$O\left({\alpha }^2\ln {(m}_{\mu }{/m}_e\right))$ corrections to the electron energy spectrum in muon decay

The $O\left({\alpha }^2\ln {(m}_{\mu }{/m}_e\right))$ corrections to the electron energy spectrum in muon decay are computed using the perturbative fragmentation function approach. The magnitude of these corrections is comparable to the anticipated precision of the TWIST experiment where the Michel parameters will be extracted from the measurement of the electron energy spectrum in muon decay.