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Title: Proton radius from electron scattering data

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 (Q 2) 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 resultsmore » that are extremely sensitive to the range of data included in the fit. Making use of the high-Q 2 data on G E to select functions which extrapolate to high Q 2, 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, G E(Q 2) = (1 + Q 2/0.66 GeV 2) -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-Q 2 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
 [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:
Grant/Contract Number:
SC0014325; AC05-060R23177
Accepted Manuscript
Journal Name:
Physical Review C
Additional Journal Information:
Journal Volume: 93; Journal Issue: 5; Journal ID: ISSN 2469-9985
American Physical Society (APS)
Research Org:
Univ. of Virginia, Charlottesville, VA (United States)
Sponsoring Org:
USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26)
Country of Publication:
United States
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Protons; Charge Distributions; Scattering
OSTI Identifier:
Alternate Identifier(s):
OSTI ID: 1254887