The electron mass from g-factor measurements on hydrogen-like carbon ¹²C⁵⁺

The electron mass in atomic mass units has been determined with a relative uncertainty of $2.8\times {10}^{-11}$ (Sturm et al 2014 Nature 506 467–70), which represents a 13-fold improvement of the 2010 CODATA value (Mohr et al 2012 Rev. Mod. Phys. 84 1527–605). The underlying measurement principle combines a high-precision measurement of the Larmor-to-cyclotron frequency ratio on a single hydrogen-like carbon ion in a Penning trap with a corresponding very accurate g-factor calculation. Here, we present the measurement results in detail, including a comprehensive discussion of the systematic shifts and their uncertainties. A special focus is set on the various sources of phase jitters, which are essential for the understanding of the applied line-shape model for the g-factor resonance. (paper)