Complete two-loop electroweak fermionic corrections to $\sin^{2} \theta^{\rm lept}_{\rm eff}$ and indirect determination of the Higgs boson mass

We present a complete calculation of the contributions to the effective leptonic weak mixing angle, sin^2theta_eff, generated by closed fermion loops at the two-loop level of the electroweak interactions. This quantity is the source of the most stringent bound on the mass, M_H, of the only undiscovered particle of the Standard Model, the Higgs boson. The size of the corrections with respect to known partial results varies between -4*10^-5 and -8*10^-5 for a realistic range of M_H from 100 to 300 GeV. This translates into a shift of the predicted (from sin^2theta_eff alone) central value of M_H by +19 GeV, to be compared with the shift induced by a recent change in the measured top quark mass which amounts to +36 GeV. Our result, together with all other known corrections is given in the form of a precise fitting formula to be used in the global fit to the electroweak data