High resolution spectroscopy of muonium

The hydrogen-like muonium atom ($\mu^+e^-$) consists of a positive muon ($\mu^+$) and an electron ($e^-$). Since it was first observed by Hughes et al. in 1960, a series of precision experiments could be carried out testing bound state Quantum Electrodynamics (QED) and the nature of the muon as a point-like leptonic particle. Precision values for fundamental constants could be obtained, including the fine structure constant $\alpha$ and the muon's magnetic moment $\mu_{\mu}$. Since no internal structure could be revealed for leptons down to dimensions of $10^{-18}$m, the accuracy of theoretical calculations of term energies is higher than for the natural hydrogen atom and its isotopes deuterium and tritium as well as exotic hydrogen-like systems which contain hadrons. Internal structure effects of these particles spoil the precision of theoretical results. Of particular interest for precision muonium experiments, which are carried out in order to test standard theory and to extract accurate values for fundamental constants, are the ground state hyperfine structure splitting $\Delta \nu_{HFS}$ and the 1s-2s interval $\Delta \nu_{1s2s}$. Both cases involve the n=1 ground state in which the atoms can be produced in sufficient quantities.