The Proton Radius from Bayesian Inference

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.

Two sentences are added in order to clarify that TPE corrections which are subtracted from the data were obtained from theoretical calculations (from box diagrams)

References in corpus (8)

• High-precision determination of the electric and magnetic form factors of the proton
• Global analysis of proton elastic form factor data with two-photon exchange corrections
• Model independent extraction of the proton charge radius from electron scattering
• The size of the proton - closing in on the radius puzzle
• Model independent extraction of the proton magnetic radius from electron scattering
• Reduction of the proton radius discrepancy by 3 sigma
• Polynomial fits and the proton radius puzzle
• Model-independent determination of the magnetic radius of the proton from spectroscopy of ordinary and muonic hydrogen

Cited by in corpus (4)

• Uncertainty Quantification for Nuclear Density Functional Theory and Information Content of New Measurements
• Theoretical Constraints and Systematic Effects in the Determination of the Proton Form Factors
• Applications of Neural Networks in Hadron Physics
• Proton Charge Radius and Precision Tests of QED