Relativistic and Recoil Corrections to Light-Fermion Vacuum Polarization for Bound Systems of Spin-0, Spin-1/2, and Spin-1 Particles

TL;DR

This paper extends the calculation of relativistic and recoil corrections to light-fermion vacuum polarization in bound systems with various particle spins, relevant for systems like pionium and muonic atoms.

Contribution

It generalizes previous treatments to include particles with spins 0, 1/2, and 1, providing new formulas for energy corrections in diverse bound systems.

Findings

Derived energy corrections of order alpha^5 * m_r for various systems.

Applied the generalized formulas to systems like pionium and muonic hydrogen.

Provided detailed analysis of excited non-S states of deuteronium.

Abstract

In bound systems whose constituent particles are heavier than the electron, the dominant radiative correction to energy levels is given by light-fermion (electronic) vacuum polarization. In consequence, relativistic and recoil corrections to the one-loop vacuum-polarization correction are phenomenologically relevant. Here, we generalize the treatment, previously accomplished for systems with orbiting muons, to bound systems of constituents with more general spins: spin-0, spin-1/2, and spin-1. We discuss the application of our more general expressions to various systems of interest, including spinless systems (pionium), muonic hydrogen and deuterium, and devote special attention to the excited non-S states of deuteronium, the bound system of a deuteron and its antiparticle. The obtained energy corrections are of order alpha^5*m_r, where alpha is the fine-structure constant and m_r is the reduced mass.