# A small proton charge radius from an electron–proton scattering experiment

## Abstract

Elastic electron–proton scattering (e–p) and the spectroscopy of hydrogen atoms are the two methods traditionally used to determine the proton charge radius, rp. In 2010, a new method using muonic hydrogen atoms1 found a substantial discrepancy compared with previous results2, which became known as the ‘proton radius puzzle’. Despite experimental and theoretical efforts, the puzzle remains unresolved. In fact, there is a discrepancy between the two most recent spectroscopic measurements conducted on ordinary hydrogen3,4. Here we report on the proton charge radius experiment at Jefferson Laboratory (PRad), a high-precision e–p experiment that was established after the discrepancy was identified. We used a magnetic-spectrometer-free method along with a windowless hydrogen gas target, which overcame several limitations of previous e–p experiments and enabled measurements at very small forward-scattering angles. Our result, rp = 0.831 ± 0.007stat ± 0.012syst femtometres, is smaller than the most recent high-precision e–p measurement5 and 2.7 standard deviations smaller than the average of all e–p experimental results6. The smaller rp we have now measured supports the value found by two previous muonic hydrogen experiments1,7. In addition, our finding agrees with the revised value (announced in 2019) for the Rydberg constant8—one of the most accurately evaluated fundamental constants in physics.

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## Data availability

The raw data from this experiment are archived in Jefferson Laboratory’s mass storage silo.

## Code availability

All computer codes used for data analysis and simulation are archived in Jefferson Laboratory’s mass storage silo.

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## Acknowledgements

This work was funded in part by the US National Science Foundation (NSF MRI PHY-1229153) and by the US Department of Energy (contract number DE-FG02-03ER41231), including contract number DE-AC05-06OR23177, under which Jefferson Science Associates, LLC operates the Thomas Jefferson National Accelerator Facility. We thank the staff of Jefferson Laboratory for their support throughout the experiment. We are also grateful to all grant agencies for providing funding support to the authors throughout this project. We acknowledge discussions about radiative corrections with A. Afanasev, I. Akushevich, A. V. Gramolin and O. Tomalak. We thank S. Danagoulian for helping to restore the light monitoring system of HyCal. We also thank S. Javalkar for help with a beam halo study.

## Author information

A.G. is the spokesperson of the experiment. H.G., D. Dutta and M.K. are co-spokespersons of the experiment. A.G. developed the initial concepts of the experiment. A.G., H.G., D. Dutta and M.K designed and proposed the experiment. The entire PRad collaboration constructed the experiment and worked on the data collection. The COMSOL simulation of the target was built by Y.Z. The Monte Carlo simulation was built and validated by C. Peng, C.G., W.X. and X.B. with input from numerous other members of the collaboration. Calibrations were carried out by W.X., M.L., X.B., C. Peng, L.Y. and X.Y., with input from I.L. Analysis software tools were developed by C. Peng, with input from X.B., M.L., I.L., L.Y., W.X. and X.Y. The data analysis was carried out by W.X., C. Peng, X.B., M.L. and C.G., with input from A.G., H.G., D. Dutta, M.K., N.L., E.P., X.Y., D.W.H., L.Y. and M.L.K. All authors reviewed the manuscript.

Correspondence to A. Gasparian or D. Dutta.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

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Peer review information Nature thanks Krzysztof Pachucki and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

## Supplementary information

### Supplementary Information

file contains Supplementary Material, including Supplementary Figures 1-16, Supplementary Table 1 and additional references

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Xiong, W., Gasparian, A., Gao, H. et al. A small proton charge radius from an electron–proton scattering experiment. Nature 575, 147–150 (2019) doi:10.1038/s41586-019-1721-2

• #### DOI

https://doi.org/10.1038/s41586-019-1721-2