Probing the microscopic origin of prompt and non-prompt $D^0$ production through event-shape engineering in proton-proton collisions at the LHC

Heavy-flavour hadrons are produced in the early stages of ultra-relativistic collisions at the LHC via hard partonic interactions and experience the whole system evolution. The study of prompt and non-prompt $D^0$ mesons provides an independent avenue to test the theories of quantum chromodynamics and to investigate beauty hadron production. Moreover, the production of both prompt and non-prompt $D^0$ is influenced by microscopic processes such as multi-partonic interactions (MPI) and hadronisation through fragmentation. In this study, an attempt is made to understand the production of prompt and non-prompt $D^0$ mesons in proton-proton collisions at $\sqrt{s}=13.6$ TeV using the PYTHIA8 event generator, which offers a qualitative description of charm production. The role of the transverse momentum transfer in the hardest partonic scattering (${\widehat{p}}_{\mathrm{T}}$), MPI, and color reconnection is systematically explored. In addition, the charged particle production in different topological regions with respect to the leading $D^0$ meson is studied to assess the influence of the $D^0$ meson on the event topology and to examine the selection biases arising from the use of charged particle multiplicity as an event classifier.