Proton radius puzzle in Hamiltonian dynamics

TL;DR

This paper investigates the proton radius puzzle by deriving effective two-body Schrödinger equations from relativistic quantum field theory, revealing a tiny scale dependence that could explain the observed discrepancy in proton radii from muon and electron bound states.

Contribution

It introduces a Hamiltonian framework from quantum field theory that reduces to a Schrödinger equation with a scale-sensitive Coulomb potential, offering a new perspective on the proton radius discrepancy.

Findings

Derived effective Schrödinger equations from quantum field theory.

Identified a tiny scale dependence in the Coulomb potential.

Proposed a possible explanation for the proton radius puzzle.

Abstract

Relativistic lepton-proton bound-state eigenvalue equations for Hamiltonians derived from quantum field theory using second-order renormalization group procedure for effective particles, are reducible to two-body Schroedinger eigenvalue equations with the effective Coulomb potential that exhibits a tiny sensitivity to the characteristic momentum-scale of the bound system. The scale dependence is shown to be relevant to the theoretical interpretation of precisely measured lepton-proton bound-state energy levels in terms of a 4 percent difference between the proton radii in muon-proton and electron-proton bound states.