Penning trap mass measurements of the deuteron and the HD⁺ molecular ion

The masses of the lightest atomic nuclei and the electron mass¹ are interlinked, and their values affect observables in atomic², molecular^3-5 and neutrino physics⁶, as well as metrology. The most precise values for these fundamental parameters come from Penning trap mass spectrometry, which achieves relative mass uncertainties of the order of 10^-11. However, redundancy checks using data from different experiments reveal considerable inconsistencies in the masses of the proton, the deuteron and the helion (the nucleus of helium-3), suggesting that the uncertainty of these values may have been underestimated. Here we present results from absolute mass measurements of the deuteron and the HD⁺ molecular ion using ¹²C as a mass reference. Our value for the deuteron mass, 2.013553212535(17) atomic mass units, has better precision than the CODATA value⁷ by a factor of 2.4 and differs from it by 4.8 standard deviations. With a relative uncertainty of eight parts per trillion, this is the most precise mass value measured directly in atomic mass units. Furthermore, our measurement of the mass of the HD⁺ molecular ion, 3.021378241561(61) atomic mass units, not only allows a rigorous consistency check of our results for the masses of the deuteron (this work) and the proton⁸, but also establishes an additional link for the masses of tritium⁹ and helium-3 (ref. ¹⁰) to the atomic mass unit. Combined with a recent measurement of the deuteron-to-proton mass ratio¹¹, the uncertainty of the reference value of the proton mass⁷ can be reduced by a factor of three.