Bootstrap-based fit of proton dipole scalar polarizabilities from real Compton scattering data

Abstract

We describe the fitting technique that we recently applied to the analysis of the proton real Compton scattering data to extract the dipole scalar polarizabilities α E1 and β M1. This fitting technique is based on the parametric bootstrap, which allows one to propagate the probability distribution of the experimental data to the fit results, with no a-priori assumption. It has never been applied before to the analysis of Compton data, and it offers several advantages: for instance, the automatic inclusion of the systematic errors and the propagation of those parameters that enter the model as inputs but that are not fitted. The most important result of our work is the definition of a realistic goodness-of-fit distribution even for those cases where the experimental points cannot be considered as independent Gaussian variables. We define a method that allows one, in different Physics domains, to define the correct p-values associated to a fit result.