Cavity control of a single-electron quantum cyclotron: Measuring the electron magnetic moment

Abstract

Measurements with a one-electron quantum cyclotron determine the electron magnetic moment, given by g/2 = 1.001 159 652 180 73(28)[0.28ppt], and the fine structure constant, α −1 = 137.035 999 084 (51)Announcements of these measurements [Phys. Rev. Lett. 97, 030801 (2006); 100, 120801 (2008)] are supplemented here with a more complete description of the one-electron quantum cyclotron and the measurement methods, a discussion of the cavity control of the radiation field, a summary of the analysis of the measurements, and a fuller discussion of the uncertainties.

Tenth-order QED contribution to the lepton anomalous magnetic moment: Sixth-order vertices containing an internal light-by-light-scattering subdiagram

“…In the amplitude M A1 , the K -operation is applied only on the explicit second-order vertex subdiagram (1,2). For other terms the full bodies of the vertex renormalization constants of the sixth-and eighth-orders are used and subtracted.…”

“…Of course, m i is independent of i and λ k is 0 independent of k. But it is useful to distinguish different For instance, the vertex subdiagram (1,2) of A1 will be denoted by (1,2), and the vertex subdiagram {2,3,4,5; 6,7,8,9; b,c,d} of A1 will be denoted by (2,3,4,5). An exception is the l-l subdiagram, which will be denoted as (6,7,8,9).…”

“…An exception is the l-l subdiagram, which will be denoted as (6,7,8,9). Under this convention the diagram A1 has five divergent subdiagrams (1, 2), (4, 5), (1, 2, 3, 4), (2,3,4,5), and (6,7,8,9). The fifteen UV subtraction terms can be constructed from these subdiagrams following the Zimmermann's forest formula [35].…”

“…(3) shows clearly that the largest source of uncertainty is the fine structure constant (2). To put it differently, a non-QED α, even the best one available at present, is too crude to test QED to the extent achieved by the theory and measurement of a e .…”

“…On the experimental side, the latest measurement of a e by the Harvard group has reached the precision of 0.24 × 10 −9 [1,2]: …”