Estimating proton radius and proportion of other non-perturbative components in the proton by the Maximum Entropy Method

TL;DR

This paper uses the Maximum Entropy Method to estimate the proton radius and quantify non-perturbative components, aligning with experimental data and proposing a new concept called 'ghost matter' to explain detectable differences.

Contribution

It introduces a novel application of the Maximum Entropy Method to proton structure, estimating the proton radius and non-perturbative components at low resolution scales.

Findings

Proton radii estimated are close to experimental values.

Non-perturbative components account for about 17.5% to 22.3%.

Proposes 'ghost matter' to explain detectable non-perturbative effects.

Abstract

In this paper, we apply the Maximum Entropy Method to estimate the proton radius and determine the valence quark distributions in the proton at extremely low resolution scale Q$^{2}_{0}$. Using the simplest functional form of the valence quark distribution and standard deviations of quark distribution functions in the estimation of the proton radius, we obtain a quadratic polynomial for the relationship between the proton radius and the momentum fraction of other non-perturbative components in the proton. The proton radii are approximately equal to the muonic hydrogen experimental result $r_p$ = 0.841~fm and the CODATA analysis $r_p$ = 0.877 fm when the other non-perturbative components account for 17.5\% and 22.3\% respectively. We propose $"ghost~~matter"$ to explain the difference in other non-perturbative components (4.8\%) that the electron can detect.