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The size of the proton

Nature volume 466, pages 213–216 (2010)Cite this article

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Abstract

The proton is the primary building block of the visible Universe, but many of its properties—such as its charge radius and its anomalous magnetic moment—are not well understood. The root-mean-square charge radius, rp, has been determined with an accuracy of 2 per cent (at best) by electron–proton scattering experiments1,2. The present most accurate value of rp (with an uncertainty of 1 per cent) is given by the CODATA compilation of physical constants3. This value is based mainly on precision spectroscopy of atomic hydrogen4,5,6,7 and calculations of bound-state quantum electrodynamics (QED; refs 8, 9). The accuracy of rp as deduced from electron–proton scattering limits the testing of bound-state QED in atomic hydrogen as well as the determination of the Rydberg constant (currently the most accurately measured fundamental physical constant3). An attractive means to improve the accuracy in the measurement of rp is provided by muonic hydrogen (a proton orbited by a negative muon); its much smaller Bohr radius compared to ordinary atomic hydrogen causes enhancement of effects related to the finite size of the proton. In particular, the Lamb shift10 (the energy difference between the 2S1/2 and 2P1/2 states) is affected by as much as 2 per cent. Here we use pulsed laser spectroscopy to measure a muonic Lamb shift of 49,881.88(76) GHz. On the basis of present calculations11,12,13,14,15 of fine and hyperfine splittings and QED terms, we find rp = 0.84184(67) fm, which differs by 5.0 standard deviations from the CODATA value3 of 0.8768(69) fm. Our result implies that either the Rydberg constant has to be shifted by −110 kHz/c (4.9 standard deviations), or the calculations of the QED effects in atomic hydrogen or muonic hydrogen atoms are insufficient.

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Figure 1: Energy levels, cascade and experimental principle in muonic hydrogen.
Figure 2: Muon beam.
Figure 3: Laser system.
Figure 4: Summed X-ray time spectra.
Figure 5: Resonance.

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Acknowledgements

We thank L. Simons and B. Leoni for setting up the cyclotron trap, H. Brückner, K. Linner, W. Simon, O. Huot and Z. Hochman for technical support, P. Maier-Komor, K. Nacke, M. Horisberger, A. Weber, L. Meier and J. Hehner for thin foils and windows, N. Schlumpf, U. Hartmann and M. Gaspar for electronics, S. Spielmann-Jaeggi and L. Carroll for optical measurements, Ch. Parthey and M. Herrmann for their help, the MEG-collaboration for a share of beam-time, and A. Voss, B. Weichelt and J. Fruechtenicht for the loan of a laser pump diode. We acknowledge the essential contributions of H. Hofer and V.W. Hughes in the initial stages of the experiment. We also thank the PSI accelerator division, the Hallendienst, the workshops at PSI, MPQ and Fribourg, and other support groups for their help. We acknowledge support from the Max Planck Society and the Max Planck Foundation, the Swiss National Science Foundation (project 200020-100632) and the Swiss Academy of Engineering Sciences, the BQR de l'UFR de physique fondamentale et appliquée de l'Université Paris 6, the program PAI Germaine de Staël no. 07819NH du ministère des affaires étrangères France, and the Fundação para a Ciência e a Tecnologia (Portugal) and FEDER (project PTDC/FIS/82006/2006 and grant SFRH/BPD/46611/2008). P.I. and E.-O.L.B. acknowledge support from the ‘ExtreMe Matter Institute, Helmholtz Alliance HA216/EMMI’.

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Author notes

  1. Adolf Giesen & Françoise Mulhauser

    Present address: Present addresses: Deutsches Zentrum für Luft- und Raumfahrt e.V. in der Helmholtz-Gemeinschaft, 70569 Stuttgart, Germany (A.G.); International Atomic Energy Agency, A-1400 Vienna, Austria (F.M.).,

Authors and Affiliations

  1. Max-Planck-Institut für Quantenoptik, Garching, 85748, Germany

    Randolf Pohl, Aldo Antognini, Theodor W. Hänsch & Tobias Nebel

  2. Laboratoire Kastler Brossel, École Normale Supérieure, CNRS, and Université P. et M. Curie-Paris 6, 75252 Paris, Cedex 05, France,

    François Nez, François Biraben, Paul Indelicato, Lucile Julien, Eric-Olivier Le Bigot & Catherine Schwob

  3. Departamento de Física, Universidade de Coimbra, Coimbra, 3004-516, Portugal

    Fernando D. Amaro, João M. R. Cardoso, Daniel S. Covita, Luis M. P. Fernandes, José A. M. Lopes, Cristina M. B. Monteiro & Joaquim M. F. dos Santos

  4. Departamento de Física, I3N, Universidade de Aveiro, Aveiro, 3810-193, Portugal

    Daniel S. Covita & João F. C. A. Veloso

  5. Physics Department, Yale University, New Haven, 06520-8121, Connecticut, USA

    Andreas Dax & Satish Dhawan

  6. Institut für Strahlwerkzeuge, Universität Stuttgart, Stuttgart, 70569, Germany

    Adolf Giesen & Thomas Graf

  7. Physics Department, National Tsing Hua University, Hsinchu, 300, Taiwan

    Cheng-Yang Kao & Yi-Wei Liu

  8. Département de Physique, Université de Fribourg, Fribourg, 1700, Switzerland

    Paul Knowles, Livia Ludhova, Françoise Mulhauser & Lukas A. Schaller

  9. Department of Chemistry, Princeton University, Princeton, 08544-1009, New Jersey, USA

    Paul Rabinowitz

  10. Dausinger & Giesen GmbH, Rotebühlstr. 87, 70178 Stuttgart, Germany,

    Karsten Schuhmann

  11. Paul Scherrer Institute, Villigen-PSI, 5232, Switzerland

    David Taqqu

  12. Institut für Teilchenphysik, ETH Zürich, 8093 Zürich, Switzerland,

    Franz Kottmann

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Contributions

R.P., A.A., F.N., F.D.A., F.B., A.D., A.G., T.G., T.W.H., L.J., C.-Y.K., Y.-W.L., T.N., P.R., K.S., C.S. and F.K. designed, built and operated parts of the laser system. R.P., A.A., F.N., D.S.C., L.M.P.F., P.K., Y.-W.L., J.A.M.L., L.L., C.M.B.M., F.M., T.N., J.M.F.d.S., L.A.S., K.S., D.T., J.F.C.A.V. and F.K. planned, built and set up the various detectors of the experiment. R.P., A.A., D.S.C., F.M., D.T., J.F.C.A.V. and F.K. designed, built, set up and operated the muon beam line. R.P., A.A., F.N., J.M.R.C., D.S.C., A.D., S.D., L.M.P.F., C.-Y.K., P.K., Y.-W.L., F.M., T.N., J.M.F.d.S., K.S., D.T., J.F.C.A.V. and F.K. designed and implemented the electronics used in the experiment. R.P., A.A., J.M.R.C., P.I., P.K., E.-O.L.B. and T.N. set up the computing infrastructure, wrote software and realized the data acquisition system. R.P., A.A., F.N., F.D.A. F.B., J.M.R.C., D.S.C., A.D., L.M.P.F., P.I., L.J., C.-Y.K., P.K., E.-O.L.B., Y.-W.L., J.A.M.L., L.L., C.M.B.M., F.M., T.N., J.M.F.d.S., K.S., C.S., D.T., J.F.C.A.V. and F.K. took part in the months-long data-taking runs. E.-O.L.B., P.I. and F.K. did work on QED theory. R.P., A.A., F.N., F.B., P.I., L.J., P.K., L.L., T.N., D.T. and F.K. analysed the data and wrote the initial manuscript. The manuscript was then read, improved and finally approved by all authors.

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Correspondence to Randolf Pohl.

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Pohl, R., Antognini, A., Nez, F. et al. The size of the proton. Nature 466, 213–216 (2010). https://doi.org/10.1038/nature09250

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