Understanding the systematic differences in extractions of the proton electric form factors at low-$Q^2$

Abstract

Systematic differences exist between values of the proton's electric form factors in the low-Q 2 region extracted by different experimental and theoretical groups, though they are all making use of basically the same electron-proton scattering data. To try understand the source of these differences, we make use of the analytically well-behaved rational (N=1, M=1) function, a predictive function that can be reasonably used for extrapolations at Q 2 → 0. First, we test how well this deceptively simple two-parameter function describes the extremely complex and state-of-the-art dispersively improved chiral effective field theory calculations. Second, we carry out a complete re-analysis of the 34 sets of eletron-proton elastic scattering cross-section data of the Mainz A1 Collaboration with its unconstrained 31 normalization parameters up to Q 2 = 0.5 (GeV/c) 2 . We find that subtle shifts in the normalization parameters can result in relatively large changes in the extracted physical qualities. As a final check of the results of this extraction, we compare it to the PRad data that was not included in the regression and find that with the well-behaved analytic function the extracted results, both charge form factor and charge radius, of the two sets of data become consistent.

Pion and nucleon relativistic electromagnetic four-current distributions

“…Applying the general definition (15) for the LF four-current distributions to the case of a spin- 1 2 target, we obtain…”

“…The electromagnetic structure of hadrons is encoded in Lorentz-invariant functions known as form factors (FFs). They have been measured with extreme precision in various scattering experiments over the past decades [3][4][5][6][7][8][9][10][11][12][13][14][15]. On the theory side, lattice QCD calculations of these FFs have witnessed tremendous progresses in the last few years [16][17][18][19][20][21][22][23][24][25][26][27].…”