A Bayesian-based approach for extracting the pion charge radius from electron-electron scattering data

Abstract

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.