Quantum electrodynamics of two-body systems with arbitrary masses

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 $Z\alpha \mathrm{/}n$, 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.