Testing the QCD formation time with reconstructed parton splittings

In high-energy elementary collisions the space-time ordering of parton branching processes is not accessible experimentally. In contrast, in heavy-ion collisions, parton showers interact with a spatially extended dense medium. This sets a reference length scale with respect to which the space-time ordering may be analysed. Here, we explore the possibility of identifying experimental signatures of the QCD formation time, $\tau_f$, on the level of a single parton splitting. Since heavy flavour offers an additional handle on tracing the propagation of individual quarks through the medium, we focus on the $g\to c\bar{c}$ splitting. Combining adapted versions of the Cambridge-Aachen and FlavourCone jet finding algorithms with grooming techniques, we show how the kinematics of such splittings can be reconstructed with high fidelity using either final state partons or hadrons, and how the formation time distribution of parton splittings can be constructed therefrom. Medium modification leads to a characteristic modification of this $\tau_f$ distribution. This effect can be used to construct experimentally-accessible ratios of $\tau_f$ distributions, in which the sensitivity of the medium modification to the QCD formation time becomes measurable.