The anomalous magnetic moment of the muon: status of Lattice QCD calculations

Abstract

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.

Contribution to the EPJA special issue "Lattice Field Theory during the COVID-19 pandemic" in replacement of a plenary talk at the 38th International Symposium on Lattice Field Theory (Lattice 2020). v2: minor corrections to match the published version. Some references have been added

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Cited by in corpus (18)

• Window observable for the hadronic vacuum polarization contribution to the muon $g-2$ from lattice QCD
• The muon anomalous magnetic moment with staggered fermions: is the lattice spacing small enough?
• $(\mathbf{g}-2{)}_{\mathbf{e},\mathbf{\mu }}$ in an extended inverse type-III seesaw
• Studying the $b\to s{\ell }^{+}{\ell }^{-}$ anomalies and $(g-2{)}_{\mu }$ in $R$-parity violating MSSM framework with the inverse seesaw mechanism
• Neutrino masses and magnetic moments of electron and muon in the Zee Model
• The muon g-2 anomaly confronts new physics in $e^{\pm }$ and ${\mu }^{\pm }$ final states scattering
• Timelike and spacelike kernel functions for the hadronic vacuum polarization contribution to the muon anomalous magnetic moment
• An explanation of experimental data of $(g-2{)}_{e,\mu }$ in 3-3-1 models with inverse seesaw neutrinos
• Probing the Dark Axion Portal with Muon Anomalous Magnetic Moment
• Heavy singly charged Higgs bosons and inverse seesaw neutrinos as origins of large $(g-2{)}_{e,\mu }$ in two higgs doublet models
• Flavor Physics Constraints on Left-Right Symmetric Models with Universal Seesaw
• Anomalous gauge couplings vis-$\grave{a}$-vis $(g-2{)}_{\mu }$ and flavor observables
• Effects of the quark flavour thresholds in the hadronic vacuum polarization contributions to the muon anomalous magnetic moment
• $(g-2{)}_{e,\mu }$ and decays $e_b\to e_a\gamma$ in a $ \mbox{SU}(4)_L \otimes \mbox{U}(1)_X$ model with inverse seesaw neutrinos
• Generalized quantum electrodynamics: one-loop correction
• FIMP DM in the Extended Hyperchargeless Higgs Triplet Model
• Sub-GeV $U(1{)}_R$ gauge boson to address the proton radius discrepancy
• Window quantities for the hadronic vacuum polarization contributions to the muon anomalous magnetic moment in spacelike and timelike domains