Three-loop electroweak corrections to the W-boson mass and [formula omitted] in the large Higgs mass limit

Abstract

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 × g 4 / ( 1024 π 3 ) × m H 4 / M W 4 . When combined with the corresponding three-loop correction to the ρ-parameter, this leads to shifts of Δ ( 3 ) sin 2 θ eff lept = 4.6 × 10 −9 × m H 4 / M W 4 in the effective weak mixing angle and Δ ( 3 ) M W = − 6.3 × 10 −4 MeV × m H 4 / M W 4 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.