Robust extraction of the proton charge radius from electron-proton scattering data

Abstract

Background: Extracting the proton charge radius from electron scattering data, requires determining the slope of the charge form factor at Q 2 of zero. As experimental data cannot reach that limit, numerous methods for making the extraction have been proposed.Purpose: In this study, we seek to find functional forms that will allow a robust extraction of the proton radius from a wide variety of functional forms. The primary motivation of this study is to have confidence in the extraction of upcoming low Q 2 experimental data. Method:We create a general framework for studying various form-factor functions along with various fitting functions. The input form factors are used to generate pseudo-data with fluctuations mimicking the binning and random uncertainty of a set of real data. All combinations of input functions and fit functions can then be tested repeatedly against regenerated pseudo-data. Since the input radius is known, this allows us to find fitting functions that are robust for proton radius extractions in an objective fashion.Results: For the range and uncertainty of the PRad data, we find that a two-parameter rational function, a two-parameter continued fraction and the second order polynomial expansion of z can extract the input radius regardless of the input charge form factor function that is used. Conclusions:We have created a framework to determine which functional forms allow for a robust extraction of the radius from pseudo-data generated from a wide variety of trial functions. By taking into account both bias and variance, the optimal functions for extracting the proton radius can be determined.

Nucleon electromagnetic form factors in the continuum limit from ( 2+1+1 )-flavor lattice QCD

“…The results of the dipole fits to the proton data shown in Fig. 36 give r p E ∼ 0.833 and r p M ∼ 0.795, which are roughly consistent with the careful analysis of electronexperiment results [43] given in Eqs. (13) and (14) and the Kelly fits shown in the bottom row of Fig.…”

“…Electromagnetic form factors of nucleons are extracted from differential cross-sections measured in the scattering of electrons off nuclei. The process of going from measurements of the differential cross-sections to nucleon form factors is nontrivial and involves modeling [1,31,43]. As already stated, we have two reasons to analyze the experimental data: to compare them against the lattice data over the range 0 < Q 2 0.8 GeV 2 , and to test the efficacy of the dipole and z-expansion fit ansätze.…”

“…In Fig. 36, we show the data for G p E (Q 2 ) and G p M (Q 2 ) compiled by Douglas Higinbotham [43,61,62] from the cross sections provided in the Lee-Arlington-Hill supplemental material [31], who rebinned the original data obtained by the A1 Collaboration using the MAMI beam at Mainz [3,63]. The neutron data, G n E (Q 2 ), are collected from Refs.…”

Properties of the Sachs electric form factor of the proton on the basis of recent e − p scattering experiments and hydrogen spectroscopy

“…The so-called proton radius puzzle appears to be resolved. The puzzle emerged in 2010 when a muonic hydrogen measurement of the n = 2 Lamb shift [1] found that the very accurately measured proton charge radius R E = 0.8409(4) fm (or using a more conservative, model-independent analysis R E = 0.8413 (15) fm) disagreed with previous measurements of regular atomic hydrogen intervals [2], quoted in 2014 as R E = 0.8751(61) fm, as well as the state-of-the-art Mainz e − p scattering experiment (MAMI) [3,4] with a result of which links atomic units to SI [7,12], and settling on it and on the proton charge radius opens the possibility for further tests of quantum electrodynamics in atomic hydrogen. In its most recent update CODATA has adopted the small (muonic) radius value of 0.8414 (19) fm [13].…”

Lower bound on the proton charge radius from electron scattering data

“…The issues of fitting and extrapolation of the form-factor data have lately been under intense discussion, see, e.g., Refs. [14,[25][26][27]. Similar extrapolation problems should exist in the extractions based on lattice QCD, since the lowest momentum-transfer therein is severely limited by the finite volume.…”