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.
Highlights
The size of proton charge distribution plays a relatively minor role in atomic physics since it is about five orders of magnitude smaller than the size of atoms
According to the renormalization group procedure for effective particles (RGPEP), the proton radius puzzle stems from the difference between Eqs. (8) and (24)
The coefficient cλ accounts for the effective nature of constituents that appear in the two-body Schrödinger equation for lepton–proton bound states
Summary
The size of proton charge distribution plays a relatively minor role in atomic physics since it is about five orders of magnitude smaller than the size of atoms. Recent experimental results are not yet well understood, but future research may reveal the true value of this radius, lead to a better understanding of its structure, or demonstrate an unexpected aspect of its interactions.” It is pointed out in this article that the front form (FF) of Hamiltonian dynamics [2] equipped with the renormalization group procedure for effective particles (RGPEP) may shed a new light on the issue [3]. The proton-size puzzle is seen here as emerging from an apparent discrepancy between, on the one hand, the Standard Model (SM) assumption that the atomic systems in question are described by a local quantum field theory (QFT) and, on the other hand, the standard atomic physics assumption that in the first approximation the electron–proton and muon–proton bound states can be described using the well-known two-body Schrödinger equation with a Coulomb potential.
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