We report on the precise measurement of the atomic mass of a single proton with a purpose-built Penning-trap system. With a precision of 32 parts-per-trillion our result not only improves on the current CODATA literature value by a factor of three, but also disagrees with it at a level of about 3 standard deviations.The properties of the basic building blocks of matter shape a network of fundamental parameters, which are crucial to develop precise quantitative understanding of nature and its symmetries. One of these fundamental constants is the mass of the proton m p , which has always been a target and yardstick of precision experiments [1][2][3][4][5]. It is thus correlated with most other parameters of atomic physics. For example, its value influences the Rydberg constant [6], and it is also required for the precise comparison of the masses of the proton and antiproton, in order to perform a stringent test of CPT invariance via a hydrogen anion [7].All recent proton mass values are based on Penningtrap measurements, where the cyclotron frequencies ν c = 1 2π q m B of the proton (or H + 2 ) and a reference ion with respective charge-to-mass ratios q /m are compared in the same magnetic field B. In this letter we report on a high-precision measurement of m p in atomic mass units, which is based on cyclotron frequency comparisons of protons and highly charged carbon ( 12 C 6+ ) ions. While the largely different charge-to-mass ratio between the proton and the 12 C 6+ ion imposes technical challenges to be discussed later, the comparison with the atomic mass standard allows us to determine the mass of the proton directly in atomic mass units. In order to do so, we have to relate the mass of the 12 C 6+ ion to that of a 12 C atom:Here, E b,i denotes the binding energies of the six removed electrons, c the speed of light in vacuum and m e the electron mass [8]. Since m( 12 C) is 12 u by definition and the atomic mass of the electron has been previously determined by our group with 2.9 × 10 −11 relative uncertainty, this relation is limited only by the knowledge of electronic binding energies. The currently tabulated values in the NIST table of ionization energies [9] allow to derive m( 12 C 6+ ) = 11.996 709 626 413 9(10) u with a relative precision of 0.08 parts-per-trillion (ppt), which does not pose any limitation on the precision of the proton's atomic mass reported here.

The precise knowledge of the atomic masses of light atomic nuclei, e.g. the proton, deuteron, triton and helion, is of great importance for several fundamental tests in physics. However, the latest high-precision measurements of these masses carried out at different mass spectrometers indicate an inconsistency of five standard deviations. To determine the masses of the lightest ions with a relative precision of a few parts per trillion and investigate this mass problem a cryogenic multi-Penning trap setup, LIONTRAP (Light ION TRAP), was constructed. This allows an independent and more precise determination of the relevant atomic masses by measuring the cyclotron frequency of single trapped ions in comparison to that of a single carbon ion. In this paper the measurement concept and the first doubly compensated cylindrical electrode Penning trap, are presented. Moreover, the analysis of the first measurement campaigns of the proton's and oxygen's atomic mass is described in detail, resulting in mp = 1.007 276 466 598 (33) u and m 16 O = 15.994 914 619 37 (87) u. The results on these data sets have already been presented in [F. Heiße et al., Phys. Rev. Lett. 119, 033001 (2017)]. For the proton's atomic mass, the uncertainty was improved by a factor of three compared to the 2014 CODATA value.

The recently established agreement between experiment and theory for the g factors of lithiumlike silicon and calcium ions manifests the most stringent test of the many-electron bound-state quantum electrodynamics (QED) effects in the presence of a magnetic field. In this Letter, we present a significant simultaneous improvement of both theoretical gth = 2.000 889 894 4 (34) and experimental gexp = 2.000 889 888 45 (14) values of the g factor of lithiumlike silicon 28 Si 11+ . The theoretical precision now is limited by the many-electron twoloop contributions of the bound-state QED. The experimental value is accurate enough to test these contributions on a few percent level.Introduction. -The magnetic moment of elementary particles and simple systems is a perfect tool for testing fundamental theories. High-precision g-factor measurements in highly charged ions [1][2][3][4][5][6][7] in combination with elaborate theoretical investigations (see, e.g., [8,9] for reviews) have provided the most stringent test of bound-state QED in the presence of a magnetic field up-to-date. Moreover, these studies resulted in the most accurate value of the electron mass [10][11][12][13]. Recent measurements with two highly charged lithiumlike calcium isotopes [6] have demonstrated the possibility to access bound-state QED beyond the Furry picture in the strong coupling regime, specifically the relativistic nuclear recoil effect [14][15][16]. While hydrogenlike ions, due to their simplicity, allow for the most accurate theoretical predictions, nuclear effects set the ultimate limits of the theoretical accuracy regardless of the progress in QED calculations. However, in combination with measurements on lithiumlike and boronlike ions, these limits can be overcome [17,18]. Here, specific differences of the g-factor values of different charge states with the same nucleus exhibit orders-of-magnitude smaller theoretical uncertainty than the individual g factors [17][18][19][20]. Based on this, an independent determination of the fine structure constant from heavy hydrogen-and boronlike ions [18] and from light hydrogen-and lithiumlike ions [20] has been proposed. Following the experiments with hydrogenlike ions [1][2][3][4], the g factor of lithiumlike silicon has been measured at the Mainz University with a relative uncertainty of 1.1 × 10 −9 [5]. Shortly after, the g factors of two lithiumlike calcium isotopes have been measured with two-times smaller uncertainty [6]. The corresponding efforts devoted to the evaluation of the many-electron contributions to the g factor of three-electron ions have led to a theoretical uncertainty of 6 × 10 −9 for silicon [22] and 13 × 10 −9 for calcium [23].In this Letter, we present simultaneous experimental (by a factor of 15) and theoretical (by a factor of 2) improvements of the g factor of lithiumlike silicon. In view of the determination of the fine structure constant [20] this represents an

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