On the electron to proton mass ratio and the proton structure

TL;DR

This paper derives a theoretical expression for the electron to proton mass ratio using lattice gauge theory and provides approximate parton distribution functions that align well with experimental data.

Contribution

It introduces a novel approach combining lattice gauge theory and Lie group analysis to estimate mass ratios and parton distributions without adjustable parameters.

Findings

Electron to nucleon mass ratio within 3% of experimental value

Derived parameter-free parton distribution functions for u and d quarks

Demonstrated the effectiveness of Lie group methods in hadron structure analysis

Abstract

We derive an expression for the electron to nucleon mass ratio from a reinterpreted lattice gauge theory Hamiltonian to describe interior baryon dynamics. We use the classical electron radius as our fundamental length scale. Based on expansions on trigonometric Slater determinants for a neutral state a specific numerical result is found to be less than three percent off the experimental value for the neutron. Via the exterior derivative on the Lie group configuration space u(3) we derive approximate parameter free parton distribution functions that compare rather well with those for the u and d valence quarks of the proton.