Prompt D$^+_s$ meson production in pp, p-Pb and Pb-Pb collisions at LHC with ALICE

The aim of this thesis is the study of the D$^+_{\rm s}$-meson production in pp collisions at the centre-of-mass energy $\sqrt{s}=7$ TeV and in p-Pb and Pb-Pb collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV, with the ALICE detector at the CERN Large Hadron Collider. Heavy quarks provide an excellent way to investigate the properties of the Quark-Gluon Plasma (QGP) created in high-energy nucleus-nucleus collisions via the measurements of the nuclear modification factor ($R_{\rm AA}$) and azimuthal anisotropy of hadrons originating from their hadronisation. At low and intermediate transverse momentum p$_{\rm T}$, the study of the D$^+_{\rm s}$ meson should also reveal information about the charm-quark hadronisation mechanism. If charm quarks hadronise by recombining with lighter quarks from the medium, the relative abundance of D$^+_{\rm s}$ mesons with respect to non-strange D mesons is expected to be larger in Pb-Pb than in pp collisions, at low and intermediate p$_{\rm T}$, due to the large abundance of strange quarks in the QGP. The analyses presented in this thesis are based on the full reconstruction of the ${\rm D}^+_{\rm s} \rightarrow K^+K^-\pi^+$ decay, exploiting the displacement of the decay vertex from the interaction point. The p$_{\rm T}$-differential cross-section of D$^+_{\rm s}$ mesons and the relative yields of D$^+_{\rm s}$ to non-strange D mesons were measured in pp and Pb-Pb collisions. In particular, the nuclear modification factors and, for the first time at LHC, the elliptic flow of D$^+_{\rm s}$ mesons were measured in Pb-Pb collisions for central, semi-peripheral and peripheral collisions. The observed increase of strange particle yield relative to pion yield with increasing particle multiplicity in pp and p-Pb collisions suggested to investigate whether a similar enhancement is observed in the relative yield of D$^+_{\rm s}$ mesons with respect to non-strange D mesons in high multiplicity p-Pb collisions. To this purpose, the relative ratios of D$^+_{\rm s}$-meson and D$^+_{\rm s}$-meson yields were measured in p-Pb collisions as a function of the event particle multiplicity in different p$_{\rm T}$ intervals.