Simple Bound-State Model of the Physical Nucleon

Abstract

A simple, but bona fide, local field-theoretic model is presented which illustrates the recently discussed bound-state concept of the physical nucleon. The scaling properties of $W_1$ and $\nu W_2$ functions in the deep-inelastic electron scattering are shown to be valid in the energy range in which the laboratory virtual-photon energy $\nu$, in units of GeV, is larger than $O\left(1\right)\mathrm{}$ but less than $O\left(\exp \right({\epsilon }^{-1\mathrm{}}\left)\right)$ where $\epsilon$ is a small, but nonzero, free parameter, assumed to be $\lesssim O\left({10}^{-1\mathrm{}}\right)$. In this model, one of the constituents of the physical proton $p$ is a local spin-½ charged field operator $\psi \mathrm{}\left(x\right)\mathrm{}$, and the usual "pointlike" assumption for the electromagnetic vertex of the constituent emerges simply as the standard minimal electromagnetic interaction in a local field theory.