Abstract For 50 years, the standard model of particle physics has been very successful in describing subatomic phenomena. In the past quarter of a century, this was challenged by a mismatch between its predictions and precision measurements of the anomalous magnetic moment of the muon, a μ. This disagreement was eventually reconciled, first through a determination in an ab initio lattice calculation 1 of the most uncertain theoretical contribution, the leading-order hadronic vacuum polarization (LO-HVP), a ^LO-HVP a μ LO-HVP, and subsequently by experimental results 2 and updates of the reference standard-model predictions using lattice results for a ^LO-HVP a μ LO-HVP (ref. 3). Here we present a new calculation for this crucial quantity, obtaining a ^LO-HVP=715. 1 (2. 5) (2. 3) 3. 4 10^-10 a μ LO-HVP = 715. 1 (2. 5) (2. 3) 3. 4 × 1 0 − 10. This reduces the uncertainty by a factor of 1. 6 compared with our earlier computation 1. We use a hybrid approach that includes a small, long-distance contribution from experiments in a low-energy regime in which they all agree. Our approach combines the strengths of experimental and lattice data in different energy ranges, achieving better precision than with either alone. Our lattice quantum chromodynamics (QCD) simulations are performed on finer lattices than in ref. 1, allowing for an even more accurate continuum extrapolation. Combined with the calculations of the other standard-model contributions summarized in ref. 3, our result leads to a prediction that differs from the recent measurement of a μ (ref. 4) by only 0. 5 standard deviations. This provides a notable validation of the standard model to 11 digits.
Boccaletti et al. (2026) studied this question.