skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Proton radius from electron scattering data

Abstract

Background: The proton charge radius extracted from recent muonic hydrogen Lamb shift measurements is significantly smaller than that extracted from atomic hydrogen and electron scattering measurements. The discrepancy has become known as the proton radius puzzle. Purpose: In an attempt to understand the discrepancy, we review high-precision electron scattering results from Mainz, Jefferson Lab, Saskatoon and Stanford. Methods: We make use of stepwise regression techniques using the F-test as well as the Akaike information criterion to systematically determine the predictive variables to use for a given set and range of electron scattering data as well as to provide multivariate error estimates. Results: Starting with the precision, low four-momentum transfer (Q2) data from Mainz (1980) and Saskatoon (1974), we find that a stepwise regression of the Maclaurin series using the F-test as well as the Akaike information criterion justify using a linear extrapolation which yields a value for the proton radius that is consistent with the result obtained from muonic hydrogen measurements. Applying the same Maclaurin series and statistical criteria to the 2014 Rosenbluth results on GE from Mainz, we again find that the stepwise regression tends to favor a radius consistent with the muonic hydrogen radius but produces results thatmore » are extremely sensitive to the range of data included in the fit. Making use of the high-Q2 data on GE to select functions which extrapolate to high Q2, we find that a Pad´e (N = M = 1) statistical model works remarkably well, as does a dipole function with a 0.84 fm radius, GE(Q2) = (1 + Q2/0.66 GeV2)-2. Conclusions: Rigorous applications of stepwise regression techniques and multivariate error estimates result in the extraction of a proton charge radius that is consistent with the muonic hydrogen result of 0.84 fm; either from linear extrapolation of the extreme low-Q2 data or by use of the Pad´e approximant for extrapolation using a larger range of data. Thus, based on a purely statistical analysis of electron scattering data, we conclude that the electron scattering result and the muonic hydrogen result are consistent. Lastly, it is the atomic hydrogen results that are the outliers.« less

Authors:
 [1];  [2];  [3];  [1];  [4];  [1]
  1. Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
  2. Kent State Univ., Kent, OH (United States). Dept. of Physics
  3. Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Western Branch High School, Chesapeake, VA (United States)
  4. Univ. of Virginia, Charlottesville, VA (United States). Dept. of Physics
Publication Date:
Research Org.:
Univ. of Virginia, Charlottesville, VA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26)
OSTI Identifier:
1417866
Alternate Identifier(s):
OSTI ID: 1254887
Grant/Contract Number:  
SC0014325; AC05-060R23177
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review C
Additional Journal Information:
Journal Volume: 93; Journal Issue: 5; Journal ID: ISSN 2469-9985
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Protons; Charge Distributions; Scattering

Citation Formats

Higinbotham, Douglas W., Kabir, Al Amin, Lin, Vincent, Meekins, David, Norum, Blaine, and Sawatzky, Brad. Proton radius from electron scattering data. United States: N. p., 2016. Web. doi:10.1103/PhysRevC.93.055207.
Higinbotham, Douglas W., Kabir, Al Amin, Lin, Vincent, Meekins, David, Norum, Blaine, & Sawatzky, Brad. Proton radius from electron scattering data. United States. doi:10.1103/PhysRevC.93.055207.
Higinbotham, Douglas W., Kabir, Al Amin, Lin, Vincent, Meekins, David, Norum, Blaine, and Sawatzky, Brad. Tue . "Proton radius from electron scattering data". United States. doi:10.1103/PhysRevC.93.055207. https://www.osti.gov/servlets/purl/1417866.
@article{osti_1417866,
title = {Proton radius from electron scattering data},
author = {Higinbotham, Douglas W. and Kabir, Al Amin and Lin, Vincent and Meekins, David and Norum, Blaine and Sawatzky, Brad},
abstractNote = {Background: The proton charge radius extracted from recent muonic hydrogen Lamb shift measurements is significantly smaller than that extracted from atomic hydrogen and electron scattering measurements. The discrepancy has become known as the proton radius puzzle. Purpose: In an attempt to understand the discrepancy, we review high-precision electron scattering results from Mainz, Jefferson Lab, Saskatoon and Stanford. Methods: We make use of stepwise regression techniques using the F-test as well as the Akaike information criterion to systematically determine the predictive variables to use for a given set and range of electron scattering data as well as to provide multivariate error estimates. Results: Starting with the precision, low four-momentum transfer (Q2) data from Mainz (1980) and Saskatoon (1974), we find that a stepwise regression of the Maclaurin series using the F-test as well as the Akaike information criterion justify using a linear extrapolation which yields a value for the proton radius that is consistent with the result obtained from muonic hydrogen measurements. Applying the same Maclaurin series and statistical criteria to the 2014 Rosenbluth results on GE from Mainz, we again find that the stepwise regression tends to favor a radius consistent with the muonic hydrogen radius but produces results that are extremely sensitive to the range of data included in the fit. Making use of the high-Q2 data on GE to select functions which extrapolate to high Q2, we find that a Pad´e (N = M = 1) statistical model works remarkably well, as does a dipole function with a 0.84 fm radius, GE(Q2) = (1 + Q2/0.66 GeV2)-2. Conclusions: Rigorous applications of stepwise regression techniques and multivariate error estimates result in the extraction of a proton charge radius that is consistent with the muonic hydrogen result of 0.84 fm; either from linear extrapolation of the extreme low-Q2 data or by use of the Pad´e approximant for extrapolation using a larger range of data. Thus, based on a purely statistical analysis of electron scattering data, we conclude that the electron scattering result and the muonic hydrogen result are consistent. Lastly, it is the atomic hydrogen results that are the outliers.},
doi = {10.1103/PhysRevC.93.055207},
journal = {Physical Review C},
number = 5,
volume = 93,
place = {United States},
year = {2016},
month = {5}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 12 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Energy spectra of X-ray clusters of galaxies
journal, November 1976


Theoretical constraints and systematic effects in the determination of the proton form factors
journal, January 2015


Evaluation of the strength of electron-proton scattering data for determining the proton charge radius
journal, January 2016


Electric and Magnetic Form Factors of the Nucleon
journal, April 1963


Extraction of the proton radius from electron-proton scattering data
journal, July 2015


Muonic Hydrogen and the Proton Radius Puzzle
journal, October 2013


Electric and magnetic form factors of the proton
journal, July 2014


Nuclear charge-density-distribution parameters from elastic electron scattering
journal, May 1987


Charge Densities of the Neutron and Proton
journal, September 2007


Recoil Polarization Measurements of the Proton Electromagnetic Form Factor Ratio to Q 2 = 8.5 GeV 2
journal, June 2010


Proton form factor from 0.15 to 0.79 fm 2
journal, June 1974


High-Precision Determination of the Electric and Magnetic Form Factors of the Proton
journal, December 2010


Review of Particle Physics
journal, August 2014


Measurements of the electric and magnetic form factors of the proton from Q 2 =1.75 to 8.83 (GeV/ c ) 2
journal, November 1994


Proton Structure from the Measurement of 2S-2P Transition Frequencies of Muonic Hydrogen
journal, January 2013


The size of the proton
journal, July 2010

  • Pohl, Randolf; Antognini, Aldo; Nez, François
  • Nature, Vol. 466, Issue 7303
  • DOI: 10.1038/nature09250

The proton radius puzzle
journal, May 2015


Absolute electron-proton cross sections at low momentum transfer measured with a high pressure gas target system
journal, January 1980


The charge distribution of 12C
journal, April 1980


Polynomial fits and the proton radius puzzle
journal, October 2014


Global analysis of proton elastic form factor data with two-photon exchange corrections
journal, September 2007


Minuit - a system for function minimization and analysis of the parameter errors and correlations
journal, December 1975


Erratum: Proton form factor from 0.15 to 0.79 fm 2
journal, November 1974


Measurements of electron-proton elastic cross sections for 0.4 < Q 2 < 5.5 ( GeV c ) 2
journal, July 2004


Implications of the discrepancy between proton form factor measurements
journal, February 2004


CODATA recommended values of the fundamental physical constants: 2010
journal, November 2012