New precise results of a measurement of the elastic electron-proton scattering cross section performed at the Mainz Microtron MAMI are presented. About 1400 cross sections were measured with negative four-momentum transfers squared up to ${Q}^{2}=1\text{ }\text{ }(\mathrm{GeV}/c{)}^{2}$ with statistical errors below 0.2%. The electric and magnetic form factors of the proton were extracted by fits of a large variety of form factor models directly to the cross sections. The form factors show some features at the scale of the pion cloud. The charge and magnetic radii are determined to be $⟨{r}_{E}^{2}{⟩}^{1/2}=0.879(5{)}_{\mathrm{stat}}(4{)}_{\mathrm{syst}}(2{)}_{\mathrm{model}}(4{)}_{\mathrm{group}}\text{ }\text{ }\mathrm{fm}$ and $⟨{r}_{M}^{2}{⟩}^{1/2}=0.777(13{)}_{\mathrm{stat}}(9{)}_{\mathrm{syst}}(5{)}_{\mathrm{model}}(2{)}_{\mathrm{group}}\text{ }\text{ }\mathrm{fm}$.

High-precision determination of the electric and magnetic form factors of the proton

The extremely precise extraction of the proton radius obtained by Pohl et al. from the measured energy difference between the 2P and 2S states of muonic hydrogen disagrees significantly with that extracted from electronic hydrogen or elastic electron–proton scattering. This discrepancy is the proton radius puzzle. In this review, we explain the origins of the puzzle and the reasons for believing it to be very significant. We identify various possible solutions of the puzzle and discuss future research needed to resolve the puzzle.

https://www.annualreviews.org/doi/pdf/10.1146/annurev-nucl-102212-170627

Muonic Hydrogen and the Proton Radius Puzzle

This paper describes a precise measurement of electron scattering off the proton at momentum transfers of 0.003 Q 2 1 GeV 2 . The average point-to-point error of the cross sections in this experiment is ∼0.37%. These data are used for a coherent new analysis together with all world data of unpolarized and polarized electron scattering from the very smallest to the highest momentum transfers so far measured. The extracted electric and magnetic form factors provide new insight into their exact shape, deviating from the classical dipole form, and of structure on top of this gross shape. The data reaching very low Q 2 values are used for a new determination of the electric and magnetic radii. An empirical determination of the two-photon-exchange correction is presented. The implications of this correction on the radii and the question of a directly visible signal of the pion cloud are addressed.

Electric and magnetic form factors of the proton

Precise measurements of the proton electromagnetic form factor ratio R = mu(p)G(E)(p)/G(M)(p) using the polarization transfer method at Jefferson Lab have revolutionized the understanding of nucleon structure by revealing the strong decrease of R with momentum transfer Q(2) for Q(2) greater than or similar to 1 GeV2, in strong disagreement with previous extractions of R from cross-section measurements. In particular, the polarization transfer results have exposed the limits of applicability of the one-photon-exchange approximation and highlighted the role of quark orbital angular momentum in the nucleon structure. The GEp-II experiment in Jefferson Lab's Hall A measured R at four Q(2) values in the range 3.5 GeV2 <= Q(2) <= 5.6 GeV2. A possible discrepancy between the originally published GEp-II results and more recent measurements at higher Q(2) motivated a new analysis of the GEp-II data. This article presents the final results of the GEp-II experiment, including details of the new analysis, an expanded description of the apparatus, and an overview of theoretical progress since the original publication. The key result of the final analysis is a systematic increase in the results for R, improving the consistency of the polarization transfer data in the high-Q(2) region. This increase is the result of an improved selection of elastic events which largely removes the systematic effect of the inelastic contamination, underestimated by the original analysis. (Less)

/pdf/final-analysis-of-proton-form-factor-ratio-data-at-q-2-4-0-4-4zu7a6gjxb.pdf

Final analysis of proton form factor ratio data at Q(2)=4.0, 4.8, and 5.6 GeV2

High-Precision Measurement of the Proton Elastic Form Factor Ratio $\mu_pG_E/G_M$ at low $Q^2$

High-precision measurements of the proton elastic form-factor ratio, {mu}{sub p}G{sub E}{sup p}/G{sub M}{sup p}, have been made at four-momentum transfer, Q{sup 2}, values between 0.2 and 0.5 GeV{sup 2}. The new data, while consistent with previous results, clearly show a ratio less than unity and significant differences from the central values of several recent phenomenological fits. By combining the new form-factor ratio data with an existing cross-section measurement, one finds that in this Q{sup 2} range the deviation from unity is primarily due to G{sub E}{sup p} being smaller than expected.

The Proton Elastic Form Factor Ratio mu(p) G**p(E)/G**p(M) at Low Momentum Transfer

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The Proton Elastic Form Factor Ratio mu(p) Gp(E)/Gp(M) at Low Momentum Transfer