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Summary Table
Summary of the contributions to $a_\mu$ a_{μ}. After the experimental
number from E821, the first block gives the main results for
the hadronic contributions from Secs. 25, 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 finestructure constant obtained from
atominterferometry measurements of the Cs atom:
bib,
cite
Contribution  Section  Equation  Value x 10^{11}  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: △a_{μ} :=
aexp μ —
aSMμ

Sec. 8  Eq. (8.14)  279(76) 