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# A 16-parts-per-trillion measurement of the antiproton-to-proton charge–mass ratio

## Abstract

The standard model of particle physics is both incredibly successful and glaringly incomplete. Among the questions left open is the striking imbalance of matter and antimatter in the observable universe1, which inspires experiments to compare the fundamental properties of matter/antimatter conjugates with high precision2,3,4,5. Our experiments deal with direct investigations of the fundamental properties of protons and antiprotons, performing spectroscopy in advanced cryogenic Penning trap systems6. For instance, we previously compared the proton/antiproton magnetic moments with 1.5 parts per billion fractional precision7,8, which improved upon previous best measurements9 by a factor of greater than 3,000. Here we report on a new comparison of the proton/antiproton charge-to-mass ratios with a fractional uncertainty of 16 parts per trillion. Our result is based on the combination of four independent long-term studies, recorded in a total time span of 1.5 years. We use different measurement methods and experimental set-ups incorporating different systematic effects. The final result, $$-{(q/m)}_{p}/{(q/m)}_{\bar{p}}=1.000000000003(16)$$, is consistent with the fundamental charge–parity–time reversal invariance, and improves the precision of our previous best measurement6 by a factor of 4.3. The measurement tests the standard model at an energy scale of 1.96 × 10−27 gigaelectronvolts (confidence level 0.68), and improves ten coefficients of the standard model extension10. Our cyclotron clock study also constrains hypothetical interactions mediating violations of the clock weak equivalence principle (WEPcc) for antimatter to less than 1.8 × 10−7, and enables the first differential test of the WEPcc using antiprotons11. From this interpretation we constrain the differential WEPcc-violating coefficient to less than 0.030.

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## Data and code availability

The datasets and analysis codes will be made available on reasonable request.

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## Acknowledgements

We acknowledge technical support by CERN, especially the Antiproton Decelerator operation group, CERN’s cryolab team and engineering department, and all other CERN groups that provide support to Antiproton Decelerator experiments. We acknowledge Y. Ding for comments in the discussion of the updated SME limits. We acknowledge financial support by RIKEN, the RIKEN EEE pioneering project funding, the RIKEN SPDR and JRA programme, the Max Planck Society, the European Union (FunI-832848, STEP-852818), CRC 1227 ‘DQ-mat’(DFG 274200144), the Cluster of Excellence ‘Quantum Frontiers’ (DFG 390837967), AVA-721559, the CERN fellowship programme and the Helmholtz-Gemeinschaft. This work was supported by the Max Planck, RIKEN, PTB Center for Time, Constants, and Fundamental Symmetries (C-TCFS).

## Author information

Authors

### Contributions

The experiment was designed and built by S.U. and C.S.; and M.J.B., J.A.D., J.A.H., T.H. and E.J.W. developed several technical upgrades. J.A.H., S.U., T.H., J.A.D., E.J.W. and M.J.B. developed the control code. J.A.H., M.J.B., T.H., J.A.D., E.J.W. and S.U. took part in the data acquisition. M.J.B., S.U., J.A.D., J.A.H., E.J.W. and M.F. performed the systematic studies. J.A.H., M.J.B., T.H., J.A.D., E.J.W., S.R.E. and S.U. contributed to the maintenance of the experiment during the measurement campaign. The data were analysed by S.U., E.J.W. and J.A.H.; and J.A.D., M.J.B., B.M.L. and C.W. contributed to the systematic analysis. The final results were discussed with all co-authors. The manuscript was written by S.U. and discussed with E.J.W., J.A.D., B.M.L., C.S. and K.B.; all co-authors discussed and approved the content.

### Corresponding author

Correspondence to S. Ulmer.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information Nature thanks the anonymous reviewers for their contribution to the peer review of this work. Peer reviewer reports are available.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Extended data figures and tables

### Extended Data Fig. 1 Energy calibration.

Upper: Measured cyclotron frequency shift as a function of the measured axial frequency shift. Lower: Measured cyclotron frequency shift as a function of particle energy E+.

### Extended Data Fig. 2 Dominant systematic uncertainty.

Upper: measured axial frequency ratio as a function of the frequency ratio of the axial detection resonators. We observe a weak linear scaling of the measured axial frequency ratio as a function of the detuning of the axial frequency with respect to the resonator centre. Green line: weighted linear fit, red and blue functions represent CL 0.68 and CL 0.95 error bands. Lower: Residuals of upper plot.

### Extended Data Fig. 3 B2-imposed uncertainty in peak frequency ratio.

Upper: Sensitivity of the frequency ratio R as a function of the coefficient B2 for different particle energy differences E+,p − E+,H, expressed as ΔRB2E+). Lower: Measured particle energy differences E+,p − E+,H throughout the peak run. The green vertical lines indicate the mean difference and the uncertainty, the vertical green lines define the frequency-ratio shift and its uncertainty caused by the uncertainties in energy similarity and B2.

## Supplementary information

### Supplementary Information

This file contains a description of the data analysis, data cleaning, and data processing. It also contains notes regarding order systematic shifts and includes Supplementary Figs 1–10 and Supplementary Tables 1–3.

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Borchert, M.J., Devlin, J.A., Erlewein, S.R. et al. A 16-parts-per-trillion measurement of the antiproton-to-proton charge–mass ratio. Nature 601, 53–57 (2022). https://doi.org/10.1038/s41586-021-04203-w

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• DOI: https://doi.org/10.1038/s41586-021-04203-w