The quest for the value of the electron's atomic mass has been subject of continuing efforts over the last decades [1,2,3,4]. [5] and which are thus responsible for its predictive power, the electron mass me plays a prominent role, as it is responsible for the structure and properties of atoms and molecules. This manifests in the close link with other fundamental constants, such as the Rydberg constant R∞ and the fine-structure constant α [6]. However, the low mass of the electron considerably complicates its precise determination. In this work we present a substantial improvement by combining a very accurate measurement of the magnetic moment of a single electron bound to a carbon nucleus with a state-of-the-art calculation in the framework of bound-state Quantum Electrodynamics. The achieved precision of the atomic mass of the electron surpasses the current CODATA [6] value by a factor of 13. Accordingly, the result presented in this letter lays the foundation for future fundamental physics experiments [7,8] and precision tests of the SM [9,10,11] Throughout the last decades, the determination of the atomic mass of the electron has been subject to several Penning-trap experiments, as continuing experimental efforts try to further explore the scope of validity of the SM and require an exceedingly precise knowledge of me. The uniform magnetic field of these traps gives the possibility to compare the cyclotron frequency of the electron with that of another ion of known atomic mass, typically carbon ions or protons. The first such direct determination dates back to 1980, when Gräff et al. made use of a Penning trap to compare the cyclotron frequencies of a cloud of electrons with that of protons, which were alternately confined in the same magnetic field, yielding a relative precision of about 0.2 ppm [2]. Since then, a number of experiments have pushed the precision by about 3 orders of magnitude [1,12,13,4]. The latest version of the CODATA compilation of fundamental constants of 2010 lists a relative uncertainty of 4•10 -10 , resulting from the weighted average of the most precise measurements (Fig. 2). Since the cyclotron frequency of the extremely light electron is subjected to troublesome relativistic mass shifts if not held at the lowest possible energy, direct ultra-high precision mass measurements are particularly delicate. To circumvent this problem, the currently most precise measurements, including this work, pursue an indirect method which allows achieving a previously unprecedented accuracy. Among the seemingly fundamental constants which parameterize the Standard Model (SM) of physicsA single electron is bound directly to the reference ion, in this case a bare carbon nucleus (Fig. 1). In this way, it becomes possible to calibrate the magnetic field B at the very place of the electron through a measurement of the cyclotron frequency

We determined the experimental value of the g factor of the electron bound in hydrogenlike ²⁸Si¹³⁺ by using a single ion confined in a cylindrical Penning trap. From the ratio of the ion's cyclotron frequency and the induced spin flip frequency, we obtain g = 1.995 348 958 7(5)(3)(8). It is in excellent agreement with the state-of-the-art theoretical value of 1.995 348 958 0(17), which includes QED contributions up to the two-loop level of the order of (Zα)² and (Zα)⁴ and represents a stringent test of bound-state quantum electrodynamics calculations.

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By measuring the cyclotron frequency ratios of (3)He(+) to HD(+) and T(+) to HD(+), and using HD(+) as a mass reference, we obtain new atomic masses for (3)He and T. Our results are M[(3)He]=3.016 029 322 43(19)  u and M[T]=3.016 049 281 78(19)  u, where the uncertainty includes an uncertainty of 0.12 nu in the mass reference. Allowing for cancellation of common systematic errors, we find the Q value for tritium β decay to be (M[T]-M[(3)He])c(2)=18 592.01(7)  eV. This allows an improved test of systematics in measurements of tritium β decay that set limits on neutrino mass.

The g factor of lithiumlike silicon (28)Si(11+) has been measured in a triple-Penning trap with a relative uncertainty of 1.1×10(-9) to be g(exp)=2.000 889 889 9(21). The theoretical prediction for this value was calculated to be g(th)=2.000 889 909(51) improving the accuracy to 2.5×10(-8) due to the first rigorous evaluation of the two-photon exchange correction. The measured value is in excellent agreement with the theoretical prediction and yields the most stringent test of bound-state QED for the g factor of the 1s(2)2s state and the relativistic many-electron calculations in a magnetic field.