Self-energy correction to the bound-electron g factor in H-like ions.

The one-loop self-energy correction to the 1s-electron g factor is evaluated to all orders in Zalpha with an accuracy essentially better than that of previous calculations of this correction. As a result, the uncertainty of the theoretical prediction for the bound-electron g factor in H-like carbon is reduced by a factor of 3. This improves the total accuracy of the recent electron-mass determination [T. Beier, Phys. Rev. Lett. 88, 011603 (2002)]]. The new value of the electron mass is found to be m(e)=0.000 548 579 909 3 (3) u.