Study of the production of nuclei and anti-nuclei at the LHC with the ALICE experiment

In the ultra-relativistic lead-lead collisions at the CERN Large Hadron Collider (LHC), a state of matter called Quark Gluon Plasma (QGP) is created. A typical signature of a heavy ion collision (HIC) correlated to the production of the QGP is the large number of particles produced ($\mathrm{d} N_{\mathrm{ch}}/\mathrm{d}\eta$ up to 2000 in Pb-Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV). This high multiplicity environment poses a tremendous experimental challenge on the experiments that have to cope with the high density of signals in their sensitive volume. A Large Ion Collider Experiment (ALICE) has been designed to deal with the harsh environment of a HIC and to study in details the characteristics of the QGP. Among the particles produced in a HIC, light nuclei and their anti-matter companions are of special interest since the production mechanism of such loosely bound states is not clear in high energy collisions. The production rate at the LHC for the lightest of these objects, the deuteron, is approximately one every ten Pb-Pb collisions with the highest charged particle density. Heavier nuclei, such as the $^{3}$He, are even more rare. The first goal of this work is to search with the ALICE experiment the haystack of particles produced in Pb-Pb collisions at $\sqrt{s_{\mathrm{NN}}}=2.76$ TeV and $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV to find (anti-)deuterons and (anti-)$^{3}$He. It is possible to distinguish some of the leading features of the main models describing the (anti-)nuclei production, by studying the characteristics of their transverse momentum spectra, their evolution with the particle multiplicity and their relation to the measured yield of protons. It will be also evident that the detailed study of heavier nuclei is limited by the amount of data collected by the ALICE experiment. In its third run, starting in 2020, the LHC will deliver Pb-Pb collisions at the unprecedented interaction rate of 50 kHz. In order to fully profit from the high luminosity delivered by the LHC, the ALICE collaboration is now working on the upgrade of its experimental apparatus. In particular, a completely new silicon Inner Tracking System (ITS) and a new computing facility for the Online and Offline (O$^2$) data handling will be installed. With these upgrades the ALICE experiment will be able to collect the data of every single Pb-Pb interaction, enabling the detailed study of rare processes such as the formation of (anti-)nuclei. In this context, the second goal of this thesis is the development of a fast ITS tracking algorithm that is able to conjugate the timing requirements imposed by the online reconstruction of all the Pb-Pb events and the reconstruction efficiency requirements of the physics analysis. The result is a tracking algorithm based on the Cellular Automata that is able to reconstruct efficiently tracks of transverse momentum down to 100 MeV/c in the Pb-Pb events with the highest track density in less than 1 second.