Phenomenology of sterile neutrinos at different mass scales : neutrinoless double beta decay and neutrino oscillations

The existence of neutrino oscillation is the first evidence of physics beyond the Standard Model. It proves that neutrinos are massive and motivates the study of the neutrino nature, mixings and mass generation models. To have a better understanding of neutrino masses and mixings, the existence and character of sterile neutrinos would be an important factor. In this thesis, we will describe the phenomena of neutrinoless double beta decay and sterile neutrino oscillations. The studies of these two topics will contribute to understanding the properties of sterile neutrinos in the heavy and light mass regime. We first study the neutrinoless double beta decay process to tackle the issue about the nature of neutrino. Establishing the nature of neutrinos, whether they are Dirac or Majorana particles is one of the fundamental questions we need to answer in particle physics, and is related to the conservation of lepton number. Neutrinoless double beta decay is the tool of choice for testing the Majorana nature of neutrinos. However, up to now, this process has not been observed, but a wide experimental effort is taking place worldwide and soon new results will become available. Different mechanisms can induce neutrinoless double beta decay and might interfere with each other, potentially leading to suppressed contributions to the decay rate. This possibility would become of great interest if upcoming neutrino mass measurements from KATRIN and cosmological observations found that neutrino mass is larger than 0.2 eV but no positive signal was observed in neutrinoless double beta decay experiments. We focus on the possible interference between light Majorana neutrino exchange with other mechanisms, such as heavy sterile neutrinos and R-parity violating supersymmetric models. We show that in some cases the use of different nuclei would allow to disentangle the different contributions and allow to test the hypothesis of destructive interference. Finally, we present a model in which such interference can emerge and we discuss the range of parameters which would lead to a significant suppression of the decay rate. Heavy sterile neutrino is involved in the studies of neutrinoless double beta decay and mass generation involve. On the other hand, the effect of light sterile neutrino may be present in the oscillation experiments. To measure the light sterile neutrino mixing, high statistics measurements are necessary. A neutrino factory has been suggested as a powerful tool for studying new physics, for example, sterile neutrinos, exploiting its near detectors. Here, we use the new version of GLoBES to study the potential of a low energy neutrino factory (LENF) in constraining the sterile mixing angles and the mass-square difference. Unlike in conventional long baseline neutrino experiments, the electron neutrino disappearance and appearance channels are also included, since they have been proved helpful in constraining some of the mixing angles. We will explore the dependence of the performance of the LENF depending on different experimental setups, such as the detector type (TASD and LiAr), the energy range, the systematic errors. etc. Moreover, the re-analysis of reactor neutrino experiments suggests the presence of neutrino oscillations due to large sterile neutrino mixing with electron neutrino. We show that, with a near detector, LENF can constrain the sterile parameter values in a very small range and helps us to check the recent Reactor Anomaly.