Complete two-loop correction to the bound-electron g factor

Abstract

Within a systematic approach based on the dimensionally regularized nonrelativistic quantum electrodynamics, we derive the complete result for the two-loop correction to order $(\alpha /\pi {)}^2(Z\alpha {)}^4$ for the $g$ factor of an electron bound in an $nS$ state of a hydrogenlike ion. The results obtained significantly improve the accuracy of the theoretical predictions for the hydrogenlike carbon and oxygen ions and influence the value of the electron mass inferred from $g$ factor measurements.

11 pages, 1 figure