The High-Z hydrogen-like atom: a model for polarized structure functions

TL;DR

This paper models high-Z hydrogen-like atoms using the Dirac equation to explore relativistic bound states and parton-like properties, providing insights into nucleon structure analogies through theoretical analysis.

Contribution

It introduces a novel approach to study relativistic two-particle bound states as partons in high-Z atoms, testing various parton distribution properties in this simplified system.

Findings

Validation of Bj{\

}rken scaling in the model

Demonstration of sum rules and inequalities for the parton distributions in the atom,

Abstract

The Dirac equation offers a precise analytical description of relativistic two-particle bound states, when one of the constituent is very heavy and radiative corrections are neglected. Looking at the high-Z hydrogen-like atom in the infinite momentum frame and treating the electron as a "parton", various properties usually attributed to the quark distributions in the nucleon are tested, in particular: Bj{\o}rken scaling; charge, helicity, transversity and momentum sum rules; existence of the parton sea; Soffer inequality; correlation between spin and transverse momentum (Sivers and Boer-Mulders effects); transverse displacement of the center-of-charge and its connection with the magnetic moment. Deep inelastic experiments with photon or positron beams at MeV energies, analogous to DIS or Drell-Yan reactions, are considered.