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HIGHLIGHTS OF 2021

# High-precision lattice QCD calculations of the muon anomalous magnetic moment

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In 2021, the most precise measurement of the muon’s anomalous magnetic moment and a new high-precision lattice quantum chromodynamics calculation have in turn kindled, then dimmed, hopes for seeing signs of new physics. State of the art calculations, made possible by a series of recent advances, will be key to understanding these conflicting results.

• In 2021, the most precise measurement of the muon’s anomalous magnetic moment was reported, showing a remarkable 4.2σ tension with the generally accepted theoretical value.

• Reported at the same time, a new high-precision lattice quantum chromodynamics calculation is at odds with the theoretical value, reducing the tension with experiment to 1.6σ, yet increasing tensions with other theoretical calculations to 3.7σ.

• The key to understanding these conflicting results lies in the value for the hadronic vacuum polarization. Advances in lattice quantum chromodynamics calculations will provide a new way to derive this quantity with high precision.

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## References

1. Abi, B. et al. Measurement of the positive muon anomalous magnetic moment to 0.46 ppm. Phys. Rev. Lett. 126, 141801 (2021).

2. Borsanyi, S. et al. Leading hadronic contribution to the muon magnetic moment from lattice QCD. Nature 593, 51–55 (2021).

3. Aoyama, T. et al. The anomalous magnetic moment of the muon in the Standard Model. Phys. Rep. 887, 1–166 (2020).

4. Davier, M., Hoecker, A., Malaescu, B. & Zhang, Z. A new evaluation of the hadronic vacuum polarisation contributions to the muon anomalous magnetic moment and to $$\alpha ({m}_{Z}^{2})$$. Eur. Phys. J. C 80, 241 (2020).

5. Keshavarzi, A., Nomura, D. & Teubner, T. g − 2 of charged leptons, $$\alpha ({m}_{Z}^{2})$$, and the hyperfine splitting of muonium. Phys. Rev. D 101, 014029 (2020).

6. Blum, T. et al. Calculation of the hadronic vacuum polarization contribution to the muon anomalous magnetic moment. Phys. Rev. Lett. 121, 022003 (2018).

7. Aubin, C. et al. Light quark vacuum polarization at the physical point and contribution to the muon g − 2. Phys. Rev. D 101, 014503 (2020).

8. Lehner, C. & Meyer, A. S. Consistency of hadronic vacuum polarization between lattice QCD and the R ratio. Phys. Rev. D 101, 074515 (2020).

9. Davies, C. T. H. et al. Hadronic-vacuum-polarization contribution to the muon’s anomalous magnetic moment from four-flavor lattice QCD. Phys. Rev. D 101, 034512 (2020).

10. Gérardin, A. G. et al. Leading hadronic contribution to (g − 2)μ from lattice QCD with Nf = 2 + 1 flavors of O(a) improved Wilson quarks. Phys. Rev. D 100, 014510 (2019).

11. Blum, T. et al. Hadronic light-by-light scattering contribution to the muon anomalous magnetic moment from lattice QCD. Phys. Rev. Lett. 124, 132002 (2020).

12. Chao, E.-H. et al. Hadronic light-by-light contribution to (g − 2)μ from lattice QCD: a complete calculation. Eur. Phys. J. C 81, 651 (2021).

13. Giusti, D. et al. Electromagnetic and strong isospin-breaking corrections to the muon g − 2 from lattice QCD+QED. Phys. Rev. D 99, 114502 (2019).

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Correspondence to Christoph Lehner.

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The author declares no competing interests.

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Lehner, C. High-precision lattice QCD calculations of the muon anomalous magnetic moment. Nat Rev Phys 4, 14–15 (2022). https://doi.org/10.1038/s42254-021-00409-z

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• DOI: https://doi.org/10.1038/s42254-021-00409-z