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The electron mass in atomic mass units has been determined with a relativeuncertainty of $2.8\cdot 10^{-11}$, which represents a 13-fold improvement ofthe 2010 CODATA value. The underlying measurement principle combines ahigh-precision measurement of the Larmor-to-cyclotron frequency ratio on asingle hydrogen-like carbon ion in a Penning trap with a corresponding veryaccurate $g$-factor calculation. Here, we present the measurement results indetail, including a comprehensive discussion of the systematic shifts and theiruncertainties. A special focus is set on the various sources of phase jitters,which are essential for the understanding of the applied line-shape model forthe $g$-factor resonance.

The electron mass from $g$-factor measurements on hydrogen-like carbon $^{12}$C$^{5+}$