Texture-zero model for the lepton mass matrices

We suggest a simple model, based on the type-I seesaw mechanism, for the lepton mass matrices. The model hinges on an Abelian symmetry which leads to mass matrices with some vanishing matrix elements. The model predicts one massless neutrino and $M_{e\mu} = 0$ ($M$ is the effective light-neutrino Majorana mass matrix). We show that these predictions perfectly agree with the present experimental data if the neutrino mass spectrum is inverted, i.e. if $m_3 = 0$, provided the Dirac phase $\delta$ is very close to maximal ($\pm \pi / 2$). In the case of a normal neutrino mass spectrum, i.e. when $m_1 = 0$, the agreement of our model with the data is less than optimal---the reactor mixing angle $\theta_{13}$ is too small in our model. Minimal leptogenesis is not an option in our model due to the vanishing elements in the Yukawa-coupling matrices.Comment: 10 pages, 3 figures; version for journal: new fit to data, new plot

New textures for the lepton mass matrices

We study predictive textures for the lepton mass matrices in which the charged-lepton mass matrix has either four or five zero matrix elements while the neutrino Majorana mass matrix has, respectively, either four or three zero matrix elements. We find that all the viable textures of these two kinds share many predictions: the neutrino mass spectrum is inverted, the sum of the light-neutrino masses is close to 0.1 eV, the Dirac phase $\delta$ in the lepton mixing matrix is close to either $0$ or $\pi$, and the mass term responsible for neutrinoless double-beta decay lies in between 12 and 22 meV.Comment: 31 pages, 6 figure

Spatially resolved physical and chemical properties of the planetary nebula NGC 3242

Optical integral-field spectroscopy was used to investigate the planetary nebula NGC 3242. We analysed the main morphological components of this source, including its knots, but not the halo. In addition to revealing the properties ofthe physical and chemical nature of this nebula, we also provided reliable spatially resolved constraints that can be used for future photoionisation modelling of the nebula. The latter is ultimately necessary to obtain a fully self-consistent 3D picture of the physical and chemical properties of the object. The observations were obtained with the VIMOS instrument attached to VLT-UT3. Maps and values for specific morphological zones for the detected emission-lines were obtained and analysed with routines developed by the authors to derive physical and chemical conditions of the ionised gas in a 2D fashion. We obtained spatially resolved maps and mean values of the electron densities, temperatures, and chemical abundances, for specific morphological structures in NGC 3242. These results show the pixel-to-pixel variations of the the small- and large-scale structures of the source. These diagnostic maps provide information free from the biases introduced by traditional single long-slit observations. In general, our results are consistent with a uniform abundance distribution for the object, whether we look at abundance maps or integrated fluxes from specified morphological structures. The results indicate that special care should be taken with the calibration of the data and that only data with extremely good signal-to-noise ratio and spectral coverage should be used to ensure the detection of possible spatial variations.Comment: 11 pages, 8 figures accepted for publication in Astronomy & Astrophysic

First- and second-order phase transitions in Ising models on small world networks, simulations and comparison with an effective field theory

We perform simulations of random Ising models defined over small-world networks and we check the validity and the level of approximation of a recently proposed effective field theory. Simulations confirm a rich scenario with the presence of multicritical points with first- or second-order phase transitions. In particular, for second-order phase transitions, independent of the dimension d_0 of the underlying lattice, the exact predictions of the theory in the paramagnetic regions, such as the location of critical surfaces and correlation functions, are verified. Quite interestingly, we verify that the Edwards-Anderson model with d_0=2 is not thermodynamically stable under graph noise.Comment: 12 pages, 12 figures, 1 tabl

Flavour symmetries in a renormalizable SO(10) model

In the context of a renormalizable supersymmetric SO(10) Grand Unified Theory, we consider the fermion mass matrices generated by the Yukawa couplings to a $\mathbf{10} \oplus \mathbf{120} \oplus \bar{\mathbf{126}}$ representation of scalars. We perform a complete investigation of the possibilities of imposing flavour symmetries in this scenario; the purpose is to reduce the number of Yukawa coupling constants in order to identify potentially predictive models. We have found that there are only 14 inequivalent cases of Yukawa coupling matrices, out of which 13 cases are generated by $Z_n$ symmetries, with suitable $n$, and one case is generated by a $Z_2 \times Z_2$ symmetry. A numerical analysis of the 14 cases reveals that only two of them---dubbed A and B in the present paper---allow good fits to the experimentally known fermion masses and mixings.Comment: 36 pages, no figures, revised fits using newer data, added fit for case A, added references, new appendices concerning the SO(10) scalar potential and inequalities for the vacuum expectation values, conclusions unchanged; some minor changes, matches published versio