$\mathrm{\Lambda_{c}^{+}}$ baryon production measurements with the ALICE experiment at the LHC

Quantum chromodynamics, the quantum field theory that describes the strong interaction, demonstrates a property known as asymptotic freedom which weakens the strong coupling constant $\alpha_s$ at high energies or short distances. The measurement of particles containing heavy quarks, i.e. charm and beauty, in high-energy particle collisions is a stringent test of the theory of quantum chromodynamics in the regime where $\alpha_s$ is small. In addition, asymptotic freedom leads to a phase transition of nuclear matter at high temperatures or energy densities to a phase known as the Quark-Gluon Plasma, where quarks and gluons are deconfined, and this state of matter can be studied in relativistic heavy-ion collisions. Particles containing heavy quarks, i.e. charm and beauty, have been proposed as probes of the properties of the Quark Gluon Plasma, where the measurement of mesons and baryons can offer insight into the transport properties of the medium and mechanisms related to the formation of hadrons during the transition back to `confined' quark states. Proton-proton and proton-lead collisions offer a crucial benchmark for these measurements, and can also reveal important insights into particle production and interaction mechanisms. The goal of this thesis is to investigate the production of the charmed baryon ${\rm \Lambda_{c}^{+}}$ in high-energy particle collisions with the ALICE detector at the Large Hadron Collider. The measurements presented will test predictions utilising perturbative (small $\alpha_s$) and non-perturbative (large $\alpha_s$) methods, will test possible cold-nuclear-matter modifications of the ${\rm \Lambda_{c}^{+}}$ yield in proton-lead collisions, and will set the stage for future measurements in lead-lead collisions. The measurements are carried out by reconstructing the hadronic decay channel ${\rm \Lambda_{c}^{+}\to p K^-\pi^+}$, making selections on its decay topology, extracting the signal via an invariant mass analysis, and finally correcting for its selection and reconstruction efficiency. A multivariate technique (Boosted Decision Trees) has been developed and is utilised in order to improve the signal extraction by optimally combining discriminating variables related to the ${\rm \Lambda_{c}^{+}}$ decay topology. This technique has also been investigated as a possible approach to measuring the ${\rm \Lambda_{c}^{+}}$ baryon in lead-lead collisions in the future, after the upgrade of the ALICE Inner Tracking System will make this measurement possible. The transverse momentum dependence of the ${\rm \Lambda_{c}^{+}}$ baryon production cross section has been measured in proton-proton collisions at a centre-of-mass energy of $7 ~$TeV and proton-lead collisions at a centre-of-mass energy per nucleon-nucleon collision of $5.02 ~$TeV, in the transverse momentum range $2 < p_{\rm T} < 12 ~\mathrm{GeV}/c$, and is shown to be under-predicted by theoretical calculations. The baryon-to-meson ratio ${\rm \Lambda_{c}^{+}}$/${\rm D^0}$ has been measured to be consistent in proton-proton collisions and proton-lead collisions and under-predicted by theoretical calculations. The nuclear modification factor $R_\mathrm{pPb}$ is measured to be consistent with unity and in agreement with the D meson $R_\mathrm{pPb}$, indicating no significant modification of the ${\rm \Lambda_{c}^{+}}$ yield in proton-lead collisions with respect to proton-proton collisions within the experimental uncertainties. Finally, Boosted Decision Trees have been shown to significantly improve the statistical precision with which the measurement of the ${\rm \Lambda_{c}^{+}}$ baryon can be made in lead-lead collisions with the ALICE detector in the future.