Massive neutrinos in the standard model and beyond

The generation of the fermion mass hierarchy in the standard model of particle physics is a long-standing puzzle. The recent discoveries from neutrino physics suggests that the mixing in the lepton sector is large compared to the quark mixings. To understand this asymmetry between the quark and lepton mixings is an important aim for particle physics. In this regard, two promising approaches from the theoretical side are grand unified theories and family symmetries. In the first part of my thesis we try to understand certain general features of grand unified theories with Abelian family symmetries by taking the simplest SU(5) grand unified theory as a prototype. We construct an SU(5) toy model with U(1) F ⊗Z'2 ⊗Z'' 2⊗Z''' 2 family symmetry that, in a natural way, duplicates the observed mass hierarchy and mixing matrices to lowest approximation. The system for generating the mass hierarchy is through a Froggatt-Nielsen type mechanism. One idea that we use in the model is that the quark and charged lepton sectors are hierarchical with small mixing angles while the light neutrino sector is democratic with larger mixing angles. We also discuss some of the difficulties in incorporating finer details into the model without making further assumptions or adding a large scalar sector.;In the second part of my thesis, the interaction of high energy neutrinos with weak gravitational fields is explored. The form of the graviton-neutrino vertex is motivated from Lorentz and gauge invariance and the non-relativistic interpretations of the neutrino gravitational form factors are obtained. We comment on the renormalization conditions, the preservation of the weak equivalence principle and the definition of the neutrino mass radius. We associate the neutrino gravitational form factors with specific angular momentum states. Based on Feynman diagrams, spin-statistics, CP invariance and symmetries of the angular momentum states in the neutrino-graviton vertex, we deduce differences between the Majorana and Dirac cases. It is then proved that in spite of the theoretical differences between the two cases, as far as experiments are considered, they would be virtually indistinguishable for any space-time geometry satisfying the weak field condition. We then calculate the transition gravitational form factors for the neutrino by evaluating the relevant Feynman diagrams at 1-loop and estimate a neutrino transition mass radius. The form factor is seen to depend on the momentum transfer very weakly. It is also seen that the neutrino transition mass radius is smaller than the typical neutrino charge radius by a couple of orders of magnitude.;In the final part of my thesis, some of the recent neutrino observations and anomalies are revisited, in the context of sterile neutrinos. Among our aims is to understand more clearly some of the analytic implications of the current global neutrino fits from short baseline experiments. Of particular interest to us are the neutrino disappearance measurements from MINOS and the recent indications of a possibly non-vanishing angle, theta13 , from T2K, MINOS and Double-CHOOZ. Based on a general parametrization motivated in the presence of sterile neutrinos, the consistency of the MINOS disappearance data with additional sterile neutrinos is discussed. We also explore the implications of sterile neutrinos for the measurement of | Umu3| in this case. We then turn our attention to the study of |Ue3| extraction in electron neutrino disappearance and appearance measurements. In particular, we study the effects of some of the additional CP phases that appear when there are sterile neutrinos. We observe that the existence of sterile neutrinos may induce a significant modification of the theta13 angle in neutrino appearance experiments like T2K and MINOS, over and above the ambiguities and degeneracies that are already present in 3-neutrino parameter extractions. There are reactor experiments, for instance those measuring nu e disappearance like Double-CHOOZ, Daya Bay and RENO, where this modification is less significant and therefore the extracted | Ue3| value when sterile neutrinos are present is close to the one that would be obtained in the 3-neutrino case. Based on our study, we also conclude that the results from T2K imply a 90% C.L. lower-bound on |Ue3|, in the "3 + 2" neutrino case, which is still within the sensitivity of future reactor neutrino experiments like Daya Bay, and consistent with the one-sigma range of sin22theta 13 recently reported by the Double-CHOOZ experiment. Finally, we argue that for the recently determined best-fit parameters, the results in the "3 + 1" scenario would be very close to the medium/long baseline results obtained in the "3 + 2" case analyzed in this work.