Recently, progress has been achieved in the theoryâ€‹ of theâ€‹ bound muon decayâ€‹. â€‹Bound states of heavy quarks share many properties with muonic atoms. QCD methods developed to describe semi-leptonic decays of heavy quarks can be applied to QED systems involving muons.
Moreover, the muon decay spectrum and the wave function are known analytically. I will show how these techniques can be used to calculate the electron spectrum in the decay of a bound muon, at the leading order and with dominant radiative corrections. In my talk I will present recent results for â€‹a â€‹muon bound â€‹with an aluminum nucleus, the planned target in muon-electron conversion searches.