Hadronisation of Heavy Quarks : Production measurements of heavy-flavour hadrons from small to large collision systems

The work presented in this dissertation is dedicated to production measurements of open charm hadrons in proton-proton (pp) and lead-lead (Pb-Pb) collisions with the ALICE detector at the Large Hadron Collider (LHC) at CERN. Studies on the production of open charm hadrons are of paramount importance to investigate charm-quark hadronisation at the LHC, particularly through the evolution of the production ratio between different charm-hadron species. The production and hadronisation of heavy quarks are both described by quantum chromodynamics (QCD), however, while perturbative QCD calculations of heavy-quark production are possible down to low transverse momenta, the typical momentum transfers in hadronisation processes are too small for meaningful QCD calculations. One thus has to resort to phenomenological models to describe hadronisation. Traditional model implementations of hadronisation like vacuum string fragmentation, tuned on (and therefore in good agreement with) ee and ep collision data, can describe well charm-meson production in small hadronic collision systems at the LHC. However, this type of hadronic modelling, without taking into account the parton phase-space density, is no longer valid in presence of a reservoir of partons. In large collision systems like Pb-Pb, where a colour-deconfined quark-gluon plasma (QGP) is formed, implementations of alternative hadronisation mechanisms are required, which predict an enhancement of charm-strange hadrons and charm baryons with respect to non-strange charm mesons. It is essential to achieve a good understanding of the hadronisation phase, since it connects what experimentally can be measured (heavy-flavour hadrons) to what theoretically is seen as a sensitive tool to investigate the fundamental aspects of QCD (heavy quarks traversing the QGP). The need of a better knowledge of hadronisation is not limited to heavy-ion collisions, also recent measurements in pp collisions, for which the standard assumption in high-energy physics was for many years that the interactions between the physical degrees of freedom are negligible, indicate that there might be more physics at play than initially thought. Many characteristics believed to be a sign of a colour-deconfined medium have been observed in pp systems nowadays, feeding the discussion if a QGP is formed in small collision systems. Regarding heavy-flavour production, measurements of the lightest charm baryon in pp and p-Pb collisions revealed unexpected features as well, not in line with any of the state-of-the-art model predictions. Typical calculations that were developed to better reproduce the charm baryon-to-meson ratio also rely on alternative hadronisation mechanisms, where some are directly taken from ideas originally developed to describe hadronisation in presence of a colour-deconfined medium. This dissertation features three independent experimental analyses of charm-hadron production and one performance simulation study of beauty-hadron production across different systems. In particular, the non-strange Dstar vector-meson is measured in minimum-bias pp collisions, the production of the charm-strange Ds meson and charm Lc baryon are studied as function of multiplicity in pp collisions, the Lc baryon is measured in central and mid-central Pb-Pb collisions, and a prospect for the measurement of the beauty-strange Bs meson in Pb-Pb collisions is presented. These measurements significantly constrain available phenomenological models for charm-quark hadronisation