Unveiling the (anti-)hypertriton properties with ALICE at the LHC

A Large Ion Collider Experiment (ALICE) is one of the four experiments installed at the CERN Large Hadron Collider (LHC). ALICE was designed and built to study a phase of the matter called Quark Gluon Plasma, which is formed in heavy-ion collisions at ultra-relativistic energies. The extreme energy densities reached in hadronic collisions at the LHC lead to a significant production of baryonic states. Among the thousands of particles produced, light (anti-)hypernuclei are of special interest. Indeed, the study of their internal structure represents a direct probe to investigate the strong interaction among hyperons and the ordinary matter. This thesis project is focused on the study of the properties of the lightest known hypernucleus, the hypertriton ($\mathrm{^{3}_{\Lambda}H}$) which is a bound state of a proton, a neutron and a $\Lambda$. The most precise measurements to date of the $\mathrm{^{3}_{\Lambda}H}$ lifetime and $\Lambda$ separation energy are performed by exploiting the large Pb--Pb data sample collected by ALICE during 2018. The $\mathrm{^{3}_{\Lambda}H}$ signal is extracted for the first time with a machine learning technique, allowing for a significant improvement in the discrimination between signal and background. The combined measurements confirm that the $\mathrm{^{3}_{\Lambda}H}$ is a loosely bound state with a large wave function radius extending up to $\sim$ 5 fm. In the second part of this thesis, the first measurement of the $\mathrm{^{3}_{\Lambda}H}$ production in p--Pb collisions is presented. Given the large spread of its wave function, the measured $\mathrm{^{3}_{\Lambda}H}$ yield in p--Pb collisions is a sensitive observable to test the nucleosynthesis in hadronic collisions and is a powerful tool for discriminating between different production models of nuclei. The $\mathrm{^{3}_{\Lambda}H}$ signal is extracted again with a machine learning approach, leading to a significance higher than 4 $\sigma$. The value of the yield favours a coalescence model to describe the nucleosynthesis, demonstrating that the $\mathrm{^{3}_{\Lambda}H}$ wave function directly influences its nuclear production mechanism in hadronic collisions. In the last part of this thesis a new algorithm for tracking the $\mathrm{^{3}_{\Lambda}H}$ and fully reconstruct its decay topology is presented: this method relies on the high granularity of the upgraded Inner Tracking System of ALICE, installed for the Run 3 of the LHC. Finally, the possibility to characterise the properties of $A\geq 4$ hypernuclei with the proposed NA60+ experiment is discussed, using the $^5_\Lambda\mathrm{He}$ as a use case.