Higher-order hadronic vacuum polarization contribution to the muon g − 2 from lattice QCD

A bstract We present the first lattice QCD calculation of the next-to-leading order hadronic vacuum polarization contribution to the muon anomalous magnetic moment with sub-percent precision. We employ the time-momentum representation for the space-like kernel, which is combined with the spatially summed vector correlator computed on CLS ensembles with N f = 2 + 1 flavors of O( a )-improved Wilson fermions, covering six lattice spacings between 0 . 039 and 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 as our final, continuum-extrapolated result $$ {a}_{\mu}^{\mathrm{hvp},\kern0.30em \mathrm{nlo}} $$ a μ hvp , nlo = −101.57(26) stat (54) syst × 10 −11 . It lies below the estimate provided by the 2025 White Paper of the Muon ( g – 2) Theory Initiative by 1.4 σ but is two times more precise. It also exhibits a strong tension of 4.6 σ with data-driven evaluations based on hadronic cross section measurements excluding the recent result by CMD-3.