Critical measures, quadratic differentials, and weak limits of zeros of Stieltjes polynomials

We investigate the asymptotic zero distribution of Heine-Stieltjes polynomials - polynomial solutions of a second order differential equations with complex polynomial coefficients. In the case when all zeros of the leading coefficients are all real, zeros of the Heine-Stieltjes polynomials were interpreted by Stieltjes as discrete distributions minimizing an energy functional. In a general complex situation one deals instead with a critical point of the energy. We introduce the notion of discrete and continuous critical measures (saddle points of the weighted logarithmic energy on the plane), and prove that a weak-* limit of a sequence of discrete critical measures is a continuous critical measure. Thus, the limit zero distributions of the Heine-Stieltjes polynomials are given by continuous critical measures. We give a detailed description of such measures, showing their connections with quadratic differentials. In doing that, we obtain some results on the global structure of rational quadratic differentials on the Riemann sphere that have an independent interest.Comment: 70 pages, 14 figures. Minor corrections, to appear in Comm. Math. Physic

Critical view of the claimed Θ+\Theta^+ pentaquark

We use a theoretical model of the $\gamma ~d \to ~K^+ K^- ~n ~p$ reaction adapted to the experiment done at LEPS where a peak was observed and associated to the $\Theta^{+}(1540)$ pentaquark. The study shows that the method used in the experiment to associate momenta to the undetected proton and neutron, together with the chosen cuts, necessarily creates an artificial broad peak in the assumed $K^+ n$ invariant mass in the region of the claimed $\Theta^{+}(1540)$. It is shown that the LEPS fit to the data, used to make the claim of the $\Theta^{+}(1540)$, grossly distorts the background. An alternative fit, assuming a background plus a fluctuation, returns a background practically equal to the theoretical one and a fluctuation identical to the one seen in the experimental $K^- p$ spectrum of 2$\sigma$ significance.Comment: Conference Proceedin

Fermion mass and mixing pattern in a minimal T7 flavor 331 model

We present a model based on the $SU(3)_{C}\otimes SU(3)_{L}\otimes U(1)_{X}$ gauge symmetry having an extra $T_{7}\otimes Z_{2}\otimes Z_{3}\otimes Z_{14}$ flavor group, which successfully describes the observed SM fermion mass and mixing pattern. In this framework, the light active neutrino masses arise via double seesaw mechanism and the observed charged fermion mass and quark mixing hierarchy is a consequence of the $Z_{2}\otimes Z_{3}\otimes Z_{14}$ symmetry breaking at very high energy. In our minimal $T_{7}$ flavor 331 model, the spectrum of neutrinos includes very light active neutrinos as well as heavy and very heavy sterile neutrinos. The model has in total 16 effective free parameters, which are fitted to reproduce the experimental values of the 18 physical observables in the quark and lepton sectors. The obtained physical observables for both quark and lepton sectors are compatible with their experimental values. The model predicts the effective Majorana neutrino mass parameter of neutrinoless double beta decay to be $$ 3 and 40 meV for the normal and the inverted neutrino spectrum, respectively. Furthermore, our model features a vanishing leptonic Dirac CP violating phase.Comment: 18 pages. Final version. To be published in Journal of Physics G. arXiv admin note: substantial text overlap with arXiv:1309.656

A predictive 331331 model with A4A_{4} flavour symmetry

We propose a predictive model based on the $SU(3)_{C}\otimes SU(3)_{L}\otimes U(1)_{X}$ gauge group supplemented by the $A_{4}\otimes Z_{3}\otimes Z_{4}\otimes Z_{6}\otimes Z_{16}$ discrete group, which successfully describes the SM fermion mass and mixing pattern. The small active neutrino masses are generated via inverse seesaw mechanism with three very light Majorana neutrinos. The observed charged fermion mass hierarchy and quark mixing pattern are originated from the breaking of the $Z_{4}\otimes Z_{6}\otimes Z_{16}$ discrete group at very high scale. The obtained values for the physical observables for both quark and lepton sectors are in excellent agreement with the experimental data. The model predicts a vanishing leptonic Dirac CP violating phase as well as an effective Majorana neutrino mass parameter of neutrinoless double beta decay, with values $m_{\beta \beta }=$ 2 and 48 meV for the normal and the inverted neutrino mass hierarchies, respectively.Comment: 20 pages. Final version published in Nuclear Physics

An analysis of the Lattice QCD spectra for Ds0∗(2317)D^*_{s0}(2317) and Ds1∗(2460)D^*_{s1}(2460)

In this talk I present the results obtained using effective field theories in a finite volume from a reanalysis of lattice data on the $KD^{(*)}$ systems, where bound states of $KD$ and $KD^*$ are found and associated with the states $D^*_{s0}(2317)$ and $D^*_{s1}(2460)$, respectively. We confirm the presence of such states on the lattice data and determine the weight of the $KD$ channel in the wave function of $D^*_{s0}(2317)$ and that of $KD^*$ in the wave function of $D^*_{s1}(2460)$. Our results indicate a large meson-meson component in both cases.Comment: Conference Proceedings, Hadron 2017, Salamanca, Spai

An automated system for lung nodule detection in low-dose computed tomography

A computer-aided detection (CAD) system for the identification of pulmonary nodules in low-dose multi-detector helical Computed Tomography (CT) images was developed in the framework of the MAGIC-5 Italian project. One of the main goals of this project is to build a distributed database of lung CT scans in order to enable automated image analysis through a data and cpu GRID infrastructure. The basic modules of our lung-CAD system, a dot-enhancement filter for nodule candidate selection and a neural classifier for false-positive finding reduction, are described. The system was designed and tested for both internal and sub-pleural nodules. The results obtained on the collected database of low-dose thin-slice CT scans are shown in terms of free response receiver operating characteristic (FROC) curves and discussed.Comment: 9 pages, 9 figures; Proceedings of the SPIE Medical Imaging Conference, 17-22 February 2007, San Diego, California, USA, Vol. 6514, 65143