Higher order QCD results for the fermionic contributions of the Higgs-boson decay into two photons and the decoupling function for the MSbar renormalized fine-structure constant

We compute the decoupling function of the MSbar renormalized fine-structure constant up to four-loop order in perturbative QCD. The results are used in order to determine the related top-quark contributions to the Higgs-boson decay into two photons in the heavy top-quark mass limit to order alpha_s^4.