  In leptophilic scenarios, dark matter interactions with nuclei, relevant for
direct detection experiments and for the capture by celestial objects, could
only occur via loop-induced processes. If the mediator is a scalar or
pseudo-scalar particle, which only couples to leptons, the dominant
contribution to dark matter-nucleus scattering would take place via two-photon
exchange with a lepton triangle loop. The corresponding diagrams have been
estimated in the literature under different approximations. Here, we present
new analytical calculations for one-body two-loop and two-body one-loop
interactions. The two-loop form factors are presented in closed analytical form
in terms of generalized polylogarithms up to weight four. In both cases, we
consider the exact dependence on all the involved scales, and study the
dependence on the momentum transfer. We show that some previous approximations
fail to correctly predict the scattering cross section by several orders of
magnitude. Moreover, we show that form factors, in the range of momentum
transfer relevant for local galactic dark matter, are smaller than their value
at zero momentum transfer, which is usually considered.
