Heavy-Flavor Jet Fragmentation and Jet-Medium Interactions in Pb--Pb Collisions

The quark-gluon plasma (QGP) is an exotic state of matter generated in ultra-relativistic heavy-ion collisions. Properties of the QGP can be determined by the use of well-defined hard probes, such as heavy-flavor particles. Heavy-flavor (charm and beauty) quarks are generated through hard scattering early in the collision and experience the full lifetime of the QGP. In the hard-scattering process, the leading-order (LO) mechanism produces heavy-quark jets back-to-back in azimuth, which undergo fragmentation into constituent particles. The fragmentation of the heavy-flavor jet can be studied differentially in phase space by utilizing azimuthal correlation measurements between a heavy-flavor trigger particle and associated charged particles. The azimuthal correlation provides a measurement of the angular distribution and number of particles correlated with the trigger. The influence of the QGP medium on the fragmentation of the heavy-quark-initiated jet and potentially the influence of the jet on the medium can be studied by performing this measurement in heavy-ion collisions. In this thesis, the azimuthal correlation of electrons from the decays of heavy-flavor hadrons with associated charged particles in Pb--Pb collisions at $\sqrt{s_{\mathrm{NN}}} = 5.02$ TeV is presented. This is the first jet-like correlation measurement in the heavy-flavor sector studied in heavy-ion collisions by the ALICE experiment. This measurement is performed in the central and semicentral centrality classes of Pb--Pb collisions to determine how the size and temperature of the medium affect the fragmentation. The per-trigger nuclear modification factor ($I_\mathrm{AA}$) is calculated to compare the correlation peak yields to those in pp collisions at $\sqrt{s} = 5.02$ TeV. The per-trigger nuclear modification factor for electron triggers from heavy-flavor hadron decays is compared with that for light-flavor and strange-particle triggers to investigate the dependence on different fragmentation processes and parton-medium dynamics.