${}_{\Lambda }^3$H studies in relativistic ion-ion collisions. Matter radius and production mechanisms

In the exploration of nuclear physics, hypernuclei stand as unique entities, introducing strangeness into the nuclear landscape and extending it to reveal new structural phenomena. Investigating their internal composition gives access to the hyperon-nucleon and hyperon-hyperon interactions, which are challenging to study directly (e.g., by elastic scattering) due to the short lifetime of hyperons. A better understanding of baryon interactions, including hyperons, improves the knowledge on the nuclear equation of state and, consequently, the inner core structure of neutron stars. Among hypernuclei, the hypertriton (${}_{\Lambda }^3$H), and specifically its size, not measured so far, has been indicated as a key probe to understand the nucleosynthesis mechanisms in relativistic heavy-ion collisions. This thesis focuses on ${}_{\Lambda }^3$H produced in relativistic ion-ion collision at GSI/SIS18 energies (up to 2 AGeV), in order to access its matter radius and possible production mechanisms. In the first part of the thesis, the concept of a new accepted experiment that will be performed in 2025 at the R${}^3$B setup in GSI using ${}^{12}$C+${}^{12}$C collisions at 1.9 AGeV is detailed. The experiment aims at the first determination of the ${}_{\Lambda }^3$H size, predicted to be a halo hypernucleus, through interaction cross section measurements. To achieve that, a new experimental method to extract the interaction cross section of hypernuclei with a target nucleus, sensitive to their matter radii, was developed. A precision of 15% or better in the interaction cross section can be achieved, allowing extraction of the unknown ${}_{\Lambda }^3$H matter radius and assessing its halo or non-halo character. In addition, realistic GEANT4 simulations have been performed in order to optimize the design of the experimental setup, including the main detector, the mini-HYDRA (HYpernuclei Decay at R${}^3$B Apparatus) time-projection chamber, and to assess the feasibility of the experiment. Finally, the design and validation of a new detector, the HYDRA plastic wall, is presented, which is intended to be used as a trigger in the measurement. The second part of the thesis focuses on the production mechanisms of ${}_{\Lambda }^3$H in heavy-ion collisions at the HADES setup in GSI. Here, the production is explored by analyzing existing datasets, taken in 2019 and 2012, with different collision energies, i.e., Ag+Ag at 1.58 AGeV and 1.23 AGeV, and Au+Au at 1.23 AGeV. While the first set is exactly at the strangeness production threshold from elementary nucleon-nucleon collisions (1.58 GeV) the others are below it. The data analysis identified clearly the ${}_{\Lambda }^3$H signal from the invariant mass of its decay products, π${}^{-}$+${}^3$He, for both the high and low energy datasets: the significance level for the peaks are 18.27, 5.16, and 4.00 for the Ag+Ag at 1.58 AGeV, 1.23 AGeV, and Au+Au at 1.23 AGeV, respectively. Following that, the associated production cross-sections at and below the strangeness production threshold are extracted and the production cross section ratio of low-to-high energy from the Ag+Ag dataset amounts to 0.30±0.08(stat.)±0.03(sys.). These findings indicate contributions from additional production mechanisms for hypernuclei that need to be further investigated by comparing the experimental results with predictions from transport models.