arXiv subjects

C. M. Shakin

Publications and source records attributed to C. M. Shakin.

At least 19 recordsLinked to original sources

arXiv2005

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.

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arXiv2005

Relativistic Calculation of Pentaquark Widths

We calculate the widths of the various pentaquarks 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. We obtain quite small widths for the decay Theta^(+) -> N+K^(+) and for Theta_c^0 -> P+D^{*-} consistent with the experimental situation. For the sum of the decay widths for Xi(bar)^(--) -> Xi^(-) + pi^(+) and Xi(bar)^(--) -> Sigma^(-) + K^(-) we find values of the order of 4-8 MeV for pentaquarks of the characteristic size considered in this work. (The experimental situation with respect to te observation of the Xi(bar)^(--) is somewhat uncertain at this time.) We also provide results for the decays N^(+) -> N + pi and N_s^(+) -> Lambda^(0) + K^(+). 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.

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arXiv2005

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.

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arXiv2004

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.

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arXiv2004

Quark Propagation in the Presence of a A_μ^aA_a^μ> Condensate

There is a good deal of current interest in the condensate g^2A_μ^aA_a^μ> which has recently be shown to be the Landau gauge version of a more general gauge-invariant expression. In the present work we consider quark propagation in the presence of such a condensate which we assume to be present in the vacuum. We describe the vacuum as a random medium of gluon fields. We discuss quark propagation in that medium and show that the quark propagator has no on-mass-shell pole indicating that a quark cannot propagate over extended distances. That is, the quark is a nonpropagating mode in the gluon condensate.

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arXiv2004

Comparison of Models of Critical Opacity in the Quark-Gluon Plasma

In this work we discuss two methods of calculation of quark propagation in the quark-gluon plasma. Both methods make use of the Nambu-Jona-Lasinio model. The essential difference of these calculations is the treatment of deconfinement. A model of confinement is not included in the work of Gastineau, Blanquier and Aichelin [hep-ph/0404207], however, the meson states they consider are still bound for temperatures greater than the deconfinement temperature T_c. On the other hand, our model deals with unconfined quarks and includes a description of the q(bar)q resonances found in lattice QCD studies that make use of the maximum entropy method (MEM). We compare the q{bar)q cross sections calculated in these models.

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arXiv2004

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.

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arXiv2004

Calculation of Screening Masses in a Chiral Quark Model

We consider a simple model for the coordinate-space vacuum polarization function which is often parametrized in terms of a screening mass. We discuss the circumstances in which the standard result for the screening mass, $m_{sc}=πT$, is obtained. In the model considered here, that result is obtained when the momenta in the relevant vacuum polarization integral are small with respect to the first Matsubara frequency.

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arXiv2004

Quark Propagation in the Quark-Gluon Plasma

It has recently been suggested that the quark-gluon plasma formed in heavy-ion collisions behaves as a nearly ideal fluid. That behavior may be understood if the quark and antiquark mean-free- paths are very small in the system, leading to a "sticky molasses" description of the plasma, as advocated by the Stony Brook group. This behavior may be traced to the fact that there are relatively low-energy $q\bar{q}$ resonance states in the plasma leading to very large scattering lengths for the quarks. These resonances have been found in lattice simulation of QCD using the maximum entropy method (MEM). We have used a chiral quark model, which provides a simple representation of effects due to instanton dynamics, to study the resonances obtained using the MEM scheme. In the present work we use our model to study the optical potential of a quark in the quark-gluon plasma and calculate the quark mean-free-path. Our results represent a specific example of the dynamics of the plasma as described by the Stony Brook group.

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arXiv2004

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.

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arXiv2003

Quark Model Calculations of Spectral Functions of Hadronic Current Correlation Functions at Finite Temperature

We calculate spectral functions associated with hadronic current correlation functions for vector and pseudoscalar currents at finite temperature. We make use of the Nambu--Jona--Lasinio (NJL) model with temperature-dependent coupling constants and temperature-dependent momentum cutoff parameters. At low energies, good fits are obtained for the spectral functions that were extracted from lattice data by means of the maximum entropy method (MEM). Our model has two parameters which are used to fix the magnitude and position of the large peak seen in the spectral functions. With those two parameters fixed, we obtain a satisfactory fit to the width of the peak. The model then also reproduces the energy of a second peak seen in the spectral functions. In the case of the pseudoscalar spectral function, the calculated peak is about 20 percent higher than that found for the spectral function obtained from the lattice data. However, it appears that the second peak is a lattice artifact [ P. Petreczky, private communication ] and our fit to the second peak may not be meaningful. We conclude that the NJL model may have a broader range of application than previously considered to be the case, if one allows for significant temperature dependence of the parameters of the model, as well as rather large values of the momentum cutoff parameter. Our treatment of temperature-dependent coupling constants and cutoff parameters is analogous to the procedure introduced by R. Casalbuoni, R. Gatto, G. Nardulli, and M. Ruggieri, [ Phys. Rev. D \textbf{68}, 034024 (2003) ], who make use of the NJL model at finite density and find that they need to use the density-dependent coupling constants and density -dependent cutoff parameters to study matter at high density.

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arXiv2003

Comparison of Temperature-Dependent Hadronic Current Correlation Functions Calculated in Lattice Simulations of QCD and with a Chiral Lagrangian Model

The Euclidean-time hadronic current correlation functions, $G_P(τ, T)$ and $G_V(τ, T)$, of pseudoscalar and vector currents have recently been calculated in lattice simulations of QCD and have been used to obtain the corresponding spectral functions. We have used the Nambu-Jona-Lasinio (NJL) model to calculate such spectral functions, as well as the Euclidean-time correlators, and have made a comparison to the lattice results for the correlators. We find evidence for the type of temperature dependence of the NJL coupling parameters that we have used in previous studies of the mesonic confinement-deconfinement transition. We also see that the spectral functions obtained when using the maximum-entropy-method (MEM) and the lattice data differ from the spectral functions that we calculate in our chiral model. However, our results for the Euclidean-time correlators are in general agreement with the lattice results, with better agreement when our temperature-dependent coupling parameters are used than when temperature-independent parameters are used for the NJL model. We also discuss some additional evidence for the utility of temperature-dependent coupling parameters for the NJL model. For example, if the constituent quark mass at T=0 is $352 {MeV}$ in the chiral limit, the transition temperature is $T_c=208 {MeV}$ for the NJL model with a standard momentum cutoff parameter. (If a Gaussian momentum cutoff is used, we find $T_c=225 {MeV}$ in the chiral limit, with $m=368 {MeV}$ at T=0.) The introduction of a weak temperature dependence for the coupling constant will move the value of $T_c$ into the range 150-170 MeV, which is more in accord with what is found in lattice simulations of QCD with dynamical quarks.

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arXiv2003

Calculation of Temperature-Dependent Hadronic Correlation Functions of Pseudoscalar and Vector Currents

We make use of the Nambu-Jona-Lasinio (NJL) formalism and real-time finite-temperature field theory to calculate hadronic current correlation functions in the deconfined phase of quantum chromodynamics (QCD). We consider both pseudoscalar and vector currents and compare our results with those obtained in lattice simulations of QCD. Our results are similar to those obtained in the lattice simulations for $T=1.5 T_c$, where $T_c$ is the temperature of the confinement-deconfinement transition. For $T=3.0 T_c$ our results do not exhibit the resonances obtained from the lattice simulations. However, the errors presented for the lattice results are large and it is possible that our results at $T=3.0 T_c$ are consistent with the lattice results when these errors are taken into account. Since the method used in the lattice analysis to obtain the spectral functions requires assumptions about the likelihood of a particular form for the spectral function, we believe our calculations will be useful to researchers who wish to calculate hadronic current correlation functions at finite temperature using lattice-based methods. Our model makes use of temperature-dependent coupling constants for the NJL model. We present an argument that such temperature dependence is necessary, if the results of the model are to be consistent with what is known concerning QCD thermodynamics.

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arXiv2002

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 $ρ\simeq 6ρ_c$, where $ρ_c$ 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.

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arXiv2002

Calculation of Hadronic Excitations of the Quark-Gluon Plasma

We present calculations of the spectral functions of various hadronic current correlators at finite temperature, making use of the Nambu--Jona-Lasinio (NJL) model and the real-time finite-temperature formalism. We study the scalar-isoscalar correlation function in a SU(3)-flavor model, as well as the pseudoscalar and vector correlation functions. We relate our analysis to our recent calculations of the properties of mesons for $T T_c$, where it is possible to neglect the effects of confinement. We find important excitations in the scalar sector corresponding to what are predominately singlet and octet states. The singlet state, which is at 247 MeV at $T=1.2 T_c$, evolves from the $f_0(980)$ which has an energy of about 400 MeV before it disappears from the spectrum of bound states for $T>0.95 T_c$. The octet state seen at $T=1.2 T_c$, which has a mass of about 860 MeV, evolves from a nodeless state that has an energy of about 1470 MeV at T=0 in our model. As noted in the literature, these modes may play an important role in the cooling and hadronization of quark-gluon droplets excited in heavy-ion collisions. We note that the real-time formalism has some advantages over the imaginary-time formalism, since the real-time formalism provides information concerning the widths of the excitations calculated using our model.

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arXiv2002

Calculation of the Pseudoscalar-Isoscalar Hadronic Current Correlation Functions of the Quark-Gluon Plasma

We report the results of calculations of pseudoscalar-isoscalar hadronic current correlators using the Nambu--Jona-Lasinio model and the real-time finite-temperature formalism. Results are presented for the temperatures range 1.2 $\leq T/T_c\leq$ 6.0, where $T_c$ is the temperature of the confinement-deconfinement transition, which we take to be $T_c=170$ MeV. Two important resonant features are seen in our calculations. In order to understand the origin of these resonances, we have performed relativistic random phase approximation (RPA)calculations of the temperature-dependent spectrum of the $η$ mesons for $T<T_c$. For the RPA calculations, use is made of a simple model in which we introduce temperature- dependent constituent quark masses calculated in a mean-field approximation and a temperature-dependent confining interaction whose form is motivated by recent studies made using lattice simulations of QCD with dynamical quarks. We also introduce temperature-dependent coupling constants in our generalized NJL model. Our motivation in the latter case is the simulation of the approach to a weakly interacting system at high temperatures. We present some evidence that supports our use of temperature-dependent coupling constants for the NJL model. We suggest that our results may be of interest to researchers who use lattice simulations of QCD to obtain temperature dependent spectral functions for various hadronic current correlation functions.

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arXiv2002

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.

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arXiv2002

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 $π(138), K(495), f_0(980), a_0(980)$ and $K_0^*(1430)$ mesons and their radial excitations. In the model chosen for this work, there are no mesonic states beyond about $2ρ_{NM}$, where $ρ_{NM}$ 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.

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