Three-loop electroweak corrections to the W-boson mass and sin² theta_eff 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*g^4/(1024 pi^3)*m_H^4/M_W^4. When combined with the corresponding three-loop correction to the rho-parameter, this leads to shifts of Delta^(3) sin^2 theta_eff = 4.6*10^-9*m_H^4/M_W^4 in the effective weak mixing angle and Delta^(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.