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${{\mathit p}}$ CHARGE RADIUS INSPIRE search

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.

S016CR

VALUE (fm)

DOCUMENT ID

TECN

COMMENT

$\bf{ 0.8409 \pm0.0004}$

OUR AVERAGE

$0.833$ $\pm0.010$

LASR

2S-2P transition in ${}^{}\mathrm {H}$

$0.831$ $\pm0.007$ $\pm0.012$

SPEC

${{\mathit e}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit e}}{{\mathit p}}$ form factor

$0.84087$ $\pm0.00026$ $\pm0.00029$

LASR

${{\mathit \mu}}{{\mathit p}}$-atom Lamb shift

• • • We do not use the following data for averages, fits, limits, etc. • • •

$0.847$ $\pm0.008$

FIT

use existing ${{\mathit e}}{{\mathit p}}$ data

$0.878$ $\pm0.011$ $\pm0.031$

ISR ${{\mathit e}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit e}}{{\mathit p}}$ reanalysis

$0.877$ $\pm0.013$

LASR

1S-3S transition in ${}^{}\mathrm {H}$

$0.8335$ $\pm0.0095$

LASR

2S-4P transition in ${}^{}\mathrm {H}$

$0.8751$ $\pm0.0061$

RVUE

2014 CODATA value

$0.895$ $\pm0.014$ $\pm0.014$

SPEC

Just 2010 Mainz data

$0.916$ $\pm0.024$

SPEC

World data, no Mainz

$0.8775$ $\pm0.0051$

RVUE

2010 CODATA, ${{\mathit e}}{{\mathit p}}$ data

$0.875$ $\pm0.008$ $\pm0.006$

SPEC

Recoil polarimetry

$0.879$ $\pm0.005$ $\pm0.006$

SPEC

${{\mathit e}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit e}}{{\mathit p}}$ form factor

$0.912$ $\pm0.009$ $\pm0.007$

reanalyzes old ${{\mathit e}}{{\mathit p}}$ data

$0.871$ $\pm0.009$ $\pm0.003$

z-expansion reanalysis

$0.84184$ $\pm0.00036$ $\pm0.00056$

LASR

See ANTOGNINI 2013

$0.8768$ $\pm0.0069$

RVUE

2006 CODATA value

$0.844$ ${}^{+0.008}_{-0.004}$

Dispersion analysis

$0.897$ $\pm0.018$

SICK 2003 + 2${{\mathit \gamma}}$ correction

$0.8750$ $\pm0.0068$

RVUE

2002 CODATA value

$0.895$ $\pm0.010$ $\pm0.013$

${{\mathit e}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit e}}{{\mathit p}}$ 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:

PRL 127 092001

Fresh Extraction of the Proton Charge Radius from Electron Scattering

EPJ A57 107

The proton charge radius extracted from the initial-state radiation experiment at MAMI

SCI 365 1007

A measurement of the atomic hydrogen Lamb shift and the proton charge radius

NAT 575 147

A small proton charge radius from an�electron?proton scattering experiment

PRL 120 183001

New Measurement of the $1S-3S$ Transition Frequency of Hydrogen: Contribution to the Proton Charge Radius Puzzle

SCI 358 79

The Rydberg Constant and Proton Size from Atomic Hydrogen

RMP 88 035009

CODATA Recommended Values of the Fundamental Physical Constants: 2014

PR D92 013013

Extraction of the Proton Radius from Electron-Proton Scattering Data

SCI 339 417

Proton Structure from the Measurement of 2$\mathit S−2\mathit P$ Transition Frequencies of Muonic Hydrogen

RMP 84 1527

CODATA Recommended Values of the Fundamental Physical Constants: 2010

PL B705 59

High-Precision Measurement of the Proton Elastic Form Factor Ratio $\mathit \mu _{p}G_{E}/G_{M}$ at low $\mathit Q{}^{2}$

PRL 105 242001

High-Precision Determination of the Electric and Magnetic Form Factors of the Proton

PR C90 015206

Electric and Magnetic Form Factors of the Proton

NP A843 59

Proton Charge and Magnetic rms Radii from the Elastic ${{\mathit e}}{{\mathit p}}$ Scattering data

PR D82 113005

Model Independent Extraction of the Proton Charge Radius from Electron Scattering

NAT 466 213

The Size of the Proton

RMP 80 633

CODATA Recomended Values of the Fundamental Physical Constants: 2006

PR C75 035202

Dispersion Analysis of the Nucleon Form Factors Including Meson Continua

PR C72 057601

Proton Radii and Two-Photon Exchange

RMP 77 1

NIST Constants

PL B576 62

On the rms-Radius of the Proton