Towards $gg\to HH$ at next-to-next-to-leading order: light-fermionic three-loop corrections

We consider light-fermion three-loop corrections to $gg\to HH$ using forward scattering kinematics in the limit of a vanishing Higgs boson mass, which covers a large part of the physical phase space. We compute the form factors and discuss the technical challenges. The approach outlined in this letter can be used to obtain the full virtual corrections to $gg\to HH$ at next-to-next-to-leading order.