Study of the hyperon-nucleon interaction via femtoscopy in elementary systems with HADES and ALICE

n this thesis the interaction of Λ Hyperons with protons is studied. This interaction is important to understand various physical systems e.g. the behavior of neutron stars. The connection of the hadron interaction and properties of neutron stars is discusses in more details in the introduction of the thesis. The method with which the interaction is investigated is femtoscopy. It is based on the measurement of pairs at small relative momenta. This allows to establish a two-particle correlation function. This is discussed in more details at the beginning of the thesis. Making different approximations allows to compare the experimental correlation function with one based on a mathmatical framework, which includes the interaction parameter of the particle pair. This allows to test and compare different predictions from theories or models. In this thesis recent calculations of a chiral effective field theory is tested. In the first part of the thesis a study of a two-particle correlation function of proton-proton and proton-Λ pairs at the HADES experiment is performed. These pairs were produced in reaction of p+Nb, where the proton had a kinetic energy of 3.5 GeV. At the beginning, all experimental correlation function were corrected for various detector effects. Here the finite momentum resolution of HADES and the effect of “track merging” played the most significant role. A comparison of the proton-proton correlation function with a model calculation allowed the extraction of the source size of the system. This allowed together with help of UrQMD simulations to fix the source size of proton-Λ. This reduced the free source size parameter of proton-Λ and the theoretical correlation function depends then only on the parameters of the interaction. It showed up that the theoretical correlation function is sensitive to the values of the interaction parameter. To see this the parameter sets of “leading-order” (LO) and “next-to-leading-order” (NLO) were tested. These two expansions differ quite significantly in the predictions of the total cross section for small Λ momenta. The collected pair statistics was not sufficient to distinguish between both predictions. In the second part of the thesis the analysis was repeated in a collision system of protons at a center of mass energy of 7 TeV. The collisions were recorded by the ALICE experiment. In this analysis the source size parameter was determined by a simultaneous fit of the proton-proton and proton-Λ correlation function. For the interaction of proton-Λ pairs the NLO parameter set was chosen. After the fit was performed the LO parameters were plugged in to the theoretical correlation function to explore possible differences. It showed up, that the correlation function is sensitive to the values of the scattering parameter. However, also there the collected pair statistics was not sufficient to draw a definite conclusion.