Λ-d and p-d correlations in pp and Pb – Pb collisions with ALICE

The aim of this work is to study the Λ-d and p-d two-particle intensity correlations at different source sizes. This is done using collision data produced at the Large Hadron Collider (LHC). Two different collision systems are investigated: proton-proton collisions (pp collisions) and the collision of two nuclei (Pb – Pb collisions). In the context of these collision systems, there are normally two production approaches discussed: the statistical hadronization model and, mostly for the formation of nuclei, also the coalescence model. The first one describes the yields of produced particles at the chemical freeze-out, the latter predicts the production of nuclei via the overlap of the wave function in phase space of its constituents. Within this thesis, a formula derived by Koonin and Pratt is used to connect the measurement of two-particle momentum correlations with theoretical calculations. The measurement is performed using data collected by the ALICE Collaboration, whose experiment is located at the Large Hadron Collider (LHC) at CERN. This setup was originally built to study the formation, evolution, and properties of the Quark-Gluon Plasma via the collision of heavy nuclei. However, its experimental range is not limited to these kinds of studies. Because of its excellent momentum resolution, also at low transverse momenta, it is a very good detector setup for correlation measurements. Two different collision systems have been analyzed: pp collisions at √s = 13 TeV and Pb – Pb collisions at √sNN = 5.02 TeV. In the case of heavy-ion collisions, two different centralities have been investigated: semi-central and central. For central collisions, the two nuclei collide head-on, whereas in case of semi-central collisions, the two nuclei only hit each other partially. For the measured correlation function to be calculated, a distribution of the relative momentum between the two particles was calculated, as well as an uncorrelated distribution. The method of event mixing was chosen for the generation of uncorrelated pairs because it is a well-established method. To calculate the mixed-event distribution, the relative momentum of two measured particles within different, but similar, events is computed. To make sure that only similar events are mixed, event classes are introduced, ensuring that only events with similar centralities and positions of the collision point in beam direction are mixed. By dividing the two distributions, same-event and mixed-event distributions, the correlation function is estimated. Since the order of magnitude of mixed-events is much higher than for same-events, the correlation has to be normalized. Therefore, a procedure is introduced to normalize the measured correlation function to one, well outside the low relative momentum range, where the strong and Coulomb interactions take place. In addition to the normalization, also a correction for the finite momentum resolution is applied. Therefore, Monte Carlo simulations for all different investigated systems have been used to receive a matrix for the generated versus reconstructed momenta, providing also a relative momentum resolution of about 4 MeV/c for low relative momentum in the investigated systems. Two alternative approaches to obtain a background distribution have been studied: pair rotation and fixing the opening angle between the particle pair. In both cases 10 particle pairs have been generated per same-event entry. Within the pair rotation method, the momentum vector of one of the particle is rotated in its azimuthal angle to obtain a new particle pair with a new relative momentum. The second approach keeps the angle between the particle pair fixed but randomizes the length of one of the particle momentum vectors to obtain a new relative momentum. The latter showed significant improvements in small source sizes (pp collisions), since all angular correlations are transferred into the background distribution. The differences between the three methods have been used to quantify the corresponding systematic uncertainties. The final corrected correlation functions of the measurement are presented for Λ-d and p-d pairs. First, a comparison between matter and antimatter for all studied systems is presented, showing no significant deviations. Therefore, the measured correlations of matter and antimatter pairs can be combined to get the maximum statistics. To evaluate the significance of the measured correlations, the so-called λ-parameters have been calculated. As such, the purity of each particle sample, as well as their primary fraction, have been estimated. These values provide insights about the amount of correctly identified primary particles within the measured correlation functions. The results show that most of the measurements have λ-parameters higher than 80 %, only with p-d in central lead collisions going down to about 75 %. The measured correlation functions, including their λ-parameters and systematic uncertainties are presented for the investigated collision systems. The correlations for p-d show a depletion towards low relative momentum, whereas the Λ-d correlation functions rise with decreasing k∗. The results of the p-d correlations are additionally compared to published correlation functions by the ALICE Collaboration. To compare the measured correlations with theoretically predicted calculations, several computations have been performed using the Lednický-Lyuboshits model, based on the effective-range approximation as well as a potential-based model for the p-d correlations. The first model depends on the scattering lengths and the effective ranges of the specific particle pair using published scattering parameters. The second model was designed to describe the p-d correlation function within high-energy collisions and is based on the 2-body Argonne v18 and 3-body Urbana IX interaction potentials. These calculated correlation functions are then used to study the size of the particle-emitting source of the particle collisions. Hereby, a special emphasis is placed on the impact of large-scale particles like deuterons on the determination procedure. In order to determine the size of the particle-emitting source, two approaches were tested. First, the source size of the collision systems is determined using a known dependence on the transverse mass of the particle system. This dependence was measured and published by the ALICE Collaboration, which can be used to estimate the corresponding source size for the six systems investigated within this analysis. In a second approach, the calculated correlation functions were used to determine the most probable size of the particle-emitting source. The two approaches do provide different results, especially for the p-d correlations in pp collisions. In addition, the latter comparison indicates a lower threshold of the determinable source size, especially for p-d correlations. One possible explanation could be the size of the deuteron, which, in the case of pp collisions, is about twice as large as the expected source size. In order to take into account this effect, the matter radius of the deuteron is used to correct the source sizes determined using the transverse-mass scaling, resulting in a better description of the experimental data. Alternatively, the transverse-mass definition could be rewritten, treating the two-particle pairs as three-body systems. This leads to an additional set of determined source sizes without a lower threshold of the resolvable source size, also describing most of the determined source sizes satisfactorily. Since the scattering parameters of the doublet-spin channel of the Λ-d particle pair are connected to the Λ separation energy of the hypertriton, an estimation of this energy could be made using the measured Λ-d correlation functions. Therefore, a simultaneous fit of the Λ-d correlations obtained in three different collision systems is performed in order to determine the doublet-spin scattering parameters. These can be used to calculate the Λ separation energy. The result is compared to a recent determination of the Λ separation energy by the STAR Collaboration using the same approach.