Analytic contributions to thegfactor of the electron in sixth order

Abstract

W e compute a precise value for three more graphs contributing to the g factor o f the electron in sixth order. After comparing with other numerical and analytic evaluations, we give an updated "best" theoretical estimate of the g factor, and compare it to the experimental value.

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

“…The graph sets from the splitting smooth the peaks of the individual graph contributions as well as the gauge-invariant sets 23 . However, this "smoothing" is not so prominent: some of the set contributions are many times greater than the total contribution (in absolute value).…”

“…• △ fail EIA is the contribution of that samples; 23 It should be noted that this smoothing is not a general principle: for example, the sum of n independent random numbers with the mean values 0 and the quadratic means a have the quadratic mean a · √ n .…”

ANALYTIC EVALUATION OF SIXTH-ORDER CONTRIBUTIONS TO THE ELECTRON'S g FACTOR

“…[8] contains a fairly complete table of integrals of the kind described above, whose left hand side involves practically all the integrands with PLD of 2 and 3, and the right hand side consists of mathemat ical constants with PLD of 3 and 4. A number of definite integrals with left hand side having PLD 4 and right hand side having PLD 5 can be found in [29] (the first coefficient in the third entry of Table IV is to be corrected into 99/16); a complete table for PLD =5 is however still missing. Definite integrals containing a function with PLD n but different powers of the rational factors t, (1 ± t) can be simplified by integrating the rational factors by parts, so obtaining a simpler definite integral involving a product of polylogarithms with lower PLD.…”

“…The number of the different ways of cutting a graph for obtaining all the contributions to its imaginary part increases quickly with the order of the graph and with its topological complexity; to keep the number of the cuts down, dispersive and hyperspherical approaches have been combined in [29] to provide high precision semi-analytic values of the "double corner" graphs , set F. The combined approach has also been used in [30] in a first attempt to show the feasibility of the analytic calculation of the "light-by-light" graphs, set N, and "corner ladder" graphs, set G. (The scalar terms have been evaluated, but the calculation is still in progress). The idea in either case is the following: once the A -+ 0 limit is taken, any contribution X to the anomaly take the self-mass form depicted in Fig.…”

Hyperspherical integration and the triple-cross vertex graphs

“…The analytical calculations of the known three-loop contributions relied on two approaches: the hyperspherical variables method [1] [2] and the dispersion relations method [2] [3], the choice being dependent on the topology of the graphs. A hybrid dispersive and hyperspherical approach turned out to be more convenient for some troublesome sets of graphs [4] [5].…”