Production locality and spatial diffusion of heavy flavour at high energy densities

Heavy-ion collisions are a unique tool to test the behaviour of matter in extreme conditions. The momentum correlations of charm and bottom hadrons have been considered for testing heavy quarks' thermalisation in the hot, dense medium produced by the collisions. In addition to these back-to-back correlations due to the quark-anti-quark pair creation dynamics, there are other important sources of momentum correlations, which allow us to explore the rich physics of heavy-ion collisions further. Here we show significant momentum correlations even in the thermalisation of charm quarks in the expanding medium, and this effect can be measured in collisions at sufficiently low energies. The momentum correlations depend on the correlations in the configuration space, more specifically, on the spatial separation between charm and anti-charm hadrons emission points. The pair production locality and spatial diffusion of the charm quarks give the latter. Using an example of central Pb+Pb collisions at the CERN SPS energies, we show that future measurements of the azimuthal correlations of charm and anti-charm hadrons should allow us to distinguish between different assumptions on their spatial correlations. This provides a unique window into a poorly understood sector of particle production at high-energy densities. The measurements can help to constrain the diffusion of charm quarks and verify assumptions concerning production locality of a charm and ant-charm quark pair.