Jets as differential probes of hot QCD matter

Ultra-relativistic heavy-ion collisions create short-lived droplets of deconfined, hot QCD matter whose evolution connects far-from-equilibrium early dynamics to the hydrodynamic quark-gluon plasma. High-energy jets, produced in early hard scatterings and modified as they traverse this evolving medium, provide multi-scale probes of its microscopic properties. In this thesis, we develop perturbative QCD tools for using differential jet substructure observables to extract detailed information about hot QCD matter through the modifications it imprints on jets.

The theoretical framework is based on the BDMPS-Z description of high-energy partons propagating through stochastic colour fields. Within this setup, we first study anisotropic QCD matter by replacing the usual scalar broadening parameter with a direction-dependent description of transverse momentum broadening. This allows anisotropic corrections to medium-induced splittings to be related to spin information and to azimuthal patterns in final-state energy flow. Energy correlators are then used as phenomenologically relevant observables sensitive to these effects, including heavy-flavour EECs, azimuthally differential EECs and clover projections designed to isolate leading anisotropy-induced harmonics. In this thesis, we also examine how energy loss affects the interpretation of modifications to jet substructure observables.

Quantile matching is used to define reconstructed energy loss as a population-level shift between vacuum and medium-modified jet spectra. We further develop energy-loss functions, which encode the distribution of energy retained by jet-originated hadrons, and show how their moments enter multi-point projected energy correlators. Finally, we go beyond single 1 → 2 medium-induced splittings by studying spin-induced correlations between successive emissions and higher-point energy correlators including contributions from medium response. Overall, the results show that differential jet substructure can probe directional properties of QCD matter and multi-point dynamics of jets propagating through it.