Motivation

The proton mass

Figure 1: Overview of the most accurate high-precision measurements of the proton - electron mass ratio μ=m_p/m_e. The grey band illustrates the literature value of CODATA 2018, the first and the second values shown are from the spectroscopy of HD⁺ molecules and antiprotonic helium pHe⁺ respectively [4, 5].

The mass of the lightest nucleus, the proton, is essential in hydrogen and muonic hydrogen spectroscopy, as it is required for the determination of the Rydberg constant or the proton radius with high precision [1]. Actually, in various atomic physics experiments, the ratio of the proton mass, m_p to the electron mass, m_e (rather than the individual masses) is a pivotal parameter and thus needs to be determined with high precision and consistency, see Figure 1. The proton's mass was the first measurement campaign of the LIONTRAP experiment with a relative precision of 3·10^-11 [2, 3]. The most precise value of the electron mass was measured with a relative accuracy of 3·10^-11 at the bound-electron g-factor experiment for highly charged ions, which is the direct predecessor of LIONTRAP experiment [6].

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The deuteron mass

The deuteron, the nucleus of the deuterium atom, is the second lightest atomic nucleus, consisting of one proton and one neutron. The mass of deuteron in combination with its measured nuclear binding energy enables the mass of the neutron to be determined with high precision. This, in turn, is significant for more precise tests of the equivalence of mass and energy (E = mc²) within special relativity at low energies [7].

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The masses of helion and triton

For a central consistency check of the KATRIN (KArlsruhe TRItium Neutrino) experiment, the mass difference of triton (atomic nucleus consisting of one proton and two neutrons) and helion (atomic nucleus of ³He, consisting of two protons and one neutron) is necessary with the highest precision [8, 9]. The aim of KATRIN is to determine the mass of the electron antineutrino m(ν_e), with an accuracy of 0.2eV/c² (=2·10^-10 u) [10]. The distribution of the kinetic energy (E_kin) of the electron emitted during the beta decay of tritium to helium-3 is measured very precisely, see Figure 2. The maximum energy of this distribution, E₀, also called the endpoint energy, depends essentially on the mass of the electron antineutrino, where: E₀= [m(T)−m(He³)−m_e−m(ν_e)]∙c². This Q-value (mass difference) is of great importance for the energy calibration of KATRIN.

Figure 2: Energy spectrum of beta decay from tritium to helium-3. Left: Total kinetic energy distribution of the emitted electron. Right: Section of this spectrum in the region of the endpoint. E₀ is the endpoint energy in the case of a massless electron antineutrino. The figure was taken from [G. Drexlin, Direct neutrino mass searches, Nucl. Phys. B Proc. Suppl. 138 (2005) 282].

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Light ion mass puzzle

The combination of high precision mass measurements of light nuclei such as proton, deuteron, and helion with ¹²C ion as reference together with a mass ratio measurement of HD⁺ molecular ion to ³He⁺ ion provides a consistency check for all these mass measurements, see Figure 3. However, currently this check fails with an inconsistency of 5 standard deviations. This "light ion mass puzzle", is thus a significant inconsistency of the values of light masses from different world-leading experiments. In other words, the mass difference of ³He⁺ and HD⁺ [11], measured in the group led by Prof. Myers at the Florida State University, deviates by five standard deviations from the one calculated based on the atomic masses of proton, deuteron and helion [2, 12]. The values for the atomic masses of deuteron and helion have been measured in the UW-PTMS experiment (University of Washington Penning-Trap Mass Spectrometer) by Prof. Van Dyck Jr at the University of Washington (UW), whereas the proton mass has been measured by the LIONTRAP group. To resolve this puzzle, an independent check of these measurements is needed, which is performed in our experiment.

Figure 3: Inconsistencies between mass measurements of light atomic nuclei. The most accurate mass measurements of light nuclei have been carried out in the research groups of Robert Van Dyck at the University of Washington (determination of the masses of proton, deuteron, helion in atomic mass units) and Edmund Myers at the University of Florida (determination of the mass ratios of helion to HD molecule and triton to HD molecule).

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References

[1]	S. G. Karshenboim and V. G. Ivanov, "Quantum Electrodynamics, High-Resolution Spectroscopy and Fundamental Constants" , in Exploring the World with the Laser, 2018, ch. Chapter 15, pp. 237-265.
[2]	F. Heiße, F. Köhler-Langes, S. Rau, J. Hou, S. Junck, A. Kracke, A. Mooser, W. Quint, S. Ulmer, G. Werth, K. Blaum, and S. Sturm, "High-Precision Measurement of the Proton's Atomic Mass" , Phys. Rev. Lett., vol. 119, no. 3, p. 033001, Jul 21 2017.
[3]	F. Heiße et al., "High-precision mass spectrometer for light ions" , Physical Review A, vol. 100, no. 2, 2019.
[4]	S. Alighanbari, M. G. Hansen, V. I. Korobov, and S. Schiller, "Rotational spectroscopy of cold and trapped molecular ions in the Lamb–Dicke regime" , Nature Physics, vol. 14, no. 6, pp. 555-559, 2018.
[5]	M. Hori, H. Aghai-Khozani, A. Soter, D. Barna, A. Dax, R. Hayano, T. Kobayashi, Y. Murakami, K. Todoroki, H. Yamada, D. Horvath, L. Venturelli, "Buffer-gas cooling of antiprotonic helium to 1.5 to 1.7 K, and antiproton-to–electron mass ratio" , Science, vol. 354, no. 6312, pp. 610-614, 04 Nov 2016 2016.
[6]	S. Sturm et al., "High-precision measurement of the atomic mass of the electron" , Nature, vol. 506, no. 7489, pp. 467-70, Feb 27 2014.
[7]	M. Jentschel and K. Blaum, "Balancing energy and mass with neutrons" , Nature Physics, vol. 14, no. 5, pp. 524-524, 2018.
[8]	KATRIN Collaboration, "KATRIN Design Report 2004" , 2005.
[9]	E. Otten, "Searching the absolute neutrino mass in tritium β-decay—interplay between nuclear, atomic and molecular physics" , Hyperfine Interactions, vol. 196, no. 1-3, pp. 3-23, 2010.
[10]	M. Aker et al., "Improved Upper Limit on the Neutrino Mass from a Direct Kinematic Method by KATRIN" , Phys. Rev. Lett., vol. 123, no. 22, p. 221802, Nov 29 2019.
[11]	S. Hamzeloui, J. A. Smith, D. J. Fink, and E. G. Myers, "Precision mass ratio of 3He+ to HD+" , Physical Review A, vol. 96, no. 6, 2017.
[12]	S. L. Zafonte and R. S. Van Dyck, "Ultra-precise single-ion atomic mass measurements on deuterium and helium-3" , Metrologia, vol. 52, no. 2, pp. 280-290, 2015.