TTP02-31 Bosonic Corrections to $\Delta r$ at the Two Loop Level

The details of the recent calculation of the two-loop bosonic corrections to the muon lifetime in the Standard Model are presented. The matching on the Fermi theory is discussed. Renormalisation in the on-shell and in the \MSb scheme is studied and transition between the schemes is shown to lead to identical results. High precision numerical methods are compared with mass difference and large mass expansions.