Test of the heavy top expansion in the evaluation of MW and sin2 θlepteff

In order to test the accuracy of the Heavy Top-mass Expansion (HTE) employed in recent two-loop calculations of MW and sin2 θlepteff, we consider their contributions to subtracted quantities of the form (MW)sub = MW(MH)−MW(MH0), where MH0 is a reference point. The results are compared with those obtained by a precise numerical evaluation of all the two-loop contributions involving both the Higgs boson and a fermion loop. For the choice MH0 = 65 GeV, and over the large range 65 GeV ≤ MH ≤ 1 TeV, we find very small differences between the precise and HTE calculations, amounting to |δMW| ≤ 0.8 MeV and |δs2eff| ≤ 1.2 × 10−5. Although corrections involving light fermions are necessary for the consistency and test of existent calculations, we also discuss the separate contributions from the top-bottom isodoublet. In this case, the differences are larger, although still small, namely |δMW| ≤ 1.9 MeV and |δs2eff| ≤ 4.5 × 10−5.