  We consider the production of a heavy quark pair in proton-proton collisions.
For bottom and charm quarks, the final state invariant mass is typically much
smaller than the collider energy (e.g. at the LHC), so that high-energy
logarithms may spoil the perturbativity of the theoretical prediction at fixed
order. The resummation of these logarithms to all orders is thus needed to
obtain reliable predictions. In this work, we extend previous results on
high-energy (or small-$x$) resummation to differential distributions in
rapidity, transverse momentum and invariant mass, and implement them in the
public code HELL.
