Theory of the Anomalous Magnetic Moment of the Electron – Numerical Approach

Lattice Calculation of the Lowest-Order Hadronic Contribution to the Muon Anomalous Magnetic Moment

“…A simple check of this procedure, which is successful, is to insert the one-loop QED vacuum polarization [6], analytically continued to Euclidean space, into Eq. 4 and compare the result to the known value of the O(α 2 ) QED contribution to a µ [7]. Finally, we note that the kernel f (K 2 ) diverges as K 2 → 0, so the integral in Eq.…”

The Anomalous Magnetic Moment of the Muon: A Theoretical Introduction

“…The value quoted in [84] is A 3 = 1.195 (26), where the error comes from the numerical procedure. In comparison, let us quote the value [85,77] A 3 = 1.176 11 (42) obtained if only a subset of 21 three loop diagrams out of the original set of 72 is evaluated numerically, relying on the analytical results for the remaining 51 ones, and recall the value A 3 = 1.181 241 456... obtained from the full analytical evaluation. The error induced on a e due to the numerical uncertainty in the second, more accurate, value is still ∆(a e ) = 5.3 × 10 −12 , whereas the experimental error is only ∆(a e )| exp = 4.3 × 10 −12 .…”

Probing a Single Isolated Electron: New Measurements of the Electron Magnetic Moment and the Fine Structure Constant

“…The 518 diagrams of Group V, with no closed lepton loops, await completion of an independent verification. However, their renormalization terms are derived by systematic reduction of original integrands applying a simple power-counting rule [81], allowing extensive cross-checking among themselves and with exactly known diagrams of lower order [82]. Numerical integrations with VEGAS [83], on many supercomputers over more than 10 years [62,84], then yields A…”