We review determinations of the electric proton charge radius from a diverse set of low-energy observables. We explore under which conditions it can be related to Wilson coefficients of appropriate effective field theories. This discussion is generalized to other low-energy constants. This provides us with a unified framework to deal with a set of low-energy constants of the proton associated with its electromagnetic interactions. Unambiguous definitions of these objects are given, as well as their relation with expectation values of QCD operators. We show that the proton radius obtained from spectroscopy and lepton–proton scattering (when both the lepton and proton move with nonrelativistic velocities) is related to the same object of the underlying field theory with $\mathcal{O}\left(\alpha \right)$ precision. The model dependence of these analyses is discussed. The prospects of constructing effective field theories valid for the kinematic configuration of present, or near-future, lepton–proton scattering experiments are explored.

我们回顾了从一组不同的低能观测值中确定的质子电荷半径。我们探索在什么条件下它可以与适当的有效场理论的威尔逊系数相关。这个讨论被推广到其他低能量常数。这为我们提供了一个统一的框架来处理一组与其电磁相互作用相关的质子的低能常数。给出了这些对象的明确定义，以及它们与 QCD 算子的期望值的关系。我们表明，从光谱学和轻子 - 质子散射（当轻子和质子都以非相对论速度移动时）获得的质子半径与基础场论的同一对象有关$\mathcal{哦}\left(\alpha \right)$精确。讨论了这些分析的模型依赖性。探索了构建适用于当前或近期轻子 - 质子散射实验的运动学配置的有效场理论的前景。