Three-loop electroweak corrections to the W-boson mass and sin2θefflept in the large Higgs mass limit

We present an analytical calculation of the leading three-loop radiative correction to the S-parameter in the standard model in the large Higgs mass limit. Numerically, S(3)=1.1105×g4/(1024π3)×mH4/MW4. When combined with the corresponding three-loop correction to the ρ-parameter, this leads to shifts of Δ(3)sin2θefflept=4.6×10−9×mH4/MW4 in the effective weak mixing angle and Δ(3)MW=−6.3×10−4MeV×mH4/MW4 in the W-boson mass. For both of these observables, the sign of the three-loop correction is equal to that of the one-loop correction.