(g−2)_µ at four loops in QED

Abstract

We review the four-loop QED corrections to the anomalous magnetic moment of the muon. The fermionic contributions with closed electron and tau contributions are discussed. Furthermore, we report on a new independent calculation of the universal four-loop contribution and compare with existing results.

Numerical calculation of high-order QED contributions to the electron anomalous magnetic moment

“…(iv) The most precise value A [15]. That value was confirmed and improved by S. Laporta in 2017 [16] with the help of a semianalytical approach: A (8) 1 = −1.9122457.... See also independent (but not such precise) calculations in [13,17] and a calculation for diagrams without lepton loops in [18].…”

Calculating the five-loop QED contribution to the electron anomalous magnetic moment: Graphs without lepton loops

“…These two calculations of A (8) 1 are in good agreement as well as another independent calculations of this value from Refs. [30,31], and for Feynman graphs without lepton loops from Ref. [32].…”

Some analytic results for the contribution to the anomalous magnetic moments of leptons due to the polarization of vacuum via lepton loops

“…To our knowledge, the corresponding expressions have not been presented before. However, their expansions in terms of the mass ratio m ℓ /m L and also the numerical valuesà (8) 2 are well known (see the book [1] and the original publications [6,7,[20][21][22][23][24][25][26]). Using the Borel transform technique in the limit when the mass ratio m ℓ /m L is small and n ≫ 1, the coefficientsà (n) 2 were obtained analytically in Ref.…”