The Proton Radius from Bayesian Inference

TL;DR

This paper employs Bayesian statistical methods to determine the proton radius from elastic electron-proton scattering data, providing a model-independent estimate and addressing systematic uncertainties, but finds disagreement with muonic atom measurements.

Contribution

It introduces a Bayesian approach with multiple parametrizations to extract the proton radius, estimating systematic errors and emphasizing the importance of two-photon exchange corrections.

Findings

Proton radius: r_E^p=0.899±0.003 fm

Proton magnetic radius: r_M^p=0.879±0.007 fm

Results disagree with muonic atom measurements

Abstract

The methods of Bayesian statistics are used to extract the value of the proton radius from the elastic $ep$ scattering data in a model independent way. To achieve that goal a large number of parametrizations (equivalent to neural network schemes) are considered and ranked by their conditional probability $P(\mathrm{parametrization}\,|\,\mathrm{data})$ instead of using the minimal error criterion. As a result the most probable proton radii values ($r_E^p=0.899\pm 0.003$ fm, $r_M^p=0.879\pm 0.007$ fm) are obtained and systematic error due to freedom in the choice of parametrization is estimated. Correcting the data for the two photon exchange effect turns out to be important to obtain the agreement between the $r_E^p$ and $r_M^p$ values. The results disagree with recent muonic atom measurements.