Proton charge radius extraction from electron scattering data using dispersively improved chiral effective field theory

Abstract

We extract the proton charge radius from the elastic form factor (FF) data using a novel theoretical framework combining chiral effective field theory and dispersion analysis. Complex analyticity in the momentum transfer correlates the behavior of the spacelike FF at finite Q 2 with the derivative at Q 2 = 0. The FF calculated in the predictive theory contains the radius as a free parameter. We determine its value by comparing the predictions with a descriptive global fit of the spacelike FF data, taking into account the theoretical and experimental uncertainties. Our method allows us to use the finite-Q 2 FF data for constraining the radius (up to Q 2 ∼ 0.5 GeV 2 and larger) and avoids the difficulties arising in methods relying on the Q 2 → 0 extrapolation. We obtain a radius of 0.844(7) fm, consistent with the high-precision muonic hydrogen results.

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

“…The quality of the predicted higher moments from Ref. [21] was previously tested on larger e − p scattering data sets [27]. Here we show that the PRad data set lends strong support to these theoretical results.…”

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

“…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.…”

Precise determination of the proton magnetic radius from electron scattering data

“…Apparent discrepancies between the different extraction methods (the "proton radius puzzle") have engendered intense experimental and theoretical efforts, including dedicated new elastic scattering experiments at low Q 2 with electron and muon beams [11,12]. Most recent experiments and reanalyses have converged around r p E = 0.84 fm [11,[13][14][15][16][17][18][19][20][21][22][23][24], while some have obtained larger values [25][26][27][28]; the CODATA Task Group and the Particle Data Group have now adopted 0.84 fm as the recommended value [29,30]. The proton magnetic radius can only be extracted from elastic FF measurements (a method using atomic measurements was proposed in Ref.…”

“…Here we report an extraction of the proton magnetic radius from electron scattering data using a novel theoretical framework based on dispersion analysis and chiral effective field theory (DIχ EFT) [20,[36][37][38]. It implements analyticity and the dynamics governing the shape of the low-Q 2 FFs and allows us to use data up to Q 2 ≈ 0.5 GeV 2 for constraining the radii, increasing the sensitivity to the magnetic FF.…”