Hadronic vacuum polarisation in the muon g−2
Resolve the disagreement between lattice-QCD and data-driven (e+e− → hadrons) evaluations of the leading hadronic vacuum polarisation contribution to the muon anomalous magnetic moment.
Cite
@misc{cairn-muon-g-2-hadronic-contribution,
title = {Hadronic vacuum polarisation in the muon g−2},
author = {{Cairn Commons contributors}},
howpublished = {\url{https://cairn-commons.com/problems/muon-g-2-hadronic-contribution}},
year = {2026},
note = {Open problem on Cairn Commons, CC BY 4.0. Accessed 2026-09-29}
} Also: CITATION.cff · Atom feed of results
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Current state
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The problem
The question. The Standard Model prediction of the muon anomaly a_μ = (g−2)/2 is limited by the leading-order hadronic vacuum polarisation (LO HVP). It can be computed from first principles with lattice QCD, or obtained from measured e+e− → hadrons cross sections via a dispersion relation. The two approaches disagree, and the e+e− data sets disagree among themselves. Why?
Known status. The Fermilab Muon g−2 experiment released its final result in June 2025, with a precision of 127 ppb. The Muon g−2 Theory Initiative's 2025 White Paper found that, after the CMD-3 π+π− measurement, data-driven evaluations were in too much tension to be combined, and based the LO HVP on lattice QCD (7132(61) × 10^-11, about 0.9% precision). Its SM value, 116 592 033(62) × 10^-11, agrees with the experimental average 116 592 071.5(14.5) × 10^-11 (difference 38(63) × 10^-11). The lattice-versus-data-driven discrepancy itself remains unexplained.
What counts as progress
- Reproducible re-analyses of public e+e− → π+π− data sets (KLOE, BaBar, CMD-3, …) that identify or exclude specific sources of the tension (radiative corrections, normalisation, correlations).
- Independent lattice cross-checks of window observables with public code and ensembles metadata.
- Syntheses that tabulate all published LO HVP evaluations with a consistent treatment of uncertainties, and documented negative results (e.g. "a new-physics contribution to e+e− → hadrons of type X cannot explain the shift because of constraint Y").
How it is checked. Reviewers re-run the analysis code on the cited public inputs and compare with the published numbers; syntheses are checked against the primary papers.