Electroweak Precision Observables: two-Loop Yukawa Corrections of Supersymmetric Particles

The dominant electroweak two-loop corrections to the precision observables M_W and s_w^eff are calculated in the MSSM. They are obtained by evaluating the two-loop Yukawa contributions of O(alpha_t^2), O(alpha_t alpha_b), O(alpha_b^2) to the quantity Delta rho. The result, involving the contributions from Standard Model fermions, sfermions, Higgs bosons and higgsinos, is derived in the gauge-less limit for arbitrary values of the lightest CP-even Higgs boson mass. A thorough discussion of the parameter relations enforced by supersymmetry is given, and two different renormalization schemes are applied. Compared to the previously known result for the quark-loop contribution we find a shift of up to +8 MeV in M_W and -4 * 10^-5 in s_w^eff. Detailed numerical estimates of the remaining uncertainties of M_W and s_w^eff from unknown higher-order contributions are obtained for different values of the supersymmetric mass scale.