Improved analytic theory of the muon anomalous magnetic moment

Abstract

We consider the recent results of Kinoshita in which he improves the accuracy of the theoretical value for the anomalous magnetic moment of the muon. This is needed now that a new, more accurate experiment has been approved at Brookhaven National Laboratory. Kinoshita's results are completely numerical. Here we perform an independent check of his results in fourth and sixth order by analytical means, using expansions in the small mass ratios which occur in the computation. Our result for the fourthorder contribution is a: ' -ai4'=5 904475.1(3)X 10-12. This is to be compared with Kinoshita's result a:4'-a64'=5 904485X 1 0 12. For the sixth-order vacuum-polarization contribution we obtain (a:' -aj6')(vacuum polarization) =24 064.8 ( 6) X lo-''. Kinoshita's result is (a:' -aj6')(vacuum polari~a t i o n ) = 2 4 0 6 9 ( 6 ) X l O -'~. Our result for the total QED contribution is a$ED = 1 165 846 943(28)(27) X lo-''. This agrees with Kinoshita's result u,U"~(K) = 1 165 846 961(44)(28) X lo-''. Our final result for the muon anomaly is ~h~' " '~ =116591901(77)X10-11. This should be compared with Kinoshita's result ahheorY = 116 591 919( 176) X lo-'' and the experimental value ayPt = 1 165 923(8.5) XOur value makes use of a recent computation of the hadronic contribution, in which the error may be overly optimistic.

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

“…The latter confirms the value 1.181 259 (4) obtained numerically [73]. Mass-dependent QED additions [74,75,76,77,78,79], …”

Precise mass-dependent QED contributions to leptonicg−2at orderα2andα3

“…The exact expression for 0 < x < 1 was reported by Elend in 1966 [10]. However, its numerical evaluation was considered tricky because of large cancellations and difficulties in the estimate of the accuracy of the results, so that common practice was to use series expansions instead [11,12,13]. Taking advantage of the properties of the dilogarithm Li 2 (z) = − z 0 (dt/t) ln(1 − t) [14], the exact result was cast in [15] in a very simple and compact analytic form, valid, contrary to the one in [10], also for x ≥ 1 (the case relevant to a QED e and part of a QED µ ):…”

“…Therefore, it will be possible to compute A The contribution of the three-loop diagrams with both µ and τ loop insertions in the photon propagator can be calculated numerically from the integral expressions of ref. [11]. We get (13), (14) and (20) we obtain the three-loop QED coefficient C (6) e = 1.181 234 016 827 (19).…”

“…The contribution of the three-loop diagrams with both electron-and muon-loop insertions in the photon propagator can be calculated numerically from the integral expressions of [11]. We get…”

The Muon g—: Status and Perspectives

“…As all fermions have different masses, the fermion-loops give rise to mass dependent effects, which were calculated at two-loops in [22,23] (see also [24,25,26]), and at three-loops in [27,28,29,30,31,32]. The leading mass dependent effects come from photon vacuum polarization, which leads to charge screening manifest in the "running" of α.…”