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HIGHLIGHTS OF 2021

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

Nature Reviews Physics volume 4, pages 14–15 (2022)Cite this article

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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.

Key advances

  • 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.

Earlier this year, the muon’s anomalous magnetic moment was measured at Fermilab1 to 0.46 parts per million precision, showing a remarkable 4.2σ tension with the theoretical value — a promising indication of new physics. However, on the day the results were announced, a high-precision lattice quantum chromodynamics (QCD) theory result was published2 that is in tension with previous theoretical values. This is the latest chapter of a story that began 100 years ago.

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Fig. 1: Theory–experiment and theory–theory tensions in the determination of the muon anomalous magnetic moment.

References

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

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

  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).

    ADS  Article  Google Scholar 

  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).

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

  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).

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

  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).

    ADS  Article  Google Scholar 

  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).

    ADS  MathSciNet  Article  Google Scholar 

  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).

    ADS  Article  Google Scholar 

  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).

    ADS  Article  Google Scholar 

  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).

    ADS  Article  Google Scholar 

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Authors and Affiliations

  1. Brookhaven National Lab, Upton, NY, USA

    Christoph Lehner

  2. University of Regensburg, Regensburg, Germany

    Christoph Lehner

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  1. Christoph Lehner
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Correspondence to Christoph Lehner.

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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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