Bound muon decay spectrum in the leading logarithmic accuracy
  We compute the dominant, logarithmically enhanced radiative corrections to the electron spectrum in the bound muon decay in the whole experimentally interesting range. The corrected spectrum fits well the TWIST results. The remaining theoretical error, dominated by the nuclear charge distribution, can be reduced in the muon-electron conversion searches by measuring the spectrum slightly below the New Physics signal window. 
Robert Szafron and Andrzej Czarnecki
hep-ph