Deuteron-to-Proton Mass Ratio from the Cyclotron Frequency Ratio of H_{2}^{+} to D^{+} with H_{2}^{+} in a Resolved Vibrational State

Mass Difference of Tritium and Helium-3

From cyclotron frequency ratios of HD^{+}/^{3}He^{+}, HD^{+}/T^{+}, and T^{+}/^{3}He^{+} we measure the mass difference between atoms of T and ^{3}He to be 1.995 940 8 (23)×10^{-5} u, corresponding to a Q value for tritium β decay of 18 592.071(22) eV. This enables an improved check on systematics of β decay experiments that set limits on neutrino mass. Using the HD^{+} mass calculated from the atomic masses of the proton and deuteron as given by Rau et al. [Nature 585, 43 (2020)NATUAS0028-083610.1038/s41586-020-2628-7], we also obtain improved atomic masses for the triton and helion (considered to be fundamental constants), namely, 3.015 500 716 066 (39) and 3.014 932 246 957 (38) u.

Trapping and Ground-State Cooling of a Single H_{2}^{+}

We demonstrate co-trapping and sideband cooling of a H_{2}^{+}-^{9}Be^{+} ion pair in a cryogenic Paul trap. We study the chemical lifetime of H_{2}^{+} and its dependence on the apparatus temperature, achieving lifetimes of up to 11_{-3}^{+6}  h at 10 K. We demonstrate cooling of two of the modes of translational motion to an average phonon number of 0.07(1) and 0.05(1), corresponding to a temperature of 22(1) and 55(3)  μK, respectively. Our results provide a basis for quantum logic spectroscopy experiments of H_{2}^{+}, as well as other light ions such as HD^{+}, H_{3}^{+}, and He^{+}.

Penning-Trap Mass Measurement of Helium-4

Light-ion trap (LIONTRAP), a high-precision Penning-trap mass spectrometer, was used to determine the atomic mass of ^{4}He. Here, we report a 12 parts-per-trillion measurement of the mass of a ^{4}He^{2+} ion, m(^{4}He^{2+})=4.001 506 179 651(48)  u. From this, the atomic mass of the neutral atom can be determined without loss of precision: m(^{4}He)=4.002 603 254 653(48)  u. This result is slightly more precise than the current CODATA18 literature value but deviates by 6.6 standard deviations.

Self-Consistent Extraction of Spectroscopic Bounds on Light New Physics

Fundamental physical constants are determined from a collection of precision measurements of elementary particles, atoms, and molecules. This is usually done under the assumption of the standard model (SM) of particle physics. Allowing for light new physics (NP) beyond the SM modifies the extraction of fundamental physical constants. Consequently, setting NP bounds using these data, and at the same time assuming the Committee on Data of the International Science Council recommended values for the fundamental physical constants, is not reliable. As we show in this Letter, both SM and NP parameters can be simultaneously determined in a consistent way from a global fit. For light vectors with QED-like couplings, such as the dark photon, we provide a prescription that recovers the degeneracy with the photon in the massless limit and requires calculations only at leading order in the small new physics couplings. At present, the data show tensions partially related to the proton charge radius determination. We show that these can be alleviated by including contributions from a light scalar with flavor nonuniversal couplings.

Two-photon exchange in (muonic) deuterium at N3LO in pionless effective field theory

We present a study of the two-photon-exchange (2 γ -exchange) corrections to the S-levels in muonic ( μ D) and ordinary (D) deuterium within the pionless effective field theory (EFT). Our calculation proceeds up to next-to-next-to-next-to-leading order (N3LO) in the EFT expansion. The only unknown low-energy constant entering the calculation at this order corresponds to the coupling of a longitudinal photon to the nucleon-nucleon system. To minimise its correlation with the deuteron charge radius, it is extracted using the information about the hydrogen-deuterium isotope shift. We find the elastic 2 γ -exchange contribution in μ D larger by several standard deviations than obtained in other recent calculations. This discrepancy ameliorates the mismatch between theory and experiment on the size of 2 γ -exchange effects, and is attributed to the properties of the deuteron elastic charge form factor parametrisation used to evaluate the elastic contribution. We identify a correlation between the deuteron charge and Friar radii, which can help one to judge how well a form factor parametrisation describes the low-virtuality properties of the deuteron. We also evaluate the higher-order 2 γ -exchange contributions in μ D, generated by the single-nucleon structure and expected to be the most important terms beyond N3LO. The uncertainty of the theoretical result is dominated by the truncation of the EFT series and is quantified using a Bayesian approach. The resulting extractions of the deuteron charge radius from the μ D Lamb shift, the 2 S - 1 S transition in D, and the 2 S - 1 S hydrogen-deuterium isotope shift, with the respective 2 γ -exchange effects evaluated in a unified EFT approach, are in perfect agreement.

Deuteron-to-Proton Mass Ratio from Simultaneous Measurement of the Cyclotron Frequencies of H_{2}^{+} and D^{+}

By simultaneously measuring the cyclotron frequencies of an H_{2}^{+} ion and a deuteron in a coupled magnetron orbit we have made an extended series of measurements of their cyclotron frequency ratio. From the observed changes in H_{2}^{+} mass energy we have followed the decay of three H_{2}^{+} ions to the vibrational ground state. We are able to assign some of our measured ratios to specific rovibrational levels, hence reducing uncertainty due to H_{2}^{+} rotational energy. Assuming the most probable assignment, we obtain a deuteron-to-proton mass ratio, m_{d}/m_{p}=1.999 007 501 272(9). Combined with the atomic mass of the deuteron [S. Rau et al., Nature (London) 585, 43 (2020).NATUAS0028-083610.1038/s41586-020-2628-7] we also obtain a new value for the atomic mass of the proton, m_{p}=1.007 276 466 574(10)  u.

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.

High-precision molecular measurement

Spectroscopy of hydrogen deuteride ions provides the proton-to-electron mass ratio

Proton-electron mass ratio from laser spectroscopy of HD+ at the part-per-trillion level

Recent mass measurements of light atomic nuclei in Penning traps have indicated possible inconsistencies in closely related physical constants such as the proton-electron and deuteron-proton mass ratios. These quantities also influence the predicted vibrational spectrum of the deuterated molecular hydrogen ion (HD+) in its electronic ground state. We used Doppler-free two-photon laser spectroscopy to measure the frequency of the v = 0→9 overtone transition (v, vibrational quantum number) of this spectrum with an uncertainty of 2.9 parts per trillion. By leveraging high-precision ab initio calculations, we converted our measurement to tight constraints on the proton-electron and deuteron-proton mass ratios, consistent with the most recent Penning trap determinations of these quantities. This results in a precision of 21 parts per trillion for the value of the proton-electron mass ratio.