# ${{\boldsymbol p}}$ CHARGE RADIUS INSPIRE search

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

There are in fact three kinds of measurements of the proton radius: with atomic hydrogen, with electron scattering off of hydrogen, and with muonic hydrogen. Most measurements of the radius of the proton involve electron-proton interactions, and most of those values, the most precise of which is ${{\mathit r}_{{p}}}$ = 0.879(8) fm (BERNAUER 2010 ), agree with one another. The MOHR 2016 value (2014 CODATA), obtained from the electronic results available at the time, is 0.8751(61) fm.

Compared to this MOHR 2016 value, however, the best measurement using muonic hydrogen got ${{\mathit r}_{{p}}}$ = 0.84087(39) fm (ANTOGNINI 2013 ), which is 16 times more precise but differs by 5.6 standard deviations.

The earlier face-off seemed to be between the two electronic methods and muonic hydrogen. But a purely statistical reanalysis of electron-scattering data by HIGINBOTHAM 2016 found consistency with muonic hydrogen---so that (the paper claims) it "is the atomic hydrogen results that are the outliers." But still more recently there is a new atomic-hydrogen value, ${{\mathit r}_{{p}}}$ = 0.8335(95) fm (BEYER 2017 ), that agrees with the muonic hydrogen value!

Since POHL 2010 (the first ${{\mathit \mu}}{{\mathit p}}$ result), there has been a lot of discussion about the disagreement, especially concerning the modeling of muonic hydrogen. Here is an incomplete list of papers: DERUJULA 2010 , CLOET 2011 , DISTLER 2011 , DERUJULA 2011 , ARRINGTON 2011 , BERNAUER 2011 , HILL 2011 , LORENZ 2014 , KARSHENBOIM 2014A, PESET 2015 , SICK 2017 , and HORBATSCH 2017 .

Until the differences between the three methods are resolved, it does not make sense to average the values together. For the present, we give both the 2014 CODATA value and the best ${{\mathit \mu}}{{\mathit p}}$ value. It is up to workers in the field to solve this puzzle.

See our 2014 edition (Chinese Physics C38 070001 (2014)) for values published before 2003.
VALUE (fm) DOCUMENT ID TECN  COMMENT
$\bf{0.8751 \pm0.0061}$
 2016
RVUE 2014 CODATA value
$\bf{0.84087 \pm0.00026 \pm0.00029}$
 2013
LASR ${{\mathit \mu}}{{\mathit p}}$ -atom Lamb shift
• • • We do not use the following data for averages, fits, limits, etc. • • •
$0.877$ $\pm0.013$ 1
 2018
LASR 1S-3S transition in ${}^{}\mathrm {H}$
$0.8335$ $\pm0.0095$ 2
 2017
LASR 2S-4P transition in ${}^{}\mathrm {H}$
$0.895$ $\pm0.014$ $\pm0.014$ 3
 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
$0.8768$ $\pm0.0069$
 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  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.
2  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.
3  Authors also provide values for combinations of all available data.
References:
 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
 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