Quantum electrodynamics of two-body systems with arbitrary masses

TL;DR

This paper calculates quantum electrodynamics effects in excited two-body systems with arbitrary masses up to order α^6μ, extending applicability to heavy ions and enabling precise fundamental constant measurements.

Contribution

It provides a comprehensive QED calculation for excited states of arbitrary two-body systems, including heavy ions, up to sixth order in α, with potential applications in fundamental physics.

Findings

Results valid for hadronic atoms with negligible strong interactions.

Effective expansion parameter for circular states is Zα/n, extending formulas to heavy ions.

Higher-order terms inclusion allows for precise measurements to determine constants and search for new interactions.

Abstract

We perform a calculation of quantum electrodynamics effects in excited states with $l>1$ of arbitrary two-body systems up to $\alpha^6\,\mu$ order. The obtained results are valid for hadronic atoms, as long as the strong interaction effects are negligible. We demonstrate that for circular states with $l\sim n$, the effective expansion parameter is $Z\,\alpha/n$, which extends the applicability of the derived formulas to heavy ions. Moreover, inclusion of higher-order terms is feasible, which indicates that accurate measurements of excited states of, for example, muonic or antiprotonic hydrogenic ions can be used to determine the fundamental constants and to search for the existence of yet unknown long-range interactions.