The muon resembles the electron but is 200 times heavier and lives for two millionths of a second. Its magnetic moment, how the particle responds to a magnetic field, has been measured with fantastic precision. Yet the measured value is slightly larger than theory predicts. The difference is tiny, like finding an extra penny every time you count your change at the store.
The vacuum is not empty: pairs of particles constantly pop in and out of existence, like bubbles in boiling water. These fleeting visitors slightly alter the muon's magnetic properties. To account for their contribution, physicists use lattice QCD — a method that slices space and time into a tiny grid, like millimeter paper. The calculations run on supercomputers and take months.
A team of researchers has for the first time achieved sub-percent precision for the next most important contribution. The resulting number is −101.57×10⁻¹¹, with an uncertainty of 0.6%. This is twice as precise as previous calculations.
The new result disagrees with estimates from accelerator data prior to the recent CMD-3 experiment by 4.6 standard deviations. Such a discrepancy is not just a technical detail. It could be a trace of new particles not in the Standard Model — the current catalog of everything. Or there might be an unnoticed error in the old experiments. The coming years will tell who is right.
as written by the authors arXiv:2604.08351
We present the first lattice QCD calculation of the next-to-leading order (NLO) hadronic vacuum polarization (HVP) contribution to the muon anomalous magnetic moment with sub-percent precision. We employ the time-momentum representation combined with the spatially summed vector correlator computed on CLS ensembles with $$N_{\mathrm{f}}=2+1$$ flavors of $$\mathrm{O}(a)$$-improved Wilson fermions, spanning six lattice spacings ($$0.039$$-$$0.097\,$$fm) and a range of pion masses including the physical value. After accounting for finite-size corrections and isospin-breaking effects, we obtain in the continuum limit $$a_\mu^{\mathrm{hvp,\,nlo}} = (-101.57 \pm 0.26_{\rm stat} \pm 0.54_{\rm syst}) \times 10^{-11}$$, corresponding to a total relative error of 0.6$$\%$$. Our result lies 1.4$$\sigma$$ below the estimate of the 2025 White Paper update and is two times more precise. It also shows a tension of $$4.6\sigma$$ with data-driven evaluations based on hadronic cross section measurements prior to the CMD-3 result.
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