Fragmentation of jets containing a J/$\psi$ meson in pp and PbPb collisions at 5~TeV with the CMS detector

The Quark-Gluon Plasma (QGP) is a state of matter where quarks and gluons are asymptotically free, and not confined in hadrons. Ultrarelativistic heavy-ion collisions are a unique tool to produce the QGP in laboratory frame. Since it cannot be directly seen, probes are used to measure its properties, one of which is the J/$\psi$ meson. The J/$\psi$ production, however, is still not completely understood.\\ In this thesis, the fragmentation of J/$\psi$ in jets is measured in pp and PbPb collisions at a center-of-mass energy of 5 TeV. Prompt and nonprompt J/$\psi$ fragmentation functions are shown and compared to the models in pp. The nuclear modification factor of J/$\psi$ in jets is also shown. The J/$\psi$-in-jets results indicate that prompt J/$\psi$ mesons are produced in parton showers and are affected by energy loss processes in the presence of a hot and dense strongly-interacting medium.