Proton source measurements in Pb—Pb collisions at the LHC with femtoscopy using an EFT model for the strong potential

In this thesis, the proton-emitting sources created in ultrarelativistic heavy-ion collisions are explored using methods of femtoscopy. The first part of this study addresses the importance of accounting for the strong interaction between protons from a theoretical point of view, and it develops an original analytical quantum mechanical calculation. The second part involves the experimental analysis of the data collected by ALICE during Run 3, presenting one- and three-dimensional femtoscopic measurements of the proton source in Pb--Pb collisions at $\sqrt{s_{NN}} = 5.36$ TeV. The experimental analysis utilizes the theoretical formalism developed in this study. The one-dimensional results, obtained as a function of the pair transverse momentum $k_T$ and centrality, indicate that the radii scale with $k_T$ due to the presence of radial flow in the system. The proton-emitting sources are found to be smaller in more peripheral collisions. The extracted radii are compared to the previous ALICE proton source measurements in Pb--Pb collisions at $\sqrt{s_{NN}} = 5.02$ TeV. The ''scaling hypothesis'' is tested by comparing multiplicity-dependent one-dimensional proton radii across different colliding systems. Signs of the common multiplicity scaling are found. New to the heavy-ion collision field, the experimental measurement of the proton source is extended to three dimensions proposing a novel approach to the problem. Three-dimensional proton radii are extracted in three centrality and three $k_T$ ranges, providing proof-of-principle that a three-dimensional experimental characterization of the proton-emitting source is viable. The behavior of the measured radii is examined and future perspectives for these measurements are discussed.