Three-loop electroweak correction to the rho parameter in the large Higgs mass limit

We present an analytical calculation of the leading three-loop radiative correction to the ρ-parameter in the Standard Model in the large Higgs mass limit. This correction, of order g6mH4/MW4, is opposite in sign to the leading two-loop correction of order g4mH2/MW2. The two corrections cancel each other for a Higgs mass of approximately 480GeV. The result shows that it is extremely unlikely that a strongly interacting Higgs sector could fit the data of electroweak precision measurements.