Three-loop large-Nc virtual corrections to gg → HH in the forward limit

A bstract 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- N c 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 $$ \overline{\textrm{MS}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>MS</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> schemes and show that the scheme dependence is significantly reduced at next-to-next-to-leading order.