We extract the proton magnetic radius from high-precision electron-proton elastic scattering cross section data. Our theoretical framework combines dispersion analysis and chiral effective field theory and implements the dynamics governing the shape of the low-${Q}^{2}$ form factors. It allows us to use data up to ${Q}^{2}\ensuremath{\approx}0.5\phantom{\rule{4pt}{0ex}}{\mathrm{GeV}}^{2}$ for constraining the radii and overcomes the difficulties of empirical fits and ${Q}^{2}\ensuremath{\rightarrow}0$ extrapolation. We obtain a magnetic radius ${r}_{M}^{p}=0.850\ifmmode\pm\else\textpm\fi{}0.001$ ($1\ensuremath{\sigma}$ fit uncertainty) ${}_{\ensuremath{-}0.004}^{+0.009}$ (full-range theory uncertainty) fm, significantly different from earlier results obtained from the same data using empirical fits, and close to our extracted electric radius ${r}_{E}^{p}=0.842\ifmmode\pm\else\textpm\fi{}0.002$ ($1\ensuremath{\sigma}$ fit uncertainty) ${}_{\ensuremath{-}0.002}^{+0.005}$ (full-range theory uncertainty) fm.

中文翻译：

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从电子散射数据精确确定质子磁半径

我们从高精度电子-质子弹性散射截面数据中提取质子磁半径。我们的理论框架结合了色散分析和手性有效场理论，并实现了控制低 ${Q}^{2}$ 形状因子形状的动力学。它允许我们使用高达 ${Q}^{2}\ensuremath{\a​​pprox}0.5\phantom{\rule{4pt}{0ex}}{\mathrm{GeV}}^{2}$ 的数据来约束半径并克服了经验拟合和 ${Q}^{2}\ensuremath{\rightarrow}0$ 外推的困难。我们得到一个磁半径 ${r}_{M}^{p}=0.850\ifmmode\pm\else\textpm\fi{}0.001$ ($1\ensuremath{\sigma}$ 拟合不确定性) ${}_{ \ensuremath{-}0.004}^{+0.009}$（全范围理论不确定性）fm，与使用经验拟合从相同数据获得的早期结果显着不同，