Differential heavy quark pair production at small $x$

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.