O(\alpha^2 \ln(m_\mu/m_e)) Corrections to Electron Energy Spectrum in   Muon Decay
  O(\alpha^2 \ln(m_\mu/m_e)) corrections to electron energy spectrum in muon decay are computed using perturbative fragmentation function approach. The magnitude of these corrections is comparable to anticipated precision of the TWIST experiment at TRIUMF where Michel parameters will be extracted from the measurement of the electron energy spectrum in muon decay. 
Andrej Arbuzov, Kirill Melnikov