Study of the production of (anti-)hypertriton at the LHC with the ALICE experiment

In the ultra-relativistic heavy ion 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 related to the production of the QGP is the large number of particles produced (d$N_{\mathrm{ch}}$/d$\eta$ up to 2000 in Pb--Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV). This high multiplicity environment is a big experimental challenge, since the experiments have to cope with a high density of signals in their sensitive volume. A Large Ion Collider Experiment (ALICE) has been designed to deal with such environment in order to study in details the characteristics of the QGP. Among the several particles produced in a heavy ion collision, light (anti-)hypernuclei are of special interest since the production mechanism of such loosely bound states is not clear at present in high energy collisions. In particular, this thesis is focused on the study of the production and the measurement of the lifetime of the lightest known $\Lambda$-hypernucleus, the hypertriton ($^{3}_{\Lambda}\mathrm{H}$) which is a bound state of a proton, a neutron and a $\Lambda$. The production rate at the LHC for this light hypernucleus is of the order of one every ten thousands Pb--Pb collisions with the highest charged particle density. The first goal of this work is the measurement of the $^{3}_{\Lambda}\mathrm{H}$ and $^{3}_{\overline{\Lambda}}\mathrm{\overline{H}}$ production in Pb--Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV with the ALICE experiment. In particular the hypertriton transverse momentum spectra have been studied together with their evolution with the particle multiplicity of the collision to have a comparison with the prediction of the models that are tipically used to describe the particle production in heavy ion collision, namely statistical-thermal and coalescence models. The second part of this thesis is related to an open question of the hypernuclear physics and in particular to the lifetime of the hypertriton. Indeed, since the beginning of the research in this field, the theory predicted the hypertriton lifetime to be close to the one of the free $\Lambda$. Many experiments using different techniques tried to face this challenge and recently new interest on this topic has been raised by the results obtained in heavy ion collision experiments, which showed a trend well below the expectation. Thus the measurement of the $^{3}_{\Lambda}\mathrm{H}$ lifetime by analysing the data sample of Pb--Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV collected by the ALICE experiment has been determined. In particular, it will be presented the lifetime determination via 2 body decay channel ($^{3}_{\Lambda}\mathrm{H}$ $\rightarrow$ $^{3}\mathrm{He}$ + $\pi^{-}$) using two different methods and the first estimate of the lifetime obtained via 3 body decay channel ($^{3}_{\Lambda}\mathrm{H}$ $\rightarrow$ d + p + $\pi^{-}$).