In this study, we utilize a potentially versatile Bayesian parameter approach to compute the value of the pion charge radius and quantify its uncertainty from several experimental datasets for the pion vector form factor. We employ dispersion relations to model the pion vector form factor to extract the radius. Nested model selection is used to determine the order of polynomial appearing in the form factor formulation that can be supported by the data, adapting the computation of Bayes evidence and Bayesian effective complexity based on Occam's razor. Our findings indicate that five out of six used datasets favor the nine-parameter model for radius extraction, and accordingly, we average the radii from the datasets. Despite some inconsistencies with the most updated radius values, our approach may serve as a more intuitive method of addressing parameter estimations in dispersion theory.

在这项研究中，我们利用一种潜在的通用贝叶斯参数方法来计算 pion 电荷半径的值并从几个实验中量化其不确定性 pion 向量形状因子的数据集。我们采用色散关系对 pion 向量形状因子进行建模以提取半径。嵌套模型选择用于确定数据可以支持的形状因子公式中出现的多项式的阶数，适应贝叶斯证据的计算和基于奥卡姆剃刀的贝叶斯有效复杂度。我们的研究结果表明，六个使用的数据集中有五个支持用于半径提取的九参数模型，因此，我们对数据集的半径进行平均。尽管与最新的半径值存在一些不一致，但我们的方法可以作为一种更直观的方法来解决色散理论中的参数估计。