Charged lepton mixing via heavy sterile neutrinos

Pseudoscalar meson decay leads to an entangled state of charged leptons ($\mu,e$) and massive neutrinos. Tracing out the neutrino degrees of freedom leads to a reduced density matrix for the charged leptons whose off-diagonal elements reveal \emph{charged lepton oscillations}. Although these decohere on unobservably small time scales $\lesssim 10^{-23} s$ they indicate charged lepton \emph{mixing} as a result of common intermediate states. The charged lepton self energy up to one loop features flavor off-diagonal terms responsible for charged lepton mixing: a dominant ``short distance'' contribution with $W$ bosons and massive neutrinos in the intermediate state, and a subdominant ``large distance'' contribution with pseudoscalar mesons and massive neutrinos in the intermediate state. Mixing angle(s) are GIM suppressed, and are \emph{momentum and chirality dependent}. The difference of negative chirality mixing angles near the muon and electron mass shells is $\theta_L(M^2_\mu) -\theta_L(M^2_e)\propto G_F \sum U_{\mu j} m^2_j U^*_{j e}$ with $m_j$ the mass of the neutrino in the intermediate state. Recent results from TRIUMF, suggest an upper bound $\theta_L(p^2\simeq M^2_\mu)-\theta_L(p^2 \simeq M^2_e) < 10^{-14}\,\Big(M_S/\mathrm{100}\,MeV\Big)^2$ for one generation of a heavy sterile neutrino with mass $M_S$. We obtain the wavefunctions for the propagating modes, and discuss the relation between the lepton flavor violating process $\mu \rightarrow e\gamma$ and charged lepton mixing, highlighting that a measurement of such process implies a mixed propagator $\mu, e$. Furthermore writing flavor diagonal vertices in terms of mass eigenstates yields novel interactions suggesting further contributions to lepton flavor violating process as a consequence of momentum and chirality dependent mixing angles.Comment: 26 pages, 5 fig

Computational studies of stereochemical effects in the synthesis of sugar mimics

Density Functional methods are used to model the tandem aza-Cope rearrangement – Mannich cyclization reaction leading to substituted acylpyrrolidines. The ultimate goal is to determine optimum reaction conditions that maximize stereoselectivity, as only one set of stereoisomers is pharmacologically active. Three aspects of the reaction are investigated. First, we determine the relative size of three rotational barriers in the interconversion of two iminium cation stereoisomers that are precursors to the aza-Cope rearrangement. The lowest energy pathway for the interconversion is identified, as well as the relative stability of the two stereoisomers for two different substituents: diphenyl and methyl. Activation barriers are found to be not much above 10 kcal/mol in all cases and therefore all stereoisomers are expected to be present in solution. We also investigate the relative stability of reactants, intermediates and products for four, differently-substituted iminium cations undergoing the aza-Cope – Mannich tandem reaction. In addition, activation barriers for each step of the reaction are calculated. Regardless of substituent size and position, the energetics of the reaction do not predict either cis or trans acylpyrrolidine product to be favored. Finally, the epimerization of these acylpyrrolidine products is examined by considering two possible mechanisms: keto-enol tautomerism and retro-Mannich - Mannich cyclization. The data suggest that epimerization is not likely to occur via either mechanism, as one of the intermediates common to both pathways is too high in energy

Topics in Neutrino Physics and Cosmology

This thesis focuses on timely issues in particle physics of neutrino phenomenology and cosmology. In this work, the methods of quantum optics, quantum field theory in curved spacetime and non-equilibrium field theory are employed to study the issues of inflation and neutrino mixing and oscillations in terrestrial and cosmological settings. Anomalies in short baseline oscillation experiments have provided hints of an additional neutrino species which are used as motivation to study potential experimental signatures through decays at rest, modifications to the treatment of appearance/disappearance oscillation experiments and experiments searching for lepton number violation. The role of decoherence and entanglement in the production mechanism of a two body decay is explored further in Minkowski and de Sitter spacetime with the aim of studying correlations in the CMB. This work is extended in Minkowski spacetime by studying decoherence issues in the cascade decay of successive two body decays with the aim of searching for new particles. The effect of initial conditions for inflation is explored with the motivation of persistent large scale anomalies and with an eye towards the soon-to-be-measured tensor to scalar ratio. Inclusion of these non-trivial initial conditions introduces large scale power suppression and potentially observable oscillations into the tensor to scalar ratio. The issue of dark matter is explored through the possibility of previously unstudied sources a sterile neutrino dark matter candidate. Pions, which are the most abundant particle after the QCD phase transition, can lead to the production of sterile neutrinos which yields a non negligible abundance of dark matter compared to established mechanisms in the literature. This additional source of sterile neutrino naturally leads to a multi component distribution function and a natural scenario for mixed dark matter. Furthersources of sterile neutrinos are discussed and the possibility of sterile neutrinos produced at electroweak temperatures is explored and leads to a generalized temperature dependence of active sterile mixing