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

Abstract: 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 (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=0.879(5)(stat.)(4)(syst.)(2)(model)(4)(group) fm and r_M=0.777(13)(stat.)(9)(syst.)(5)(model)(2)(group) fm.

• The paper reports a high-precision determination of the proton’s electric and magnetic form factors using over 1400 elastic scattering measurements at MAMI.
• It employs diverse experimental techniques and model fits, achieving statistical errors below 0.2% and extracting radii of 0.879 fm (electric) and 0.777 fm (magnetic).
• The findings reconcile discrepancies between previous experiments and prompt refinement of theoretical models, including multi-photon and pion cloud effects.

Analysis of the Proton's Electric and Magnetic Form Factors

The paper entitled "High-precision determination of the electric and magnetic form factors of the proton" delivers a comprehensive examination of the proton's electromagnetic properties, as investigated through elastic electron-proton scattering. The experimental research, conducted at the Mainz Microtron MAMI, harnesses precision measurement techniques to extract the electric $G_E$ and magnetic $G_M$ form factors of the proton. This study capitalizes on over 1400 cross-section measurements achieved with statistical errors below 0.2%, and these measurements span up to a four-momentum transfer squared value of $Q^2=1\,(\mathrm{GeV}/c)^2$.

Methodology and Results

Utilizing an electron beam of energies between 180 and 855 MeV, the experiment employed three high-resolution spectrometers from the A1 Collaboration. Critical to the endeavor was the meticulous control of measurement redundancy, ensuring comprehensive validation of data across several areas of the spectrometer with variations in beam currents from below 1 nA to over 10 µA. This multifaceted approach enabled accurately determining luminosities and, consequently, the magnitudes of the cross sections.

The extraction of the form factors was executed by fitting a variety of theoretical models directly to the measured cross sections. The models assessed included both single-dipole and sum-of-two-dipoles approaches, as well as polynomial and spline-based models. Through this robust methodology, the electric and magnetic radii of the proton were determined to be $$\left\langle r_{E}^2\right\rangle^\frac{1}{2} = 0.879 \, \mathrm{fm}$$ and $$\left\langle r_{M}^2\right\rangle^\frac{1}{2} = 0.777 \, \mathrm{fm}$$, respectively. Notably, these values reflect consistency with existing atomic data, yet they diverge from recent Lamb shift measurements in muonic hydrogen, presenting an intriguing discrepancy that remains to be elucidated.

Implications and Theoretical Considerations

The findings presented hold significant consequence for the ongoing pursuit of characterizing nucleon structure, particularly regarding the debated topic of the pion cloud's influence on the proton's form factors. The results indicate a structure at low $Q^2$ and a deviation of $G_M$ from previous experiments, potentially reconciling differences observed in polarized and unpolarized electron experiments. This suggests the necessity of revisiting theoretical models to accommodate such intricacies.

Additionally, the results challenge us to explore further corrections to the electromagnetic processes that contribute to elastic scattering, such as multi-photon exchanges. While Coulomb corrections have been duly applied, enhancements in theoretical calculations may allow more precise determinations of radii and form factors, refining future predictions and experimental validations.

Future Directions

In light of these determinations, future avenues of research could focus on refining theoretical descriptions that integrate both QCD paradigms and effective models for nucleon interactions, particularly concerning the role of the pion cloud. Furthermore, new experimentation leveraging advanced accelerators might provide deeper insights into the complexities of proton structure, potentially aligning discrepancies observed in various experimental approaches.

In conclusion, the precision measurements carried out and detailed in this paper extend our understanding of the proton's internal dynamics, emphasizing the necessity of high-accuracy data for theoretical advancement. Such detailed investigations are vital in forming a more comprehensive picture of nucleon behavior under quantum chromodynamics frameworks, propelling further theoretical and experimental pursuits.