward shift of the total SM prediction, which now reads $a_\mu^\text{SM} = 116\,592\,033(62)\times 10^{-11}$ (530 ppb). When compared against the current experimental average based on the E821 experiment and runs 1-6 of E989 at Fermilab, one finds $a_\mu^\text{exp} - a_\mu^\text{SM} =38(63)\times 10^{-11}$, which implies that there is no tension between the SM and experiment at the current level of precision. The final precision of E989 (127 ppb) is the target of future efforts by the Theory Initiative. The resolution of the tensions among data-driven dispersive evaluations of the LO HVP contribution will be a key element in this endeavor.

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

2 major / 2 minor

Summary. The manuscript updates the Standard Model prediction for the muon anomalous magnetic moment a_μ, consolidating QED and electroweak contributions while updating hadronic terms. The key development is the adoption of a lattice-QCD average for the leading-order hadronic vacuum polarization (LO HVP) at ~0.9% precision, motivated by tensions among data-driven dispersive evaluations following the CMD-3 e⁺e⁻→π⁺π⁻ measurement. This yields a_μ^SM = 116592033(62)×10^{-11} (530 ppb), with a_μ^exp - a_μ^SM = 38(63)×10^{-11}, implying no tension with the experimental average from E821 and E989 runs 1-6. Progress in hadronic light-by-light scattering reduces its uncertainty by nearly a factor of two.

Significance. If the consolidated lattice-QCD LO HVP average is robust, the update produces a major upward shift in the SM prediction that eliminates the prior discrepancy with experiment. This provides a new benchmark at 530 ppb precision, emphasizes lattice methods for controlling hadronic uncertainties, and sets targets for the final E989 precision (127 ppb) and future theory efforts. The reduced uncertainty in the hadronic light-by-light contribution is a clear technical advance.

major comments (2)
  1. [Abstract and LO HVP contribution section] The central no-tension claim and the 38(63)×10^{-11} difference rest entirely on replacing prior data-driven LO HVP values with the lattice-QCD average. The abstract and LO HVP section state that CMD-3 tensions make data-driven combination impossible, but supply no quantitative demonstration (e.g., via explicit comparison of finite-volume, chiral-extrapolation, or discretization systematics) that the lattice average is free of biases at the 0.9% level quoted. This substitution is load-bearing for the upward shift and consistency conclusion.
  2. [Uncertainty budget and final result section] The total uncertainty of 62×10^{-11} is stated to be dominated by hadronic contributions. An explicit propagation table or equation showing how the 0.9% lattice uncertainty combines with QED, EW, and HLbL terms (including any correlations) is needed to verify the final error budget.
minor comments (2)
  1. [Abstract] The abstract would be strengthened by quoting the previous WP20 central value and uncertainty for direct comparison of the shift magnitude.
  2. [Introduction or results section] Notation for the final result (e.g., the 530 ppb figure) should be defined explicitly in the text rather than only in the abstract.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our update of the Standard Model prediction for the muon anomalous magnetic moment. We address the two major comments point by point below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [Abstract and LO HVP contribution section] The central no-tension claim and the 38(63)×10^{-11} difference rest entirely on replacing prior data-driven LO HVP values with the lattice-QCD average. The abstract and LO HVP section state that CMD-3 tensions make data-driven combination impossible, but supply no quantitative demonstration (e.g., via explicit comparison of finite-volume, chiral-extrapolation, or discretization systematics) that the lattice average is free of biases at the 0.9% level quoted. This substitution is load-bearing for the upward shift and consistency conclusion.

    Authors: We agree that the no-tension conclusion depends on adopting the lattice-QCD LO HVP average. The tensions among data-driven evaluations after CMD-3 are established in the cited literature and preclude a reliable combination. The lattice average is formed from several independent calculations by different groups employing distinct fermion discretizations, volumes, and chiral extrapolations; the quoted 0.9% precision reflects their mutual consistency within uncertainties. Individual papers already contain detailed finite-volume, chiral, and discretization studies. To make this more transparent in the manuscript, we will insert a short summary table in the LO HVP section that tabulates the main systematic contributions and quoted uncertainties from the principal lattice results entering the average, together with references. revision: yes

  2. Referee: [Uncertainty budget and final result section] The total uncertainty of 62×10^{-11} is stated to be dominated by hadronic contributions. An explicit propagation table or equation showing how the 0.9% lattice uncertainty combines with QED, EW, and HLbL terms (including any correlations) is needed to verify the final error budget.

    Authors: We concur that an explicit breakdown would strengthen the presentation. The total uncertainty is dominated by the hadronic terms, with the LO HVP lattice uncertainty providing the largest single contribution. We will add a dedicated uncertainty-budget table in the final-result section that lists each component (pure QED, electroweak, LO HVP, NLO HVP, HLbL, etc.) with its central value and uncertainty, shows the quadratic summation, and states the (negligible) correlations assumed between sectors. This table will make the propagation transparent and allow direct verification of the quoted 62×10^{-11} total error. revision: yes

Circularity Check

0 steps flagged

No circularity: SM prediction aggregates independent external calculations

full rationale

The paper compiles the SM prediction as a sum of QED, electroweak, and hadronic contributions. The LO HVP term is taken directly from a consolidated lattice-QCD average computed by external groups; no equation in the paper defines this average in terms of the final a_mu^SM or fits any parameter to the experimental datum. The final comparison a_mu^exp - a_mu^SM is performed after the prediction is assembled and does not enter the derivation. All cited prior results (including WP20) are treated as independent inputs rather than self-referential steps.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

This is a community consensus update that aggregates existing calculations rather than introducing new derivations. The dominant input is the external lattice-QCD average for LO HVP; all other pieces are taken from prior literature.

axioms (1)
  • domain assumption The Standard Model framework correctly describes QED, electroweak, and hadronic contributions to a_mu at the current precision.
    Invoked throughout the abstract when combining the separate contributions into a single SM prediction.

pith-pipeline@v0.9.0 · 7038 in / 1508 out tokens · 65100 ms · 2026-05-15T13:14:56.426058+00:00 · methodology

discussion (0)

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Forward citations

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