解析选择如何影响从弹性电子散射截面数据中提取电磁形状因子
How Analytic Choices Can Affect the Extraction of Electromagnetic Form Factors from Elastic Electron Scattering Cross Section Data
摘要：
科学家们经常尝试将先验知识纳入他们的回归算法中，例如特定的分析行为或运动学端点的已知值。不幸的是，通常没有唯一的方法来利用这种先验知识，因此，不同的分析选择可能会导致同一组数据的回归结果非常不同。为了说明这一点的质子电磁形状因子的上下文中，我们使用美因茨弹性数据与它的1422个截面点和31个归一化参数。从一个复杂的非束缚非线性回归开始，我们将展示如何添加一个单一的理论驱动的约束，从磁性形状因子的振荡和移动提取的质子电荷半径。然后，我们使用相同的算法重复两次回归，但使用的是美因茨数据集的重组版本。这些示例说明了分析选择（例如正在使用的函数甚至数据的分箱）如何显著影响复杂回归的结果。这些结果也证明了为什么在使用回归算法时，无论是考虑物理模型还是坚实的数学基础都是至关重要的
英文摘要：
Scientists often try to incorporate prior knowledge into their regression algorithms, such as a particular analytic behavior or a known value at a kinematic endpoint. Unfortunately, there is often no unique way to make use of this prior knowledge, and thus, different analytic choices can lead to very different regression results from the same set of data. To illustrate this point in the context of the proton electromagnetic form factors, we use the Mainz elastic data with its 1422 cross section points and 31 normalization parameters. Starting with a complex unbound non-linear regression, we will show how the addition of a single theory-motivated constraint removes an oscillation from the magnetic form factor and shifts the extracted proton charge radius. We then repeat both regressions using the same algorithm, but with a rebinned version of the Mainz dataset. These examples illustrate how analytic choices, such as the function that is being used or even the binning of the data, can dramatically affect the results of a complex regression. These results also demonstrate why it is critical when using regression algorithms to have either a physical model in mind or a firm mathematical basis
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
