Complete two-loop correction to the bound-electron<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>g</mml:mi></mml:math>factor

Abstract

Within a systematic approach based on dimensionally regularized nonrelativistic quantum electrodynamics, we derive a complete result for the two-loop correction to order ${(\ensuremath{\alpha}∕\ensuremath{\pi})}^{2}{(Z\ensuremath{\alpha})}^{4}$ 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.