The Perfect Atom: Bound States of Supersymmetric Quantum Electrodynamics

TL;DR

This paper analyzes supersymmetric hydrogen-like atoms, calculating their energy spectrum and revealing the absence of hyperfine structure due to supersymmetry, with states organized into supermultiplets.

Contribution

It provides the first detailed spectrum calculation of supersymmetric bound states and highlights differences from non-supersymmetric atoms, such as missing hyperfine splitting.

Findings

Spectrum calculated to fourth order in fine structure constant

Absence of hyperfine structure in supersymmetric atoms

Eigenstates organized into supermultiplets

Abstract

We study hydrogen-like atoms in N=1 supersymmetric quantum electrodynamics with an electronic and a muonic family. These atoms are bound states of an anti-muon and an electron or their superpartners. The exchange of a photino converts different bound states into each other. We determine the energy eigenstates and calculate the spectrum to fourth order in the fine structure constant. A difference between these perfect atoms and non-supersymmetric ones is the absence of hyperfine structure. We organize the eigenstates into super multiplets of the underlying symmetry algebra.