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Description
This study calculates the energy decay rates ($r$) for both up and down quarks and the electric form factors ($G_E$) of the proton using low four-momentum transfer ($Q^2$) data from the PRad and MaMi electron-proton scattering experiments. The extracted decay rates for u and d quarks were nearly identical with $r≈3.94$, demonstrating a consistent exponential decay behavior across increasing $Q^2$. Moreover, analysis of the electric form factor confirmed that the calculated values closely match with PRad and MaMi data at low $Q^2$, validating the model in this region. However, increasing residuals and deviations from both MaMi data and the standard dipole form factor assumption at higher $Q^2$ indicate the model’s limitations. The results underscore the sensitivity of both decay rates and $G_E$ to the momentum transfer range and the need for a refined theoretical framework that incorporates higher-order QED corrections and spin-spin interactions. The extracted average proton charge radius is $0.8291 ±0.0019(stat) ±0.0004(std) fm$, aligns closely with PRad results, supporting evidence for a smaller proton radius.
