Strange and non-strange D-meson production in pp, p-Pb, and Pb-Pb collisions with ALICE at the LHC

The ALICE experiment at the CERN LHC was designed to study the colour-deconfined state of the nuclear matter created in heavy-ion collisions, called Quark-Gluon Plasma (QGP). Heavy flavours (i.e. charm and beauty quarks) represent an ideal probe of the QGP, since they are produced via hard-scattering processes in short time scales and hence experience the full system evolution, loosing energy via elastic and inelastic scatterings with the medium constituents. The measurement of open-heavy flavour hadrons represents also an important test for the understanding of the hadronisation mechanism in the hot environment created in heavy-ion collisions. In fact, if a fraction of heavy quarks hadronises via recombination with the medium constituents, the relative abundance of open heavy-flavour hadrons containing strange quarks with respect to those without strange-quark content is expected to be larger in heavy-ion collisions compared to proton-proton (pp) collisions, due to the enhanced production of strange quarks in the QGP. The aim of the studies presented in this Thesis is the precise measurement of charmed mesons with and without strange-quark content, reconstructed in the three-body decay channels $\mathrm{D}_\mathrm{s}^+\rightarrow\phi\pi^+\rightarrow\mathrm{K^+K^-}\pi^+$ and $\mathrm{D}^+\rightarrow\mathrm{K^-}\pi^+\pi^+$. The measurement of the $\mathrm{D}_\mathrm{s}^+$-meson production in pp collisions at a centre-of-mass energy of $\sqrt{s}=5.02~$TeV is described by perturbative QCD calculations. The abundance of $\mathrm{D}_\mathrm{s}^+$ mesons relative to that of non-strange D mesons is found to be compatible with that measured in $e^+e^-$ collisions, indicating that the charm-quark hadronisation mechanism is not significantly modified in pp collisions. The multiplicity-dependent nuclear modification factor of $\mathrm{D}^+$ mesons $Q_\mathrm{pA}$ measured in p-Pb collisions at a centre-of-mass-energy per nucleon pair of $\sqrt{s_\mathrm{NN}}=5.02~$TeV was found compatible with unity, with a hint of enhancement for the transverse-momentum interval $2 < p_\mathrm{T} < 10~\mathrm{GeV}/c$. A strong suppression of the $p_\mathrm{T}$-differential yields of $\mathrm{D}^+$ and $\mathrm{D}_\mathrm{s}^+$ mesons, increasing with the collision centrality, is observed in Pb-Pb collisions at $\sqrt{s_\mathrm{NN}}=5.02~$TeV. The nuclear modification factor $R_\mathrm{AA}$ of $\mathrm{D}^+$ mesons is found to be higher than that of charged particles for $p_\mathrm{T}