Composition Operators on the Dirichlet Space and Related Problems

In this paper we investigate the following problem: when a bounded analytic function $\phi$ on the unit disk $\mathbb{D}$, fixing 0, is such that $\{\phi^n : n = 0, 1, 2, . . . \}$ is orthogonal in $\mathbb{D}$?, and consider the problem of characterizing the univalent, full self-maps of $\mathbb{D}$ in terms of the norm of the composition operator induced. The first problem is analogous to a celebrated question asked by W. Rudin on the Hardy space setting that was answered recently ([3] and [15]). The second problem is analogous to a problem investigated by J. Shapiro in [14] about characterization of inner functions in the setting of $H^2$.Comment: 8 pages, 1 figure. See also http://webdelprofesor.ula.ve/nucleotachira/gchacon or http://webdelprofesor.ula.ve/humanidades/grchaco

Kaon oscillations in the Standard Model and Beyond using Nf=2 dynamical quarks

We compute non-perturbatively the B-parameters of the complete basis of four-fermion operators needed to study the Kaon oscillations in the SM and in its supersymmetric extension. We perform numerical simulations with two dynamical maximally twisted sea quarks at three values of the lattice spacing on configurations generated by the ETMC. Unwanted operator mixings and O(a) discretization effects are removed by discretizing the valence quarks with a suitable Osterwalder-Seiler variant of the Twisted Mass action. Operators are renormalized non-perturbatively in the RI/MOM scheme. Our preliminary result for BK(RGI) is 0.73(3)(3).Comment: 7 pages, 3 figures, 1 table, proceedings of the XXVII Int'l Symposyum on Lattice Field Theory (LAT2009), July 26-31 2009, Peking University, Beijing (China

B-physics computations from Nf=2 tmQCD

We present an accurate lattice QCD computation of the b-quark mass, the B and Bs decay constants, the B-mixing bag-parameters for the full four-fermion operator basis, as well as estimates for \xi and f_{Bq}\sqrt{B_q} extrapolated to the continuum limit and the physical pion mass. We have used Nf = 2 dynamical quark gauge configurations at four values of the lattice spacing generated by ETMC. Extrapolation in the heavy quark mass from the charm to the bottom quark region has been carried out using ratios of physical quantities computed at nearby quark masses, having an exactly known infinite mass limit.Comment: 7 pages, 4 figures, presented at the 31st International Symposium on Lattice Field Theory (Lattice 2013), 29 July - 3 August 2013, Mainz, German

K^0-\bar{K}^0 mixing in the Standard Model from Nf=2+1+1 Twisted Mass Lattice QCD

We present preliminary results at {\beta} = 1.95 (a = 0.077 fm) on the first unquenched N_f=2+1+1 lattice computation of the B_K parameter which controls the neutral kaon oscillations in the Standard Model. Using N_f=2+1+1 maximally twisted sea quarks and Osterwalder-Seiler valence quarks we achieve O(a) improvement and a continuum-like renormalization pattern for the four-fermion operator. Our results are extrapolated/interpolated to the physical light/strange quark mass but not yet to the continuum limit. The computation of the relevant renormalization constants is performed non perturbatively in the RI'-MOM scheme using dedicated simulations with N_f=4 degenerate sea quark flavours produced by the ETM collaboration. We get B_K^{RGI} (a = 0.077) = 0.747(18), which when compared to our previous unquenched N_f=2 determination and most of the existing results, suggests a rather weak B_K^{RGI} dependence on the number of dynamical flavours. We are at the moment analysing lattice data at two additional {\beta} values which will allow us to perform an extrapolation to the continuum limit.Comment: 7 pages, 8 figures, Proceedings of Lattice 2011, XXIX International Symposium on Lattice Field Theory, Squaw Valley, Lake Tahoe, Californi

Development of Large area Gamma-ray Camera with GSO(Ce) Scintillator Arrays and PSPMTs

We have developed a position-sensitive scintillation camera with a large area absorber for use as an advanced Compton gamma-ray camera. At first we tested GSO(Ce) crystals. We compared light output from the GSO(Ce) crystals under various conditions: the method of surface polishing, the concentration of Ce, and co-doping Zr. As a result, we chose the GSO(Ce) crystals doped with only 0.5 mol% Ce, and its surface polished by chemical etching as the scintillator of our camera. We also made a 16$\times$16 cm$^2$ scintillation camera which consisted of 9 position-sensitive PMTs (PSPMTs Hamamatsu flat-panel H8500), the each of which had 8$\times$8 anodes with a pitch of 6 mm and coupled to 8$\times$8 arrays of pixelated 6$\times6\times$13 mm$^3$ GSO(Ce) scintillators. For the readout system of the 576 anodes of the PMTs, we used chained resistors to reduce the number of readout channels down to 48 to reduce power consumption. The camera has a position resolution of less than 6mm and a typical energy resolution of 10.5% (FWHM) at 662 keV at each pixel in a large area of 16$\times$16 cm$^2$. %to choose the best scintillator for our project. Furthermore we constructed a 16$\times$16 array of 3$\times3\times$13 mm$^3$ pixelated GSO(Ce) scintillators, and glued it to a PMT H8500. This camera had the position resolution of less than 3mm, over an area of 5$\times$5 cm$^2$, except for some of the edge pixels; the energy resolution was typically 13% (FWHM) at 662 keV.Comment: Proceedings of PSD7 appear in NIM

K^0-\bar{K}^0 Mixing Beyond the SM from Nf=2 tmQCD

We present preliminary results on the of neutral kaon oscillations in extensions of the Standard Model. Using Nf=2 maximally twisted sea quarks and Osterwalder-Seiler valence quarks, we achieve both O(a)-improvement and continuum-like renormalization pattern for the relevant four-fermion operators. We perform simulations at three values of the lattice spacing and extrapolate/interpolate our results to the continuum limit and physical light/strange quark mass. The calculation of the renormalization constants of the complete operator basis is performed non- perturbatively in the RI-MOM scheme.Comment: 7 pages, 2 figures; presented at the XXVIII International Symposium on Lattice Field Theory Villasimius, Sardinia, Ital