Neutrino oscillations at the ESSnuSB experiment

Sammanfattning: This report aims to study the phenomenon of neutrino oscillations through derivation of the formulas for their transition probabilities in two flavors and expansions thereof in three flavors. By studying the series expansions of the transition probabilities in three flavors, one could get a clearer understanding of the effect of matter and the CP-violating phase, $\delta_{CP}$ on neutrino oscillations. The purpose of investigating this is to be able to investigate the impact of matter and $\delta_{CP}$ at the potential experiment ESSnuSB. The ESSnuSB experiment would be an extension of the linear accelerator project European Spallation Source, ESS, that is currently under construction in Lund, Sweden. The ESSnuSB aims to study neutrino oscillations at the second oscillation maximum which, through the derivations, was found at 540 km from the ESS which is consistent with other studies. The mine in Garpenberg is located 540~km from the ESS, which makes it a prime candidate for a detector to be built within.