Next-to-next-to-leading orderO(α2αs2)results for top quark pair production in photon-photon collisions: The one-loop squared contributions

We calculate the one-loop squared contributions to the next-to-next-to-leading order $\mathcal{O}({\alpha }^2{\alpha }_s^2)$ radiative QCD corrections for the production of heavy quark pairs in the collisions of unpolarized on-shell photons. In particular, we present analytical results for the squared matrix elements that correspond to the product of the one-loop amplitudes. All results of the perturbative calculation are given in the dimensional regularization scheme. These results represent the Abelian part of the corresponding gluon-induced next-to-next-to-leading order cross section for heavy quark pair hadroproduction.