{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T23:31:43Z","timestamp":1776900703694,"version":"3.51.2"},"reference-count":64,"publisher":"Springer Science and Business Media LLC","issue":"7843","license":[{"start":{"date-parts":[[2021,1,27]],"date-time":"2021-01-27T00:00:00Z","timestamp":1611705600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2021,1,27]],"date-time":"2021-01-27T00:00:00Z","timestamp":1611705600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Nature"],"published-print":{"date-parts":[[2021,1,28]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The energy levels of hydrogen-like atomic systems can be calculated with great precision. Starting from their quantum mechanical solution, they have been refined over the years to include the electron spin, the relativistic and quantum field effects, and tiny energy shifts related to the complex structure of the nucleus. These energy shifts caused by the nuclear structure are vastly magnified in hydrogen-like systems formed by a negative muon and a nucleus, so spectroscopy of these muonic ions can be used to investigate the nuclear structure with high precision. Here we present the measurement of two 2S\u20132P transitions in the muonic helium-4 ion that yields a precise determination of the root-mean-square charge radius of the \u03b1 particle of 1.67824(83)\u00a0femtometres. This determination from atomic spectroscopy is in excellent agreement with the value from electron scattering<jats:sup>1<\/jats:sup>, but a factor of 4.8 more precise, providing a benchmark for few-nucleon theories, lattice quantum chromodynamics and electron scattering. This agreement also constrains several beyond-standard-model theories proposed to explain the proton-radius puzzle<jats:sup>2\u20135<\/jats:sup>, in line with recent determinations of the proton charge radius<jats:sup>6\u20139<\/jats:sup>, and establishes spectroscopy of light muonic atoms and ions as a precise tool for studies of nuclear properties.<\/jats:p>","DOI":"10.1038\/s41586-021-03183-1","type":"journal-article","created":{"date-parts":[[2021,1,27]],"date-time":"2021-01-27T17:03:15Z","timestamp":1611766995000},"page":"527-531","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":115,"title":["Measuring the \u03b1-particle charge radius with muonic helium-4 ions"],"prefix":"10.1038","volume":"589","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7769-650X","authenticated-orcid":false,"given":"Julian J.","family":"Krauth","sequence":"first","affiliation":[]},{"given":"Karsten","family":"Schuhmann","sequence":"additional","affiliation":[]},{"given":"Marwan Abdou","family":"Ahmed","sequence":"additional","affiliation":[]},{"given":"Fernando D.","family":"Amaro","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5257-6728","authenticated-orcid":false,"given":"Pedro","family":"Amaro","sequence":"additional","affiliation":[]},{"given":"Fran\u00e7ois","family":"Biraben","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2243-5780","authenticated-orcid":false,"given":"Tzu-Ling","family":"Chen","sequence":"additional","affiliation":[]},{"given":"Daniel S.","family":"Covita","sequence":"additional","affiliation":[]},{"given":"Andreas J.","family":"Dax","sequence":"additional","affiliation":[]},{"given":"Marc","family":"Diepold","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7061-8768","authenticated-orcid":false,"given":"Luis M. P.","family":"Fernandes","sequence":"additional","affiliation":[]},{"given":"Beatrice","family":"Franke","sequence":"additional","affiliation":[]},{"given":"Sandrine","family":"Galtier","sequence":"additional","affiliation":[]},{"given":"Andrea L.","family":"Gouvea","sequence":"additional","affiliation":[]},{"given":"Johannes","family":"G\u00f6tzfried","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8466-073X","authenticated-orcid":false,"given":"Thomas","family":"Graf","sequence":"additional","affiliation":[]},{"given":"Theodor W.","family":"H\u00e4nsch","sequence":"additional","affiliation":[]},{"given":"Jens","family":"Hartmann","sequence":"additional","affiliation":[]},{"given":"Malte","family":"Hildebrandt","sequence":"additional","affiliation":[]},{"given":"Paul","family":"Indelicato","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7010-8314","authenticated-orcid":false,"given":"Lucile","family":"Julien","sequence":"additional","affiliation":[]},{"given":"Klaus","family":"Kirch","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3767-950X","authenticated-orcid":false,"given":"Andreas","family":"Knecht","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1090-0665","authenticated-orcid":false,"given":"Yi-Wei","family":"Liu","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0383-4882","authenticated-orcid":false,"given":"Jorge","family":"Machado","sequence":"additional","affiliation":[]},{"given":"Cristina M. B.","family":"Monteiro","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2429-3314","authenticated-orcid":false,"given":"Fran\u00e7oise","family":"Mulhauser","sequence":"additional","affiliation":[]},{"given":"Boris","family":"Naar","sequence":"additional","affiliation":[]},{"given":"Tobias","family":"Nebel","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3478-7521","authenticated-orcid":false,"given":"Fran\u00e7ois","family":"Nez","sequence":"additional","affiliation":[]},{"given":"Joaquim M. F.","family":"dos Santos","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5890-0971","authenticated-orcid":false,"given":"Jos\u00e9 Paulo","family":"Santos","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6125-7948","authenticated-orcid":false,"given":"Csilla I.","family":"Szabo","sequence":"additional","affiliation":[]},{"given":"David","family":"Taqqu","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7107-7203","authenticated-orcid":false,"given":"Jo\u00e3o F. C. A.","family":"Veloso","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9664-6265","authenticated-orcid":false,"given":"Jan","family":"Vogelsang","sequence":"additional","affiliation":[]},{"given":"Andreas","family":"Voss","sequence":"additional","affiliation":[]},{"given":"Birgit","family":"Weichelt","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6435-659X","authenticated-orcid":false,"given":"Randolf","family":"Pohl","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1837-0419","authenticated-orcid":false,"given":"Aldo","family":"Antognini","sequence":"additional","affiliation":[]},{"given":"Franz","family":"Kottmann","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,1,27]]},"reference":[{"key":"3183_CR1","doi-asserted-by":"publisher","first-page":"041302","DOI":"10.1103\/PhysRevC.77.041302","volume":"77","author":"I Sick","year":"2008","unstructured":"Sick, I. Precise root-mean-square radius of 4He. Phys. Rev. C 77, 041302 (2008).","journal-title":"Phys. Rev. C"},{"key":"3183_CR2","doi-asserted-by":"publisher","first-page":"213","DOI":"10.1038\/nature09250","volume":"466","author":"R Pohl","year":"2010","unstructured":"Pohl, R. et al. The size of the proton. Nature 466, 213\u2013216 (2010).","journal-title":"Nature"},{"key":"3183_CR3","doi-asserted-by":"publisher","first-page":"417","DOI":"10.1126\/science.1230016","volume":"339","author":"A Antognini","year":"2013","unstructured":"Antognini, A. et al. Proton structure from the measurement of 2S\u20132P transition frequencies of muonic hydrogen. Science 339, 417\u2013420 (2013).","journal-title":"Science"},{"key":"3183_CR4","doi-asserted-by":"publisher","first-page":"175","DOI":"10.1146\/annurev-nucl-102212-170627","volume":"63","author":"R Pohl","year":"2013","unstructured":"Pohl, R. et al. Muonic hydrogen and the proton radius puzzle. Annu. Rev. Nucl. Part. Sci. 63, 175\u2013204 (2013).","journal-title":"Annu. Rev. Nucl. Part. Sci."},{"key":"3183_CR5","doi-asserted-by":"publisher","first-page":"59","DOI":"10.1016\/j.ppnp.2015.01.002","volume":"82","author":"CE Carlson","year":"2015","unstructured":"Carlson, C. E. The proton radius puzzle. Prog. Part. Nucl. Phys. 82, 59\u201377 (2015).","journal-title":"Prog. Part. Nucl. Phys."},{"key":"3183_CR6","doi-asserted-by":"publisher","first-page":"669","DOI":"10.1126\/science.aaf2468","volume":"353","author":"R Pohl","year":"2016","unstructured":"Pohl, R. et al. Laser spectroscopy of muonic deuterium. Science 353, 669\u2013673 (2016).","journal-title":"Science"},{"key":"3183_CR7","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1126\/science.aah6677","volume":"358","author":"A Beyer","year":"2017","unstructured":"Beyer, A. et al. The Rydberg constant and proton size from atomic hydrogen. Science 358, 79\u201385 (2017).","journal-title":"Science"},{"key":"3183_CR8","doi-asserted-by":"publisher","first-page":"1007","DOI":"10.1126\/science.aau7807","volume":"365","author":"N Bezginov","year":"2019","unstructured":"Bezginov, N. et al. A measurement of the atomic hydrogen Lamb shift and the proton charge radius. Science 365, 1007\u20131012 (2019).","journal-title":"Science"},{"key":"3183_CR9","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1038\/s41586-019-1721-2","volume":"575","author":"W Xiong","year":"2019","unstructured":"Xiong, W. et al. A small proton charge radius from an electron\u2013proton scattering experiment. Nature 575, 147\u2013150 (2019).","journal-title":"Nature"},{"key":"3183_CR10","doi-asserted-by":"publisher","first-page":"245","DOI":"10.1016\/S0146-6410(01)00156-9","volume":"47","author":"I Sick","year":"2001","unstructured":"Sick, I. Elastic electron scattering from light nuclei. Prog. Part. Nucl. Phys. 47, 245\u2013318 (2001).","journal-title":"Prog. Part. Nucl. Phys."},{"key":"3183_CR11","doi-asserted-by":"publisher","first-page":"158","DOI":"10.1016\/j.ppnp.2012.09.001","volume":"68","author":"W Leidemann","year":"2013","unstructured":"Leidemann, W. & Orlandini, G. Modern ab initio approaches and applications in few-nucleon physics with A \u2265 4. Prog. Part. Nucl. Phys. 68, 158\u2013214 (2013).","journal-title":"Prog. Part. Nucl. Phys."},{"key":"3183_CR12","doi-asserted-by":"publisher","first-page":"183001","DOI":"10.1103\/PhysRevLett.120.183001","volume":"120","author":"H Fleurbaey","year":"2018","unstructured":"Fleurbaey, H. et al. New measurement of the 1S\u20133S transition frequency of hydrogen: contribution to the proton charge radius puzzle. Phys. Rev. Lett. 120, 183001 (2018).","journal-title":"Phys. Rev. Lett."},{"key":"3183_CR13","doi-asserted-by":"publisher","first-page":"3553","DOI":"10.1103\/PhysRevLett.74.3553","volume":"74","author":"D Shiner","year":"1995","unstructured":"Shiner, D., Dixson, R. & Vedantham, V. Three-nucleon charge radius: a precise laser determination using 3He. Phys. Rev. Lett. 74, 3553\u20133556 (1995).","journal-title":"Phys. Rev. Lett."},{"key":"3183_CR14","doi-asserted-by":"publisher","first-page":"143001","DOI":"10.1103\/PhysRevLett.108.143001","volume":"108","author":"P Cancio Pastor","year":"2012","unstructured":"Cancio Pastor, P. et al. Frequency metrology of helium around 1083 nm and determination of the nuclear charge radius. Phys. Rev. Lett. 108, 143001 (2012).","journal-title":"Phys. Rev. Lett."},{"key":"3183_CR15","doi-asserted-by":"publisher","first-page":"1383","DOI":"10.1103\/RevModPhys.85.1383","volume":"85","author":"ZT Lu","year":"2013","unstructured":"Lu, Z. T. et al. Laser probing of neutron-rich nuclei in light atoms. Rev. Mod. Phys. 85, 1383\u20131400 (2013).","journal-title":"Rev. Mod. Phys."},{"key":"3183_CR16","doi-asserted-by":"publisher","first-page":"1132","DOI":"10.1038\/s41567-018-0242-5","volume":"14","author":"RJ Rengelink","year":"2018","unstructured":"Rengelink, R. J. et al. Precision spectroscopy of helium in a magic wavelength optical dipole trap. Nat. Phys. 14, 1132\u20131137 (2018).","journal-title":"Nat. Phys."},{"key":"3183_CR17","doi-asserted-by":"publisher","first-page":"263002","DOI":"10.1103\/PhysRevLett.119.263002","volume":"119","author":"X Zheng","year":"2017","unstructured":"Zheng, X. et al. Measurement of the frequency of the 23S\u201323P transition of 4He. Phys. Rev. Lett. 119, 263002 (2017).","journal-title":"Phys. Rev. Lett."},{"key":"3183_CR18","doi-asserted-by":"publisher","first-page":"062507","DOI":"10.1103\/PhysRevA.101.062507","volume":"101","author":"YJ Huang","year":"2020","unstructured":"Huang, Y. J. et al. Precision laser spectroscopy of the 21S0\u201331D2 two-photon transition in 3He. Phys. Rev. A 101, 062507 (2020).","journal-title":"Phys. Rev. A"},{"key":"3183_CR19","doi-asserted-by":"publisher","first-page":"062516","DOI":"10.1103\/PhysRevA.101.062516","volume":"101","author":"V Patk\u00f3\u0161","year":"2020","unstructured":"Patk\u00f3\u0161, V., Yerokhin, V. A. & Pachucki, K. Nonradiative \u03b17m QED effects in Lamb shift of helium triplet states. Phys. Rev. A 101, 062516 (2020).","journal-title":"Phys. Rev. A"},{"key":"3183_CR20","doi-asserted-by":"publisher","first-page":"052505","DOI":"10.1103\/PhysRevA.79.052505","volume":"79","author":"M Herrmann","year":"2009","unstructured":"Herrmann, M. et al. Feasibility of coherent xuv spectroscopy on the 1S\u20132S transition in singly ionized helium. Phys. Rev. A 79, 052505 (2009).","journal-title":"Phys. Rev. A"},{"key":"3183_CR21","first-page":"049","volume":"353","author":"JJ Krauth","year":"2019","unstructured":"Krauth, J. J. et al. Paving the way for fundamental physics tests with singly-ionized helium. Proc. Sci. 353, 049 (2019).","journal-title":"Proc. Sci."},{"key":"3183_CR22","doi-asserted-by":"publisher","first-page":"241","DOI":"10.1103\/PhysRev.72.241","volume":"72","author":"WE Lamb","year":"1947","unstructured":"Lamb, W. E. & Retherford, R. C. Fine structure of the hydrogen atom by a microwave method. Phys. Rev. 72, 241\u2013243 (1947).","journal-title":"Phys. Rev."},{"key":"3183_CR23","doi-asserted-by":"publisher","first-page":"220","DOI":"10.1016\/j.aop.2018.07.015","volume":"396","author":"M Diepold","year":"2018","unstructured":"Diepold, M. et al. Theory of the Lamb shift and fine structure in muonic 4He ions and the muonic 3He\u20134He isotope shift. Ann. Phys. 396, 220\u2013244 (2018).","journal-title":"Ann. Phys."},{"key":"3183_CR24","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1016\/j.physletb.2017.10.056","volume":"775","author":"RN Faustov","year":"2017","unstructured":"Faustov, R. N. et al. Radiative nonrecoil nuclear finite size corrections of order \u03b1(Z\u03b1)5 to the Lamb shift in light muonic atoms. Phys. Lett. B 775, 79\u201383 (2017).","journal-title":"Phys. Lett. B"},{"key":"3183_CR25","doi-asserted-by":"publisher","first-page":"064002","DOI":"10.1103\/PhysRevC.90.064002","volume":"90","author":"I Sick","year":"2014","unstructured":"Sick, I. Zemach moments of 3He and 4He. Phys. Rev. C 90, 064002 (2014).","journal-title":"Phys. Rev. C"},{"key":"3183_CR26","doi-asserted-by":"publisher","first-page":"093002","DOI":"10.1088\/1361-6471\/aad3eb","volume":"45","author":"C Ji","year":"2018","unstructured":"Ji, C. et al. Ab initio calculation of nuclear-structure corrections in muonic atoms. J. Phys. G 45, 093002 (2018).","journal-title":"J. Phys. G"},{"key":"3183_CR27","doi-asserted-by":"publisher","first-page":"062511","DOI":"10.1103\/PhysRevA.97.062511","volume":"97","author":"K Pachucki","year":"2018","unstructured":"Pachucki, K., Patk\u00f3\u0161, V. & Yerokhin, V. A. Three-photon-exchange nuclear structure correction in hydrogenic systems. Phys. Rev. A 97, 062511 (2018).","journal-title":"Phys. Rev. A"},{"key":"3183_CR28","unstructured":"Dittus, F. B. Experimentelle Untersuchung \u00fcber Bildung und Zerfall myonischer Heliumionen im metastabilen 2S-Zustand. PhD thesis, ETH Zurich (1985)."},{"key":"3183_CR29","doi-asserted-by":"publisher","first-page":"040501","DOI":"10.1103\/PhysRevA.75.040501","volume":"75","author":"L Ludhova","year":"2007","unstructured":"Ludhova, L. et al. Muonic hydrogen cascade time and lifetime of the short-lived 2S state. Phys. Rev. A 75, 040501 (2007).","journal-title":"Phys. Rev. A"},{"key":"3183_CR30","doi-asserted-by":"publisher","first-page":"232","DOI":"10.1016\/0370-2693(84)91152-3","volume":"136","author":"HP von Arb","year":"1984","unstructured":"von Arb, H. P. et al. Measurement of the lifetime and quenching rate of metastable 2S muonic helium ions. Phys. Lett. B 136, 232\u2013236 (1984).","journal-title":"Phys. Lett. B"},{"key":"3183_CR31","doi-asserted-by":"publisher","first-page":"053102","DOI":"10.1063\/1.4921195","volume":"86","author":"M Diepold","year":"2015","unstructured":"Diepold, M. et al. Improved X-ray detection and particle identification with avalanche photodiodes. Rev. Sci. Instrum. 86, 053102 (2015).","journal-title":"Rev. Sci. Instrum."},{"key":"3183_CR32","doi-asserted-by":"publisher","first-page":"022514","DOI":"10.1103\/PhysRevA.92.022514","volume":"92","author":"P Amaro","year":"2015","unstructured":"Amaro, P. et al. Quantum interference effects in laser spectroscopy of muonic hydrogen, deuterium, and helium-3. Phys. Rev. A 92, 022514 (2015).","journal-title":"Phys. Rev. A"},{"key":"3183_CR33","doi-asserted-by":"publisher","first-page":"143402","DOI":"10.1103\/PhysRevLett.111.143402","volume":"111","author":"C Ji","year":"2013","unstructured":"Ji, C. et al. Nuclear polarization corrections to the \u03bc4He+ Lamb shift. Phys. Rev. Lett. 111, 143402 (2013).","journal-title":"Phys. Rev. Lett."},{"key":"3183_CR34","doi-asserted-by":"publisher","first-page":"022504","DOI":"10.1103\/PhysRevA.89.022504","volume":"89","author":"CE Carlson","year":"2014","unstructured":"Carlson, C. E., Gorchtein, M. & Vanderhaeghen, M. Nuclear-structure contribution to the Lamb shift in muonic deuterium. Phys. Rev. A 89, 022504 (2014).","journal-title":"Phys. Rev. A"},{"key":"3183_CR35","doi-asserted-by":"publisher","first-page":"034004","DOI":"10.1103\/PhysRevC.99.034004","volume":"99","author":"N Nevo Dinur","year":"2019","unstructured":"Nevo Dinur, N. et al. Zemach moments and radii of 2,3H and 3,4He. Phys. Rev. C 99, 034004 (2019).","journal-title":"Phys. Rev. C"},{"key":"3183_CR36","doi-asserted-by":"publisher","first-page":"917","DOI":"10.1007\/s00601-014-0809-3","volume":"55","author":"C Ji","year":"2014","unstructured":"Ji, C. et al. Nuclear polarization effects in muonic atoms. Few Body Syst. 55, 917\u2013921 (2014).","journal-title":"Few Body Syst."},{"key":"3183_CR37","doi-asserted-by":"publisher","first-page":"01002","DOI":"10.1051\/epjconf\/20146601002","volume":"66","author":"S Bacca","year":"2014","unstructured":"Bacca, S. Electromagnetic reactions and few-nucleon dynamics. EPJ Web Conf. 66, 01002 (2014).","journal-title":"EPJ Web Conf."},{"key":"3183_CR38","doi-asserted-by":"publisher","first-page":"381","DOI":"10.1016\/0375-9474(77)90089-6","volume":"278","author":"G Carboni","year":"1977","unstructured":"Carboni, G. et al. Precise measurement of the 2S1\/2\u20132P3\/2 splitting in the (\u03bc\u22124He)+ muonic ion. Nucl. Phys. A 278, 381\u2013386 (1977).","journal-title":"Nucl. Phys. A"},{"key":"3183_CR39","doi-asserted-by":"publisher","first-page":"229","DOI":"10.1016\/0370-2693(78)90843-2","volume":"73","author":"G Carboni","year":"1978","unstructured":"Carboni, G. et al. Measurement of the 2S1\/2\u20132P1\/2 splitting in the (\u03bc\u22124He)+ muonic ion. Phys. Lett. B 73, 229\u2013231 (1978).","journal-title":"Phys. Lett. B"},{"key":"3183_CR40","doi-asserted-by":"publisher","first-page":"2363","DOI":"10.1103\/PhysRevA.46.2363","volume":"46","author":"P Hauser","year":"1992","unstructured":"Hauser, P. et al. Search for the 2S\u20132P energy difference in muonic 4He ions. Phys. Rev. A 46, 2363\u20132377 (1992).","journal-title":"Phys. Rev. A"},{"key":"3183_CR41","doi-asserted-by":"publisher","first-page":"011803","DOI":"10.1103\/PhysRevLett.107.011803","volume":"107","author":"B Batell","year":"2011","unstructured":"Batell, B., McKeen, D. & Pospelov, M. New parity-violating muonic forces and the proton charge radius. Phys. Rev. Lett. 107, 011803 (2011).","journal-title":"Phys. Rev. Lett."},{"key":"3183_CR42","doi-asserted-by":"publisher","first-page":"101702","DOI":"10.1103\/PhysRevD.83.101702","volume":"83","author":"D Tucker-Smith","year":"2011","unstructured":"Tucker-Smith, D. & Yavin, I. Muonic hydrogen and MeV forces. Phys. Rev. D 83, 101702 (2011).","journal-title":"Phys. Rev. D"},{"key":"3183_CR43","doi-asserted-by":"publisher","first-page":"055204","DOI":"10.1103\/PhysRevC.91.055204","volume":"91","author":"GA Miller","year":"2015","unstructured":"Miller, G. A. Nonperturbative lepton-sea fermions in the nucleon and the proton radius puzzle. Phys. Rev. C 91, 055204 (2015).","journal-title":"Phys. Rev. C"},{"key":"3183_CR44","doi-asserted-by":"publisher","first-page":"1350094","DOI":"10.1142\/S0217732313500946","volume":"28","author":"LB Wang","year":"2013","unstructured":"Wang, L. B. & Ni, W. T. Proton radius puzzle and large extra dimensions. Mod. Phys. Lett. A 28, 1350094 (2013).","journal-title":"Mod. Phys. Lett. A"},{"key":"3183_CR45","doi-asserted-by":"publisher","first-page":"1078","DOI":"10.1016\/j.physletb.2012.11.016","volume":"718","author":"GA Miller","year":"2013","unstructured":"Miller, G. A. Proton polarizability contribution: muonic hydrogen Lamb shift and elastic scattering. Phys. Lett. B 718, 1078\u20131082 (2013).","journal-title":"Phys. Lett. B"},{"key":"3183_CR46","doi-asserted-by":"publisher","first-page":"095024","DOI":"10.1103\/PhysRevD.92.095024","volume":"92","author":"CE Carlson","year":"2015","unstructured":"Carlson, C. E. & Freid, M. Extending theories on muon-specific interactions. Phys. Rev. D 92, 095024 (2015).","journal-title":"Phys. Rev. D"},{"key":"3183_CR47","doi-asserted-by":"publisher","first-page":"062514","DOI":"10.1103\/PhysRevA.88.062514","volume":"88","author":"UD Jentschura","year":"2013","unstructured":"Jentschura, U. D. Light sea fermions in electron\u2013proton and muon\u2013proton interactions. Phys. Rev. A 88, 062514 (2013).","journal-title":"Phys. Rev. A"},{"key":"3183_CR48","doi-asserted-by":"publisher","first-page":"114638","DOI":"10.1016\/j.nuclphysb.2019.114638","volume":"944","author":"YS Liu","year":"2019","unstructured":"Liu, Y. S., Clo\u00ebt, I. C. & Miller, G. A. Eta decay and muonic puzzles. Nucl. Phys. B 944, 114638 (2019).","journal-title":"Nucl. Phys. B"},{"key":"3183_CR49","doi-asserted-by":"publisher","first-page":"023002","DOI":"10.1088\/0954-3899\/43\/2\/023002","volume":"43","author":"LE Marcucci","year":"2016","unstructured":"Marcucci, L. E. et al. Electromagnetic structure of few-nucleon ground states. J. Phys. G 43, 023002 (2016).","journal-title":"J. Phys. G"},{"key":"3183_CR50","doi-asserted-by":"publisher","first-page":"051301","DOI":"10.1103\/PhysRevC.91.051301","volume":"91","author":"A Ekstr\u00f6m","year":"2015","unstructured":"Ekstr\u00f6m, A. et al. Accurate nuclear radii and binding energies from a chiral interaction. Phys. Rev. C 91, 051301 (2015).","journal-title":"Phys. Rev. C"},{"key":"3183_CR51","doi-asserted-by":"publisher","first-page":"102502","DOI":"10.1103\/PhysRevLett.103.102502","volume":"103","author":"D Gazit","year":"2009","unstructured":"Gazit, D., Quaglioni, S. & Navr\u00e1til, P. Three-nucleon low-energy constants from the consistency of interactions and currents in chiral effective field theory. Phys. Rev. Lett. 103, 102502 (2009).","journal-title":"Phys. Rev. Lett."},{"key":"3183_CR52","doi-asserted-by":"publisher","first-page":"432","DOI":"10.1016\/j.physletb.2019.06.023","volume":"795","author":"SG Karshenboim","year":"2019","unstructured":"Karshenboim, S. G. et al. The Lamb shift of the 1s state in hydrogen: two-loop and three-loop contributions. Phys. Lett. B 795, 432\u2013437 (2019).","journal-title":"Phys. Lett. B"},{"key":"3183_CR53","doi-asserted-by":"publisher","first-page":"1800324","DOI":"10.1002\/andp.201800324","volume":"531","author":"VA Yerokhin","year":"2019","unstructured":"Yerokhin, V. A., Pachucki, K. & Patk\u00f3\u0161, V. Theory of the Lamb shift in hydrogen and light hydrogen-like ions. Ann. Phys. 531, 1800324 (2019).","journal-title":"Ann. Phys."},{"key":"3183_CR54","doi-asserted-by":"publisher","first-page":"012123","DOI":"10.1103\/PhysRevA.92.012123","volume":"92","author":"UD Jentschura","year":"2015","unstructured":"Jentschura, U. D. Muonic bound systems, virtual particles, and proton radius. Phys. Rev. A 92, 012123 (2015).","journal-title":"Phys. Rev. A"},{"key":"3183_CR55","doi-asserted-by":"publisher","first-page":"035202","DOI":"10.1103\/PhysRevC.99.035202","volume":"99","author":"GA Miller","year":"2019","unstructured":"Miller, G. A. Defining the proton radius: a unified treatment. Phys. Rev. C 99, 035202 (2019).","journal-title":"Phys. Rev. C"},{"key":"3183_CR56","doi-asserted-by":"publisher","first-page":"13050","DOI":"10.1364\/OE.22.013050","volume":"22","author":"J Vogelsang","year":"2014","unstructured":"Vogelsang, J. et al. Multipass laser cavity for efficient transverse illumination of an elongated volume. Opt. Express 22, 13050\u201313062 (2014).","journal-title":"Opt. Express"},{"key":"3183_CR57","doi-asserted-by":"publisher","first-page":"169","DOI":"10.1016\/j.nima.2004.11.017","volume":"540","author":"L Ludhova","year":"2005","unstructured":"Ludhova, L. et al. Planar LAAPDs: temperature dependence, performance, and application in low-energy X-ray spectroscopy. Nucl. Instrum. Methods Phys. Rev. A 540, 169\u2013179 (2005).","journal-title":"Nucl. Instrum. Methods Phys. Rev. A"},{"key":"3183_CR58","unstructured":"Borie, E. Lamb shift in light muonic atoms \u2013 revisited. Preprint at https:\/\/arxiv.org\/abs\/1103.1772 (2014)."},{"key":"3183_CR59","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1134\/S1063776115010033","volume":"120","author":"A Krutov","year":"2015","unstructured":"Krutov, A. et al. Theory of the Lamb shift in muonic helium ions. J. Exp. Theor. Phys. 120, 73\u201390 (2015).","journal-title":"J. Exp. Theor. Phys."},{"key":"3183_CR60","doi-asserted-by":"publisher","first-page":"032509","DOI":"10.1103\/PhysRevA.85.032509","volume":"85","author":"SG Karshenboim","year":"2012","unstructured":"Karshenboim, S. G., Ivanov, V. G. & Korzinin, E. Y. Relativistic recoil corrections to the electron-vacuum-polarization contribution in light muonic atoms. Phys. Rev. A 85, 032509 (2012).","journal-title":"Phys. Rev. A"},{"key":"3183_CR61","doi-asserted-by":"publisher","first-page":"125019","DOI":"10.1103\/PhysRevD.88.125019","volume":"88","author":"EY Korzinin","year":"2013","unstructured":"Korzinin, E. Y., Ivanov, V. G. & Karshenboim, S. G. \u03b12(Z\u03b1)4m contributions to the Lamb shift and the fine structure in light muonic atoms. Phys. Rev. D 88, 125019 (2013).","journal-title":"Phys. Rev. D"},{"key":"3183_CR62","doi-asserted-by":"publisher","first-page":"357","DOI":"10.1140\/epjd\/e2011-20338-2","volume":"65","author":"UD Jentschura","year":"2011","unstructured":"Jentschura, U. D. & Wundt, B. J. Semi-analytic approach to higher-order corrections in simple muonic bound systems: vacuum polarisation, self-energy and radiative-recoil. Eur. Phys. J. D 65, 357\u2013366 (2011).","journal-title":"Eur. Phys. J. D"},{"key":"3183_CR63","doi-asserted-by":"publisher","first-page":"7","DOI":"10.1140\/epjd\/e2010-10414-6","volume":"61","author":"UD Jentschura","year":"2011","unstructured":"Jentschura, U. D. Proton radius, Darwin\u2013Foldy term and radiative corrections. Eur. Phys. J. D 61, 7\u201314 (2011).","journal-title":"Eur. Phys. J. D"},{"key":"3183_CR64","doi-asserted-by":"publisher","first-page":"151","DOI":"10.1016\/0003-4916(79)90300-2","volume":"122","author":"JL Friar","year":"1979","unstructured":"Friar, J. L. Nuclear finite-size effects in light muonic atoms. Ann. Phys. 122, 151\u2013196 (1979).","journal-title":"Ann. Phys."}],"updated-by":[{"DOI":"10.1038\/s41586-021-03360-2","type":"correction","label":"Correction","source":"publisher","updated":{"date-parts":[[2021,2,27]],"date-time":"2021-02-27T00:00:00Z","timestamp":1614384000000}}],"container-title":["Nature"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.nature.com\/articles\/s41586-021-03183-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s41586-021-03183-1","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s41586-021-03183-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,1,28]],"date-time":"2023-01-28T17:05:29Z","timestamp":1674925529000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.nature.com\/articles\/s41586-021-03183-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1,27]]},"references-count":64,"journal-issue":{"issue":"7843","published-print":{"date-parts":[[2021,1,28]]}},"alternative-id":["3183"],"URL":"https:\/\/doi.org\/10.1038\/s41586-021-03183-1","relation":{"correction":[{"id-type":"doi","id":"10.1038\/s41586-021-03360-2","asserted-by":"object"}]},"ISSN":["0028-0836","1476-4687"],"issn-type":[{"value":"0028-0836","type":"print"},{"value":"1476-4687","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1,27]]},"assertion":[{"value":"3 July 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 November 2020","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 January 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 February 2021","order":4,"name":"change_date","label":"Change Date","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"Correction","order":5,"name":"change_type","label":"Change Type","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"A Correction to this paper has been published:","order":6,"name":"change_details","label":"Change Details","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"https:\/\/doi.org\/10.1038\/s41586-021-03360-2","URL":"https:\/\/doi.org\/10.1038\/s41586-021-03360-2","order":7,"name":"change_details","label":"Change Details","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors declare no competing interests.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}]}}