Probing the Possible TeV Scale See-saw Origin of Neutrino Masses with Charged Lepton Flavour Violation Processes and Neutrino Mass Spectroscopy Using Atoms

In the first part of this thesis, we perform a detailed analysis of lepton flavour violation (LFV) within minimal see-saw type extensions of the Standard Model (SM), which give a viable mechanism of neutrino mass generation and provide new particle content at the electroweak scale. We focus, mainly, on predictions and constraints set on each scenario from muon and tau decays ($\mu\to e \gamma$, $\mu\to 3e$, $\tau\to (\mu,e) \gamma$ and $\tau\to 3\mu$) and $\mu-e$ conversion in the nuclei. In particular, we show that in some regions of the parameters space of type I and type II see-saw models, the Dirac and Majorana phases of the neutrino mixing matrix, the ordering and hierarchy of the light neutrino mass spectrum as well as the value of the reactor mixing angle $\theta_{13}$ may considerably affect the size of the LFV observables. Besides, the possibilities to observe the LFV processes in the present and future experiments are also considered. The analytic results of the LFV rates might help to discriminate between the three types of neutrino mass generation models considered. In the second part of the thesis, we study a process of collective de-excitation of atoms in a metastable level into emission mode of a single photon plus a neutrino pair, called radiative emission of neutrino pair (RENP). This process is sensitive to the absolute neutrino mass scale, to the neutrino mass hierarchy and to the nature (Dirac or Majorana) of massive neutrinos. We investigate how the indicated neutrino mass and mixing observables can be determined from the measurement of the corresponding continuous photon spectrum on the example of a transition between specific levels of the Yb atom. The possibility of determining the nature of massive neutrinos and, if neutrinos are Majorana fermions, of obtaining information about the Majorana phases in the neutrino mixing matrix, is analyzed in the cases of normal hierarchical, inverted hierarchical and quasi-degenerate types of neutrino mass spectrum. We find, in particular, that the sensitivity to the nature of massive neutrinos depends critically on the atomic level energy difference relevant in the RENP. \vspace{1cm} The content of this thesis is based on the following works: \begin{itemize} \item[ I, ] D.~N.~Dinh, A.~Ibarra, E.~Molinaro and S.~T.~Petcov, \\ \textit{The $\mu\to e$ Conversion in Nuclei, $\mu\rightarrow e +\gamma$, $\mu\rightarrow 3e$ Decays and TeV Scale See-Saw Scenarios of Neutrino Mass Generation},\\ JHEP {\bf 1208} (2012) 125, Erratum-ibid. 1309 (2013) 023 [arXiv:hep-ph/1205.4671v4]. %%% \item[ II, ] D.~N.~Dinh and S.~T.~Petcov,\\ \textit{Lepton Flavor Violating $\tau$ Decays in TeV Scale Type I See-saw and Higgs Triplet Models},\\ JHEP {\bf 09} (2013) 086 [arXiv:hep-ph/1308.4311]. %%% \item[ III, ] D.~N.~Dinh, S.~T.~Petcov, N.~Sasao, M.~Tanaka and M.~Yoshimura,\\ \textit{Observables in Neutrino Mass Spectroscopy Using Atoms},\\ Phys.\ Lett.\ B {\bf 719} (2013) 154 [arXiv:hep-ph/1209.4808]. \end{itemize} Other papers of the same author, which are not discussed in the thesis: \begin{itemize} \item[ I, ] D.~N.~Dinh and S.~T.~Petcov,\\ \textit{Sterile Neutrino Determination Using Radiative Emission of Neutrino Pair},\\ Work in progress. %%% \item[ II, ] D.~N.~Dinh, N.~A.~Ky, N.~T.~H.~Van and P.~Q.~Van,\\ \textit{Model of neutrino effective masses},\\ Phys.\ Rev.\ D {\bf 74} (2006) 077701. \end{itemize

Energies of the ground state and first excited 0+0^{+} state in an exactly solvable pairing model

Several approximations are tested by calculating the ground-state energy and the energy of the first excited $0^{+}$ state using an exactly solvable model with two symmetric levels interacting via a pairing force. They are the BCS approximation (BCS), Lipkin - Nogami (LN) method, random-phase approximation (RPA), quasiparticle RPA (QRPA), the renormalized RPA (RRPA), and renormalized QRPA (RQRPA). It is shown that, in the strong-coupling regime, the QRPA which neglects the scattering term of the model Hamiltonian offers the best fit to the exact solutions. A recipe is proposed using the RRPA and RQRPA in combination with the pairing gap given by the LN method. Applying this recipe, it is shown that the normal-superfluid phase transition is avoided, and a reasonably good description for both of the ground-state energy and the energy of the first excited $0^{+}$ state is achieved.Comment: 18 pages, 4 figure