Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

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


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.

This is a preview of subscription content, access via your institution

Access options

Rent or buy this article

Prices vary by article type



Prices may be subject to local taxes which are calculated during checkout

Fig. 1: The PRad experimental setup.
Fig. 2: Event reconstruction.
Fig. 3: The measured cross-section and form factor.
Fig. 4: The proton charge radius.

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.


  1. Pohl, R. et al. The size of the proton. Nature 466, 213–216 (2010).

    Article  CAS  ADS  Google Scholar 

  2. Mohr, P. J., Taylor, B. N. & Newell, D. B. CODATA recommended values of the fundamental physical constants: 2006. Rev. Mod. Phys. 80, 633–730 (2008).

    Article  CAS  ADS  Google Scholar 

  3. Beyer, A. et al. The Rydberg constant and proton size from atomic hydrogen. Science 358, 79–85 (2017).

    Article  CAS  ADS  MathSciNet  Google Scholar 

  4. Fleurbaey, H. New measurement of the 1S–3S transition frequency of hydrogen: contribution to the proton charge radius puzzle. Phys. Rev. Lett. 120, 183001 (2018).

    Article  CAS  ADS  Google Scholar 

  5. Bernauer, J. C. et al. High-precision determination of the electric and magnetic form factors of the proton. Phys. Rev. Lett. 105, 242001 (2010).

    Article  CAS  ADS  Google Scholar 

  6. Mohr, P. J., Newell, D. B. & Taylor, B. N. CODATA recommended values of the fundamental physical constants: 2014. J. Phys. Chem. Ref. Data 45, 043102 (2016).

    Article  ADS  Google Scholar 

  7. Antognini, A. et al. Proton structure from the measurement of 2S–2P transition frequencies of muonic hydrogen. Science 339, 417–420 (2013).

    Article  CAS  ADS  Google Scholar 

  8. Mohr, P. J., Newell, D. B. & Taylor, B. N. CODATA recommended values of the fundamental physical constants: 2018. (2019).

  9. Hasan, N. et al. Computing the nucleon charge and axial radii directly at Q 2 = 0 in lattice QCD. Phys. Rev. D 97, 034504 (2018).

    Article  CAS  ADS  Google Scholar 

  10. Mohr, P. J., Taylor, B. N. & Newell, D. B. CODATA recommended values of the fundamental physical constants: 2010. Rev. Mod. Phys. 84, 1527–1605 (2012).

    Article  CAS  ADS  Google Scholar 

  11. Carlson, C. E. The proton radius puzzle. Prog. Part. Nucl. Phys. 82, 59–77 (2015).

    Article  CAS  ADS  Google Scholar 

  12. Liu, Y. S. & Miller, G. A. Validity of the Weizsäcker–Williams approximation and the analysis of beam dump experiments: production of an axion, a dark photon, or a new axial-vector boson. Phys. Rev. D 96, 016004 (2017).

    Article  ADS  Google Scholar 

  13. Miller, G. A. Defining the proton radius: a unified treatment. Phys. Rev. C 99, 035202 (2019).

    Article  CAS  ADS  Google Scholar 

  14. Miller, G. A. Proton polarizability contribution: muonic hydrogen Lamb shift and elastic scattering. Phys. Lett. B 718, 1078–1082 (2013).

    Article  CAS  ADS  Google Scholar 

  15. Antognini, A. et al. Theory of the 2S–2P Lamb shift and 2S hyperfine splitting in muonic hydrogen. Ann. Phys. 331, 127–145 (2013).

    Article  CAS  ADS  Google Scholar 

  16. Lee, G., Arrington, J. R. & Hill, R. J. Extraction of the proton radius from electron–proton scattering data. Phys. Rev. D 92, 013013 (2015).

    Article  ADS  Google Scholar 

  17. Higinbotham, D. W. et al. Proton radius from electron scattering data. Phys. Rev. C 93, 055207 (2016).

    Article  ADS  Google Scholar 

  18. Griffioen, K., Carlson, C. & Maddox, S. Consistency of electron scattering data with a small proton radius. Phys. Rev. C 93, 065207 (2016).

    Article  ADS  Google Scholar 

  19. Gasparian, A. et al. High Precision Measurement of the Proton Charge Radius. Proposal to Jefferson Lab, PAC-38 C12-11-106 (2011).

  20. Gasparian, A. A high performance hybrid electromagnetic calorimeter at Jefferson Lab. In Proc. 11th Int. Conf. on Calorimetry in Particle Physics (eds Cecchi, C. et al.) 109–115 (World Scientific, 2005).

  21. Mecking, B. et al. The CEBAF large acceptance spectrometer (CLAS). Nucl. Instrum. Meth. A 503, 513–553 (2003).

    Article  CAS  ADS  Google Scholar 

  22. Agostinelli, S. et al. GEANT4: a simulation toolkit. Nucl. Instrum. Meth. A 506, 250–303 (2003).

    Article  CAS  ADS  Google Scholar 

  23. Akushevich, I., Gao, H., Ilyichev, A. & Meziane, M. Radiative corrections beyond the ultra relativistic limit in unpolarized ep elastic and Møller scatterings for the PRad experiment at Jefferson Laboratory. Eur. Phys. J. A 51, 1 (2015).

    Article  CAS  ADS  Google Scholar 

  24. Gramolin, A. V. et al. A new event generator for the elastic scattering of charged leptons on protons. J. Phys. G Nucl. Phys. 41, 115001 (2014).

    Article  ADS  Google Scholar 

  25. Christy, M. E. & Bosted, P. E. Empirical fit to precision inclusive electron–proton cross-sections in the resonance region. Phys. Rev. C 81, 055213 (2010).

    Article  ADS  Google Scholar 

  26. Kelly, J. J. Simple parametrization of nucleon form factors. Phys. Rev. C 70, 068202 (2004).

    Article  ADS  Google Scholar 

  27. Venkat, S., Arrington, J., Miller, G. A. & Zhan, X. Realistic transverse images of the proton charge and magnetic densities. Phys. Rev. C 83, 015203 (2011).

    Article  ADS  Google Scholar 

  28. Higinbotham, D. W. & McClellan, R. E. How analytic choices can affect the extraction of electromagnetic form factors from elastic electron scattering cross section data. Preprint at (2018).

  29. Yan, X. et al. Robust extraction of the proton charge radius from electron–proton scattering data. Phys. Rev. C 98, 025204 (2018).

    Article  CAS  ADS  Google Scholar 

  30. Alarcón, J. M., Higinbotham, D. W., Weiss, C. & Ye, Z. Proton charge radius from electron scattering data using dispersively improved chiral effective field theory. Phys. Rev. C 99, 044303 (2019).

    Article  ADS  Google Scholar 

Download references


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

Authors and Affiliations



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.

Corresponding authors

Correspondence to A. Gasparian or D. Dutta.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

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

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Xiong, W., Gasparian, A., Gao, H. et al. A small proton charge radius from an electron–proton scattering experiment. Nature 575, 147–150 (2019).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

This article is cited by


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing