In recent years, the anomalous magnetic moment of the muon has triggered a lot of activity in the lattice QCD community because a persistent tension of about \(3.5~\sigma \) is observed between the phenomenological estimate and the Brookhaven measurement. The current best phenomenological estimate has an uncertainty comparable to the experimental one and the error is completely dominated by hadronic effects: the leading order hadronic vacuum polarization (HVP) contribution and the hadronic light-by-light (HLbL) scattering contribution. Both are accessible via lattice simulations and a reduction of the error by a factor 4 is required in view of the forthcoming experiments at Fermilab and J-PARC whose results, expected in the next few years, should reduce the experimental precision down to the level of 0.14 ppm. In this article, I review the status of lattice calculations of those quantities, starting with the HVP. This contribution has now reached sub-percent precision and requires a careful understanding of all sources of systematic errors. The HLbL contribution, that is much smaller, still contributes significantly to the error. This contribution is more challenging to compute, but rapid progress has been made on the lattice in the last few years.

近年来，μ子的反常磁矩引发了格子 QCD 社区的大量活动，因为大约\(3.5~\sigma \)的持续张力在现象学估计和布鲁克海文测量之间观察到。目前最好的现象学估计具有与实验估计相当的不确定性，并且误差完全由强子效应决定：主要顺序强子真空极化 (HVP) 贡献和强子逐光 (HLbL) 散射贡献。两者都可以通过晶格模拟获得，并且考虑到即将在费米实验室和 J-PARC 进行的实验，需要将误差减少 4 倍，预计在未来几年内，这些实验的结果应该会将实验精度降低到0.14 ppm。在本文中，我将从 HVP 开始回顾这些量的晶格计算状态。这一贡献现已达到亚百分比精度，需要仔细了解系统误差的所有来源。HLbL 贡献虽然小得多，但仍然对错误有很大贡献。这种贡献在计算上更具挑战性，但在过去几年中，晶格取得了快速进展。