Complete Two Loop Bosonic Contributions to the Muon Lifetime in the Standard Model

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The last missing correction to the muon lifetime in the Standard Model at O(alpha^2) coming from gauge and Higgs boson loops is presented. The associated contribution to the parameter Delta r in the on-shell scheme ranges from 6 times 10^{-5} to -4 times 10^{-5} for Higgs boson masses from 100 GeV to 1 TeV. This result translates into a shift of the W boson mass which does not exceed +/- 1 MeV in the same range and amounts in particular to approximately -0.8 MeV for a 115 GeV Higgs boson.
4 pages, 3 figures, references added, final version to appear in Phys. Rev. Lett

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