Two gamma quarkonium and positronium decays with Two-Body Dirac equations of constraint dynamics

Two-Body Dirac equations of constraint dynamics provide a covariant framework to investigate the problem of highly relativistic quarks in meson bound states. This formalism eliminates automatically the problems of relative time and energy, leading to a covariant three dimensional formalism with the same number of degrees of freedom as appears in the corresponding nonrelativistic problem. It provides bound state wave equations with the simplicity of the nonrelativistic Schroedinger equation. Unlike other three-dimensional truncations of the Bethe-Salpeter equation, this covariant formalism has been thoroughly tested in nonperturbatives contexts in QED, QCD, and nucleon-nucleon scattering. Here we continue the important studies of this formalism by extending a method developed earlier for positronium decay into two photons to tests on the sixteen component quarkonium wave function solutions obtained in meson spectroscopy. We examine positronium decay and then the two-gamma quarkonium decays of eta_c, eta'_c, chi_0c, chi_2c, and pi-zero The results for the pi-zero, although off the experimental rate by 13%, is much closer than the usual expectations from a potential model.Comment: 4 pages. Presented at Second Meeting of APS Topical Group on Hadron Physics, Nashville, TN, Oct 22-24. Proceedings to be published by Journal of Physics (UK), Conference Serie

Asymptotic properties of eigenmatrices of a large sample covariance matrix

Let $S_n=\frac{1}{n}X_nX_n^*$ where $X_n=\{X_{ij}\}$ is a $p\times n$ matrix with i.i.d. complex standardized entries having finite fourth moments. Let $Y_n(\mathbf {t}_1,\mathbf {t}_2,\sigma)=\sqrt{p}({\mathbf {x}}_n(\mathbf {t}_1)^*(S_n+\sigma I)^{-1}{\mathbf {x}}_n(\mathbf {t}_2)-{\mathbf {x}}_n(\mathbf {t}_1)^*{\mathbf {x}}_n(\mathbf {t}_2)m_n(\sigma))$ in which $\sigma>0$ and $m_n(\sigma)=\int\frac{dF_{y_n}(x)}{x+\sigma}$ where $F_{y_n}(x)$ is the Mar\v{c}enko--Pastur law with parameter $y_n=p/n$; which converges to a positive constant as $n\to\infty$, and ${\mathbf {x}}_n(\mathbf {t}_1)$ and ${\mathbf {x}}_n(\mathbf {t}_2)$ are unit vectors in ${\Bbb{C}}^p$, having indices $\mathbf {t}_1$ and $\mathbf {t}_2$, ranging in a compact subset of a finite-dimensional Euclidean space. In this paper, we prove that the sequence $Y_n(\mathbf {t}_1,\mathbf {t}_2,\sigma)$ converges weakly to a $(2m+1)$-dimensional Gaussian process. This result provides further evidence in support of the conjecture that the distribution of the eigenmatrix of $S_n$ is asymptotically close to that of a Haar-distributed unitary matrix.Comment: Published in at http://dx.doi.org/10.1214/10-AAP748 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Algebraic techniques in designing quantum synchronizable codes

Quantum synchronizable codes are quantum error-correcting codes that can correct the effects of quantum noise as well as block synchronization errors. We improve the previously known general framework for designing quantum synchronizable codes through more extensive use of the theory of finite fields. This makes it possible to widen the range of tolerable magnitude of block synchronization errors while giving mathematical insight into the algebraic mechanism of synchronization recovery. Also given are families of quantum synchronizable codes based on punctured Reed-Muller codes and their ambient spaces.Comment: 9 pages, no figures. The framework presented in this article supersedes the one given in arXiv:1206.0260 by the first autho

Frequency modulation television analysis: Distortion analysis

Computer simulation is used to calculate the time-domain waveform of standard T-pulse-and-bar test signal distorted in passing through an FM television system. The simulator includes flat or preemphasized systems and requires specification of the RF predetection filter characteristics. The predetection filters are modeled with frequency-symmetric Chebyshev (0.1-db ripple) and Butterworth filters. The computer was used to calculate distorted output signals for sixty-four different specified systems, and the output waveforms are plotted for all sixty-four. Comparison of the plotted graphs indicates that a Chebyshev predetection filter of four poles causes slightly more signal distortion than a corresponding Butterworth filter and the signal distortion increases as the number of poles increases. An increase in the peak deviation also increases signal distortion. Distortion also increases with the addition of preemphasis