Relativistic Calculation of the Width of the Theta (1540) Pentaquark

We calculate the width of the Theta(1540) pentaquark in a relativistic model in which the pentaquark is considered to be composed of a scalar diquark and a spin 1/2 triquark. We consider both positive and negative parity for the pentaquark. There is a single parameter in our model which we vary and which describes the size of the pentaquark. If the pentaquark size is somewhat smaller than that of the nucleon, we find quite small widths for the pentaquark of about 1 MeV or less. Our model of confinement plays an important role in our analysis and makes it possible to use Feynman diagrams to describe the decay of the pentaquark.Comment: 11 pages, 5 figure

Relativistic Model of Triquark Structure

At this point it is still unclear whether pentaquarks exist. While they have be seen in some experiments there are many experiments in which they are not found. On the assumption that pentaquarks exist, several authors have studied the properties of pentaquarks. One description considered is that of pentaquarks which consist of a diquark coupled to a triquark. There is a quite extensive literature concerning the properties of diquarks and their importance in the description of the nucleon has been considered by several authors. On the other hand, there is little work reported concerning the description of triquarks. In the present work we study a model for the triquark in which it is composed of a component which contains a quark coupled to a scalar diquark and another two components in which there is a quark coupled to a kaon. We solve for the wave function of the triquark and obtain a mass for the triquark of 0.81 GeV which is quite close to the value of 0.80 GeV obtained in a QCD sum rule study of triquark properties.Comment: 11 pages and 7 figure

Description of Deconfinement at Finite Matter Density in a Generalized Nambu--Jona-Lasinio Model

Recent years have seen extensive applications of the Nambu--Jona-Lasinio (NJL) model in the study of matter at high density. There is a good deal of interest in the predictions of diquark condensation and color superconductivity, with suggested applications to the study the properties of neutron stars. As the researchers in this field note, the NJL model does not describe confinement, so that one is limited to the study of the deconfined phase, which may set in at several times nuclear matter density. Recently, we have extended the NJL model to include a covariant confinement model. In the present work our goal is to include a phenomenological model of deconfinement at finite matter density, using some analogy to what is known concerning "string breaking" and deconfinement at finite temperature. Various models may be used, but for this work we choose a specific model for the density dependence of the parameters of our confining interaction. We perform relativistic random-phase-approximation (RPA) calculations of the properties of the $\pi(138), K(495), f_0(980), a_0(980)$ and $K_0^*(1430)$ mesons and their radial excitations. In the model chosen for this work, there are no mesonic states beyond about $2\rho_{NM}$, where $\rho_{NM}$ is the density of nuclear matter. This inability of the model to support hadronic excitations at large values of the density is taken as a signal of deconfinement. In addition to the density dependence of the confining interaction, we use the density-dependent quark mass values obtained in either the SU(2) or SU(3)-flavor versions of the NJL model.Comment: 28 pages, 10 figures, revtex

Chiral Symmetry Restoration and Deconfinement of Light Mesons at Finite Temperature

There has been a great deal of interest in understanding the properties of quantum chromodynamics (QCD) for a finite value of the chemical potential and for finite temperature. Studies have been made of the restoration of chiral symmetry in matter and at finite temperature. The phenomenon of deconfinement is also of great interest, with studies of the temperature dependence of the confining interaction reported recently. In the present work we study the change of the properties of light mesons as the temperature is increased. For this study we make use of a Nambu--Jona-Lasinio (NJL) model that has been generalized to include a covariant model of confinement. The parameters of the confining interaction are made temperature-dependent to take into account what has been learned in lattice simulations of QCD at finite temperature. The constituent quark masses are calculated at finite temperature using the NJL model. A novel feature of our work is the introduction of a temperature dependence of the NJL interaction parameters. (This is a purely phenomenological feature of our model, which we do not attempt to derive from more fundamental considerations.) With the three temperature-dependent aspects of the model mentioned above, we find that the mesons we study are no longer bound when the temperature reaches the critical temperature, $T_c$, which we take to be 170 MeV. We believe that ours is the first model that is able to describe the interplay of chiral symmetry restoration and deconfinement for mesons at finite temperature. The introduction of temperature-dependent coupling constants is a feature of our work whose further consequences should be explored in future work.Comment: 17 pages, 10 figures, Revtex4 tex fil

Numerical accuracy of Bogomolny's semiclassical quantization scheme in quantum billiards

We use the semiclassical quantization scheme of Bogomolny to calculate eigenvalues of the Lima\c con quantum billiard corresponding to a conformal map of the circle billiard. We use the entire billiard boundary as the chosen surface of section (SOS) and use a finite approximation for the transfer operator in coordinate space. Computation of the eigenvalues of this matrix combined with a quantization condition, determines a set of semiclassical eigenvalues which are compared with those obtained by solving the Schr\"odinger equation. The classical dynamics of this billiard system undergoes a smooth transition from integrable (circle) to completely chaotic motion, thus providing a test of Bogomolny's semiclassical method in coordinate space in terms of the morphology of the wavefunction. We analyze the results for billiards which exhibit both soft and hard chaos.Comment: 21 Revtex pages, 6 ps figures, accepted for publication in J. Phys.

MIMO UWB Radar System with Compressive Sensing

A multiple input multiple output ultra-wideband cognitive radar based on compressive sensing is presented in this letter. For traditional UWB radar, high sampling rate analog to digital converter at the receiver is required to meet Shannon theorem, which increases hardware complexity. In order to bypass the bottleneck of ADC or further increase the radar bandwidth using the latest wideband ADC, we propose to exploit CS for signal reconstruction at the receiver of UWB radar for the sparse targets in the surveillance area. Besides, the function of narrowband interference cancellation is integrated into the proposed MIMO UWB radar. The field demonstration proves the feasibility and reliability of the proposed algorithm.Comment: 4 page

Chiral Quark Model Calculation of the Momentum Dependence of Hadronic Current Correlation Functions at Finite Temperature

We calculate spectral functions associated with hadronic current correlation functions for vector currents at finite temperature. We make use of a model with chiral symmetry, temperature-dependent coupling constants and temperature-dependent momentum cutoff parameters. Our model has two parameters which are used to fix the magnitude and position of the large peak seen in the spectral functions. In our earlier work, good fits were obtained for the spectral functions that were extracted from lattice data by means of the maximum entropy method (MEM). In the present work we extend our calculations and provide values for the three-momentum dependence of the vector correlation function at $T=1.5T_c$. These results are used to obtain the correlation function in coordinate space, which is usually parametrized in terms of a screening mass. Our results for the three-momentum dependence of the spectral functions are similar to those found in a recent lattice QCD calculation for charmonium [S. Datta, F. Karsch, P. Petreczky and I. Wetzorke, hep-lat/0312037]. However, we do not find the expontential behavior in coordinate space that is usually assumed for the spectral function for $T>T_c$ and which allows for the definition of a screening mass.Comment: 16 pages, 5 figures, revtex

Excitations of the Quark- Gluon Plasma

We will discuss the spectrum of the eta mesons making use of the Nambu-Jona-Lasinio (NJL) model supplemented with a model of confinement. We will go on to discuss the properties of mesons at finite temperature and the phenomenon of deconfinement. We will then discuss some excited states of the quark-gluon plasma calculated in lattice QCD models.These resonances are thought to be created in heavy-ion collisions.We consider the role these states play in leading to a hydrodynamic description of the plasma at early stages of its formation.Comment: 24 Pages, 19 Figures. Invited talk presented by C. M. Shakin at "Physics of the Microworld: From Quarks to Nanostructures", NYSS A{S Symposium, Brooklyn, New Yrok, Oct. 15-16, 200

Calculation of the Momentum Dependence of Hadronic Current Correlation Functions at Finite Temperature

We have calculated spectral functions associated with hadronic current correlation functions for vector currents at finite temperature. We made use of a model with chiral symmetry, temperature-dependent coupling constants and temperature-dependent momentum cutoff parameters. Our model has two parameters which are used to fix the magnitude and position of the large peak seen in the spectral functions. In our earlier work, good fits were obtained for the spectral functions that were extracted from lattice data by means of the maximum entropy method (MEM). In the present work we extend our calculations and provide values for the three-momentum dependence of the vector correlation function at T=1.5T_c. These results are used to obtain the correlation function in coordinate space, which is usually parametrized in terms of a screening mass. Our results for the three-momentum dependence of the spectral functions are similar to those found in a recent lattice QCD calculation for charmonium [S. Datta, F. Karsch, P. Petreczky and I. Wetzorke, hep-lat/0312037]. For a limited range we find the exponential behavior in coordinate space that is usually obtained for the spectral function for T>T_c and which allows for the definition of a screening mass.Comment: 16 pages, 4 figure

Calculation of the Excitations of Dense Quark Matter at Zero Temperature

Recently there has been a great deal of interest in studying the properties of dense quark matter, with particular reference to diquark condensates and color superconductivity. In the present work we report calculations made for the excitations of quark matter for relatively low densities of the deconfined phase and in the absence of meson or diquark condensation. Here, we are interested in elucidating the role of "Pauli blocking", as such blocking affects the calculation vector, scalar and pseudoscalar $q\bar q$ excitations. As a byproduct of our analysis, we extend our calculations to higher densities and explore some consequences of the use of density-dependent coupling parameters for the Nambu--Jona-Lasinio model. (Such density-dependent parameters have been used in some of our previous work.) For our analysis made at large values of the matter density, we assume that at about 13 times nuclear matter density quark matter has only minimal nonperturbative interactions. At that high density we compare the result for hadronic current correlation functions calculated with density-dependent and density-independent NJL coupling constants. We find evidence for the use of density-dependent parameters, since the results with the density-independent constants do not go over to the perturbative description which we assume to be correct for $\rho\simeq 6\rho_c$, where $\rho_c$ is the matter density for the finite-density confinement-deconfinement transition. The use of density-dependent coupling constants in the study of diquark condensates and color superconductivity has not been explored as yet, and is a topic requiring further investigation, particularly given the strong interest in the properties of dense quark matter and color superconductivity.Comment: 16 pages, 9 figures, RevTex