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Hadronic vacuum polarization (HVP) and hadronic light-by-light scattering (HLbL)
M. Davier et al., Eur. Phys. J. C80 (2020) 3, 241
A. Keshavarzi et al., Phys. Rev. D97 (2018) 114025
T. Blum et al., Phys. Rev. Lett. 118 (2017) 022005
G. Colangelo et al., Phys. Rev. Lett. 118 (2017) 232001

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Summary Table

Summary of the contributions to $a_\mu$ aμ. After the experimental number from E821, the first block gives the main results for the hadronic contributions from Secs. 2-5, as well as the combined result for HLbL scattering from phenomenology and lattice QCD constructed in Sec. 8. The second block summarizes the quantities entering our recommended SM value, in particular, the total HVP contribution, evaluated from e+e- data, and the total HLbL number. The construction of the total HVP and HLbL contributions takes into account correlations among the terms at different orders, and the final rounding includes subleading digits at intermediate stages. In the Citation Refs. column the references upon which the corresponding results are based are listed as downloadable bib files together with the citation commands.
The HVP evaluation is mainly based on the experimental references: bib, cite.
In addition, the HLbL evaluation uses input from the experimental references: bib, cite.
The lattice QCD calculation of the HLbL contribution builds on crucial methodological advances from the referneces: bib, cite.
Finally, the QED value uses the fine-structure constant obtained from atom-interferometry measurements of the Cs atom: bib, cite

Contribution Section Equation Value x 1011 Citation Refs
Experiment (E821)   Eq. (8.13) 116 592 089(63) bib, cite
HVP LO (ⅇ+ⅇ-) Sec. 2.3.7 Eq. (2.33) 6931(40) bib, cite
HVP NLO (ⅇ+ⅇ-) Sec. 2.3.8 Eq. (2.34) -98.3(7) bib, cite
HVP NNLO (ⅇ+ⅇ-) Sec. 2.3.8 Eq. (2.35) 12.4(1) bib, cite
HVP LO (lattice, udsc) Sec. 3.5.1 Eq. (3.49) 7116(184) bib, cite
HLbL (phenomenology) Sec. 4.9.4 Eq. (4.92) 92(19) bib, cite
HLbL NLO (phenomenology) Sec. 4.8 Eq. (4.91) 2(1) bib, cite
HLbL (lattice, uds) Sec. 5.7 Eq. (5.49) 79(35) bib, cite
HLbL (phenomenology + lattice) Sec. 8 Eq. (8.10) 90(17) bib, cite
QED Sec. 6.5 Eq. (6.30) 116 584 718.931(104) bib, cite
Electroweak Sec. 7.4 Eq. (7.16) 153.6(1.0) bib, cite
HVP (ⅇ+ⅇ-, LO + NLO + NNLO) Sec. 8 Eq. (8.5) 6845(40) bib, cite
HLbL (phenomenology + lattice + NLO) Sec. 8 Eq. (8.11) 92(18) bib, cite
Total SM Value Sec. 8 Eq. (8.12) 116 591 810(43) bib, cite
Difference: △aμ := aexp
μ
aSM
μ
Sec. 8 Eq. (8.14) 279(76)