The Oscillation of the Sterile Neutrino

Built from the foundational concepts of quantum mechanics, the standard model of physics lays out explicitly the fundamental particles of the universe and their interactions. Neutrinos are the most mysterious particles in the standard model, as they are both incredibly difficult to detect and there is still much to discover about their properties. One such example is that for many years neutrinos were thought to be massless, only to be disproved by the winners of the 2015 Nobel Prize in physics, yet we still do not know the exact mass of each type of neutrino. Neutrinos have experimentally been found to change between the three known types as the particles travel long distances. When these neutrinos switch between types we find that the probability that the neutrino exists within one of the three known types does not add up to one. This gap allows for the existence of a new kind of neutrino, which physicists have proposed as the sterile neutrino. The concept of the sterile neutrino first arose when neutrino detectors found that neutrinos were oscillating over distances that were too short for conventional neutrinos both in the 1990s and again in 2018. Physicists began to explore alternatives to the active neutrinos, arriving at the sterile neutrino. Using fundamental charge-parity symmetry and the lepton mixing matrix, researchers have explored the potential for a sterile neutrino as an addition to the standard model through calculating its probability of oscillation with other neutrino flavors. This sterile neutrino has the potential to explain many phenomena in our universe, such as the composition of dark matter, the mass of neutrinos, and the standard model itself. This thesis will begin with an overview of quantum mechanics to introduce to the reader crucial concepts for later calculations regarding the sterile neutrino. I will subsequently dive deeper into the standard model of physics and both the properties and history of the neutrino. Afterwards I will go in depth about the various categories and origins of neutrinos, such as geo-neutrinos from the core of the earth. I will go into detail about detection methods, particularly the liquid scintillator method used to detect the first neutrinos. Once comfortable with the concept of neutrinos, I will seek to explore their probability of oscillation by introducing the lepton mixing matrix. Through calculating the probability of oscillation in the case of the conventional neutrinos, this will demonstrate that the probability that a neutrino exists in one of these three states does not add up to one thus allowing for the possibility of a fourth sterile neutrino. Subsequently I will expand upon this concept by calculating the probability of oscillation for the introduction of a fourth sterile neutrino, and show that by including an additional type of neutrino the probability of being in one of the four states adds up to one. Finally, I will explore the implications of this on a larger scale for future physics research