This is the rms electric charge radius, $\sqrt {\langle r{}^{2}_{E}\rangle }$.

There are three kinds of measurements of the proton radius: via transitions in atomic hydrogen; via electron scattering off hydrogen; and via muonic hydrogen Lamb shift. Most measurements of the radius of the proton involve electron-proton interactions, the most recent of which is the electron scattering measurement ${{\mathit r}_{{p}}}$ = 0.831(14) fm (XIONG 2019 ), and the atomic-hydrogen value, ${{\mathit r}_{{p}}}$ = 0.833(10) fm (BEZGINOV 2019 ). These agree well with another recent atomic-hydrogen value ${{\mathit r}_{{p}}}$ = 0.8335(95) fm (BEYER 2017 ), and with the best measurement using muonic hydrogen ${{\mathit r}_{{p}}}$ = 0.84087(39) fm (ANTOGNINI 2013 ), that is far more precise.

The MOHR 2016 value (2014 CODATA), obtained from the electronic results available at the time, was 0.8751(61) fm. This differs by 5.6 standard deviations from the muonic hydrogen value, leading to the so-called proton charge radius puzzle. See our 2018 edition (Physical Review D98 030001 (2018)) for a further discussion of interpretations of this puzzle. However, reflecting the new electronic measurements, the 2018 CODATA, TIESINGA 2021 , recommended value is 0.8414(19) fm, and the puzzle appears to be resolved.

See our 2014 edition (Chinese Physics C38 070001 (2014)) for values published before 2003.

VALUE (fm) DOCUMENT ID TECN  COMMENT $\bf{ 0.8409 \pm0.0004}$ OUR AVERAGE $0.833$ $\pm0.010$ 1 BEZGINOV 2019 LASR 2S-2P transition in ${}^{}\mathrm {H}$ $0.831$ $\pm0.007$ $\pm0.012$ 2 XIONG 2019 SPEC ${{\mathit e}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit e}}{{\mathit p}}$ form factor $0.84087$ $\pm0.00026$ $\pm0.00029$ ANTOGNINI 2013 LASR ${{\mathit \mu}}{{\mathit p}}$ -atom Lamb shift • • We do not use the following data for averages, fits, limits, etc. • • $0.847$ $\pm0.008$ 3 CUI 2021 FIT use existing ${{\mathit e}}{{\mathit p}}$ data $0.878$ $\pm0.011$ $\pm0.031$ 4 MIHOVILOVIC 2021 ISR ${{\mathit e}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit e}}{{\mathit p}}$ reanalysis $0.877$ $\pm0.013$ 5 FLEURBAEY 2018 LASR 1S-3S transition in ${}^{}\mathrm {H}$ $0.8335$ $\pm0.0095$ 6 BEYER 2017 LASR 2S-4P transition in ${}^{}\mathrm {H}$ $0.8751$ $\pm0.0061$ MOHR 2016 RVUE 2014 CODATA value $0.895$ $\pm0.014$ $\pm0.014$ 7 LEE 2015 SPEC Just 2010 Mainz data $0.916$ $\pm0.024$ LEE 2015 SPEC World data, no Mainz $0.8775$ $\pm0.0051$ MOHR 2012 RVUE 2010 CODATA, ${{\mathit e}}{{\mathit p}}$ data $0.875$ $\pm0.008$ $\pm0.006$ ZHAN 2011 SPEC Recoil polarimetry $0.879$ $\pm0.005$ $\pm0.006$ BERNAUER 2010 SPEC ${{\mathit e}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit e}}{{\mathit p}}$ form factor $0.912$ $\pm0.009$ $\pm0.007$ BORISYUK 2010 reanalyzes old ${{\mathit e}}{{\mathit p}}$ data $0.871$ $\pm0.009$ $\pm0.003$ HILL 2010 z-expansion reanalysis $0.84184$ $\pm0.00036$ $\pm0.00056$ POHL 2010 LASR See ANTOGNINI 2013 $0.8768$ $\pm0.0069$ MOHR 2008 RVUE 2006 CODATA value $0.844$ ${}^{+0.008}_{-0.004}$ BELUSHKIN 2007 Dispersion analysis $0.897$ $\pm0.018$ BLUNDEN 2005 SICK 2003 + 2${{\mathit \gamma}}$ correction $0.8750$ $\pm0.0068$ MOHR 2005 RVUE 2002 CODATA value $0.895$ $\pm0.010$ $\pm0.013$ SICK 2003 ${{\mathit e}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit e}}{{\mathit p}}$ reanalysis 1  BEZGINOV 2019 measures the 2${{\mathit S}_{{1/2}}}$ to 2${{\mathit P}_{{1/2}}}$ transition frequency in atomic hydrogen using the frequency-offset separated oscillatory field (FOSOF) technique. The result agrees well with the muonic hydrogen Lamb shift value. 2  The XIONG 2019 value from ${{\mathit e}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit e}}{{\mathit p}}$ scattering and supports the muonic hydrogen Lamb shift value. 3  CUI 2021 employ a new mathematical procedure (statistical SPM, Schlessinger point method) based on form-unbiased interpolations of existing ${{\mathit e}}{{\mathit p}}$ scattering data. 4  MIHOVILOVIC 2021 reports a value of $0.878$ $\pm0.011$ $\pm0.031$ $\pm0.002$ fm where the last uncertainty comes from the dependence on the model form factor function. 5  FLEURBAEY 2018 measures the 1S-3S transition frequency in hydrogen and in combination with the 1S-2S transition frequency deduces the proton radius and the Rydberg constant. 6  The BEYER 2017 result is 3.3 combined standard deviations below the MOHR 2016 (2014 CODATA) value. The experiment measures the 2S-4P transition in hydrogen and gets the proton radius and the Rydberg constant. 7  Authors also provide values for combinations of all available data.

References:

CUI 2021 PRL 127 092001 Fresh Extraction of the Proton Charge Radius from Electron Scattering MIHOVILOVIC 2021 EPJ A57 107 The proton charge radius extracted from the initial-state radiation experiment at MAMI BEZGINOV 2019 SCI 365 1007 A measurement of the atomic hydrogen Lamb shift and the proton charge radius XIONG 2019 NAT 575 147 A small proton charge radius from an electron?proton scattering experiment FLEURBAEY 2018 PRL 120 183001 New Measurement of the $1S-3S$ Transition Frequency of Hydrogen: Contribution to the Proton Charge Radius Puzzle BEYER 2017 SCI 358 79 The Rydberg Constant and Proton Size from Atomic Hydrogen MOHR 2016 RMP 88 035009 CODATA Recommended Values of the Fundamental Physical Constants: 2014 LEE 2015 PR D92 013013 Extraction of the Proton Radius from Electron-Proton Scattering Data ANTOGNINI 2013 SCI 339 417 Proton Structure from the Measurement of 2$\mathit S−2\mathit P$ Transition Frequencies of Muonic Hydrogen MOHR 2012 RMP 84 1527 CODATA Recommended Values of the Fundamental Physical Constants: 2010 ZHAN 2011 PL B705 59 High-Precision Measurement of the Proton Elastic Form Factor Ratio $\mathit \mu _{p}G_{E}/G_{M}$ at low $\mathit Q{}^{2}$ BERNAUER 2010 PRL 105 242001 High-Precision Determination of the Electric and Magnetic Form Factors of the Proton Also PR C90 015206 Electric and Magnetic Form Factors of the Proton BORISYUK 2010 NP A843 59 Proton Charge and Magnetic rms Radii from the Elastic ${{\mathit e}}{{\mathit p}}$ Scattering data HILL 2010 PR D82 113005 Model Independent Extraction of the Proton Charge Radius from Electron Scattering POHL 2010 NAT 466 213 The Size of the Proton MOHR 2008 RMP 80 633 CODATA Recomended Values of the Fundamental Physical Constants: 2006 BELUSHKIN 2007 PR C75 035202 Dispersion Analysis of the Nucleon Form Factors Including Meson Continua BLUNDEN 2005 PR C72 057601 Proton Radii and Two-Photon Exchange MOHR 2005 RMP 77 1 NIST Constants SICK 2003 PL B576 62 On the rms-Radius of the Proton