Bound electron g-2

Journal ClubJanuary 2007

Andrzej Czarnecki University of Alberta

based on Karshenboim, PLA 266, 380 (2000)

Outline

How to compute the energy shift due to the B-field?

Connection between Dirac and Schrödinger wave functions

Theoretical prediction and why it’s useful

B-field as perturbation

How are these two descriptions related?

Dirac Schrödinger

We get gb from this comparison:

Example: p2 (neglect V-E)

The spin-dependent part gives:

Complete correction

Main new result in that paper: effect of short-range perturbations of the Coulomb potential

For a perturbation

the change of the g-factor is

From Werth

Electron mass from bound-electron g-2

Motion in a Penning trap:

Electron mass from bound-electron g-2

2 4

622

3 6

Z Zg O Z

2

4 5

41 402

11 ln

6

ZZ a a O Z

Z

224

41 402

10.65.. 1 ln ..

6

ZZ b b

Z

e

40 16.4b Pachucki, AC, Jentschura, Yerokhin , 2005

Electron mass: two-loop bound-state effect

12 5

exp th0.00054857990931 29 1em C u

Using the Mainz group measurements of νL/ νC we get

The free-electron mass determination,

expfree 0.000 548 579 91110 120em u

van Dyck, Farnham, Schwinberg 1995