#### ${{\mathit p}}$ CHARGE RADIUS

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 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
 2019
LASR 2S-2P transition in ${}^{}\mathrm {H}$
$0.831$ $\pm0.007$ $\pm0.012$ 2
 2019
SPEC ${{\mathit e}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit e}}{{\mathit p}}$ form factor
$0.84087$ $\pm0.00026$ $\pm0.00029$
 2013
LASR ${{\mathit \mu}}{{\mathit p}}$ -atom Lamb shift
• • We do not use the following data for averages, fits, limits, etc. • •
$0.877$ $\pm0.013$ 3
 2018
LASR 1S-3S transition in ${}^{}\mathrm {H}$
$0.8335$ $\pm0.0095$ 4
 2017
LASR 2S-4P transition in ${}^{}\mathrm {H}$
$0.8751$ $\pm0.0061$
 2016
RVUE 2014 CODATA value
$0.895$ $\pm0.014$ $\pm0.014$ 5
 2015
SPEC Just 2010 Mainz data
$0.916$ $\pm0.024$
 2015
SPEC World data, no Mainz
$0.8775$ $\pm0.0051$
 2012
RVUE 2010 CODATA, ${{\mathit e}}{{\mathit p}}$ data
$0.875$ $\pm0.008$ $\pm0.006$
 2011
SPEC Recoil polarimetry
$0.879$ $\pm0.005$ $\pm0.006$
 2010
SPEC ${{\mathit e}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit e}}{{\mathit p}}$ form factor
$0.912$ $\pm0.009$ $\pm0.007$
 2010
reanalyzes old ${{\mathit e}}{{\mathit p}}$ data
$0.871$ $\pm0.009$ $\pm0.003$
 2010
z-expansion reanalysis
$0.84184$ $\pm0.00036$ $\pm0.00056$
 2010
LASR See ANTOGNINI 2013
$0.8768$ $\pm0.0069$
 2008
RVUE 2006 CODATA value
$0.844$ ${}^{+0.008}_{-0.004}$
 2007
Dispersion analysis
$0.897$ $\pm0.018$
 2005
SICK 2003 + 2${{\mathit \gamma}}$ correction
$0.8750$ $\pm0.0068$
 2005
RVUE 2002 CODATA value
$0.895$ $\pm0.010$ $\pm0.013$
 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 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.
 4 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.
 5 Authors also provide values for combinations of all available data.
References:
 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