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Summary Table
Summary of the contributions to $a_\mu$. 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 |
|---|---|---|---|---|
| Experimental average (E821+E989) | [updated] | 116 592 061(41) | 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: $\Delta a_\mu\colon= a_\mu^{\text{exp}}-a_\mu^{\text{SM}}$ | Sec. 8 | [updated] | 251(59) |