Three-loop large-N$_c$ virtual corrections to gg → HH in the forward limit

We compute the three-loop form factors for gg -> HH in the limit of vanishing transverse momentum of the Higgs boson which provides a reasonable approximation of the cross section. In our calculations we adopt the large-Nc limit and restrict ourselves to the contributions with one closed top quark loop, which already includes non-trivial non-planar Feynman diagrams. We discuss the results for top quark masses in the pole and MS\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \overline{\textrm{MS}} $$\end{document} schemes and show that the scheme dependence is significantly reduced at next-to-next-to-leading order.