Renormalization Group Evolution of Dirac Neutrino Masses

There are good reasons why neutrinos could be Majorana particles, but there exist also a number of very good reasons why neutrinos could have Dirac masses. The latter option deserves more attention and we derive therefore analytic expressions describing the renormalization group evolution of mixing angles and of the CP phase for Dirac neutrinos. Radiative corrections to leptonic mixings are in this case enhanced compared to the quark mixings because the hierarchy of neutrino masses is milder and because the mixing angles are larger. The renormalization group effects are compared to the precision of current and future neutrino experiments. We find that, in the MSSM framework, radiative corrections of the mixing angles are for large \tan\beta comparable to the precision of future experiments.Comment: 19 pages, 5 figures; error in eq. 8 corrected, references adde

S4 Flavor Symmetry and Fermion Masses: Towards a Grand Unified theory of Flavor

Pursuing a bottom-up approach to explore which flavor symmetry could serve as an explanation of the observed fermion masses and mixings, we discuss an extension of the standard model (SM) where the flavor structure for both quarks and leptons is determined by a spontaneously broken S4 and the requirement that its particle content is embeddable simultaneously into the conventional SO(10) grand unified theory (GUT) and a continuous flavor symmetry G_f like SO(3)_f or SU(3)_f. We explicitly provide the Yukawa and the Higgs sector of the model and show its viability in two numerical examples which arise as small deviations from rank one matrices. In the first case, the corresponding mass matrix is democratic and in the second one only its 2-3 block is non-vanishing. We demonstrate that the Higgs potential allows for the appropriate vacuum expectation value (VEV) configurations in both cases, if CP is conserved. For the first case, the chosen Yukawa couplings can be made natural by invoking an auxiliary Z2 symmetry. The numerical study we perform shows that the best-fit values for the lepton mixing angles theta_12 and theta_23 can be accommodated for normal neutrino mass hierarchy. The results for the quark mixing angles turn out to be too small. Furthermore the CP-violating phase delta can only be reproduced correctly in one of the examples. The small mixing angle values are likely to be brought into the experimentally allowed ranges by including radiative corrections. Interestingly, due to the S4 symmetry the mass matrix of the right-handed neutrinos is proportional to the unit matrix.Comment: 27 pages, published version with minor change

Synthesis of Stable 1H-Azirines Reinvestigated: A Structural Corrigendum

The isoquinoline-catalyzed synthesis of pretended 1H-azirines from phenacyl bromides and N,N\'-dialkylcarbodiimides was repeated. The products do not possess the structure of antiaromatic 1H-azirines, but simple N-acyl-N,N\'-dialkylureas were formed instead. This structural corrigendum was confirmed by the independent synthesis of the known ureas and comparison of their 1H NMR and 13C NMR spectroscopic data in the case of six compounds. Thus,1H-azirines keep their classification as very short-lived intermediates

Fermion Masses and Mixings from Dihedral Flavor Symmetries with Preserved Subgroups

We perform a systematic study of dihedral groups usedas flavor symmetry. The key feature here is the fact that we do not allow the dihedral groups to be broken in an arbitrary way, but in all cases some (non-trivial) subgroup has to be preserved. In this way we arrive at only five possible (Dirac) mass matrix structures which can arise, if we require that the matrix has to have a non-vanishing determinant and that at least two of the three generations of left-handed (conjugate) fermions are placed into an irreducible two-dimensional representation of the flavor group.We show that there is no difference between the mass matrix structures for single- and double-valued dihedral groups. Furthermore, we comment on possible forms of Majorana mass matrices. As a first application we find a way to express the Cabibbo angle, i.e. the CKM matrix element |V_{us}|, in terms of group theory quantities only, the group index n, the representation index j and the index m_{u,d} of the different preserved subgroups in the up and down quark sector: |V_{us}|=| cos (pi (m_{u}-m_{d}) j/n ) | which is |cos (3 pi/7)| \approx 0.2225 for n=7, j=1, m_{u}=3 and m_{d}=0. We prove that two successful models which lead to maximal atmospheric mixing and vanishing theta_{13} in the lepton sector are based on the fact that the flavor symmetry is broken in the charged lepton, Dirac neutrino and Majorana neutrino sector down to different preserved subgroups whose mismatch results in the prediction of these mixing angles. This also demonstrates the power of preserved subgroups in connection with the prediction of mixing angles in the quark as well asin the lepton sector

Direct observation and characterisation of 3-azido-2H-azirines: postulated, but highly elusive intermediates

For the first time, successful synthesis of an unknown class of compounds, 3-azido-2H-azirines, which are implicated as highly reactive intermediates in the thermolysis of the corresponding 1,1-diazidoethenes, has been performed. These elusive heterocycles have been detected and characterised by low-temperature NMR and in situ IR spectroscopy. Even the parent compound, 3-azido-2H-azirine, has been observed via low-temperature photolysis of 1,1-diazidoethene, as a highly reactive species with a half-life period of only 12 min at −40 °C.Dieser Beitrag ist aufgrund einer (DFG-geförderten) Allianz- bzw. Nationallizenz frei zugänglich

Synthesis, Characterization and Reactions of (Azidoethynyl)trimethylsilane

Synthesis of azido(trimethylsilyl)acetylene (6) was performed by treating the iodonium salt 5 with highly soluble hexadecyltributylphosphonium azide (QN3) at −40 °C. Although this product is very unstable, it can nevertheless be trapped by the click reaction with cyclooctyne to give the corresponding 1,2,3-triazole, and also directly characterized by 1H- and 13C-NMR data as well as IR-spectra, which were measured in solution at low temperature and in the gas phase. The thermal or photochemical decay of azide 6 leads to cyano(trimethylsilyl)carbene. This is demonstrated not only by quantum chemical calculations, but also by the trapping reactions with the help of isobutene