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