Temperature Dependence of the Effective Bag Constant and the Radius of a Nucleon in the Global Color Symmetry Model of QCD

We study the temperature dependence of the effective bag constant, the mass, and the radius of a nucleon in the formalism of the simple global color symmetry model in the Dyson-Schwinger equation approach of QCD with a Gaussian-type effective gluon propagator. We obtain that, as the temperature is lower than a critical value, the effective bag constant and the mass decrease and the radius increases with the temperature increasing. As the critical temperature is reached, the effective bag constant and the mass vanish and the radius tends to infinity. At the same time, the chiral quark condensate disappears. These phenomena indicate that the deconfinement and the chiral symmetry restoration phase transitions can take place at high temperature. The dependence of the critical temperature on the interaction strength parameter in the effective gluon propagator of the approach is given.Comment: 10 pages, 9 figure

Dyson-Schwinger Equations with a Parameterized Metric

We construct and solve the Dyson-Schwinger equation (DSE) of quark propagator with a parameterized metric, which connects the Euclidean metric with the Minkowskian one. We show, in some models, the Minkowskian vacuum is different from the Euclidean vacuum. The usual analytic continuation of Green function does not make sense in these cases. While with the algorithm we proposed and the quark-gluon vertex ansatz which preserves the Ward-Takahashi identity, the vacuum keeps being unchanged in the evolution of the metric. In this case, analytic continuation becomes meaningful and can be fully carried out.Comment: 10 pages, 7 figures. To appear in Physical Review

Phase diagram and critical endpoint for strongly-interacting quarks

We introduce a method based on the chiral susceptibility, which enables one to draw a phase diagram in the chemical-potential/temperature plane for strongly-interacting quarks whose interactions are described by any reasonable gap equation, even if the diagrammatic content of the quark-gluon vertex is unknown. We locate a critical endpoint (CEP) at (\mu^E,T^E) ~ (1.0,0.9)T_c, where T_c is the critical temperature for chiral symmetry restoration at \mu=0; and find that a domain of phase coexistence opens at the CEP whose area increases as a confinement length-scale grows.Comment: 4 pages, 3 figure

Quark spectral density and a strongly-coupled QGP

The maximum entropy method is used to compute the dressed-quark spectral density from the self-consistent numerical solution of a rainbow truncation of QCD's gap equation at temperatures above that for which chiral symmetry is restored. In addition to the normal and plasmino modes, the spectral function also exhibits an essentially nonperturbative zero mode for temperatures extending to 1.4-1.8-times the critical temperature, T_c. In the neighbourhood of T_c, this long-wavelength mode contains the bulk of the spectral strength and so long as this mode persists, the system may fairly be described as a strongly-coupled state of matter.Comment: 4 pages, 2 figure

Practical corollaries of transverse Ward-Green-Takahashi identities

The gauge principle is fundamental in formulating the Standard Model. Fermion--gauge-boson couplings are the inescapable consequence and the primary determining factor for observable phenomena. Vertices describing such couplings are simple in perturbation theory and yet the existence of strong-interaction bound-states guarantees that many phenomena within the Model are nonperturbative. It is therefore crucial to understand how dynamics dresses the vertices and thereby fundamentally alters the appearance of fermion--gauge-boson interactions. We consider the coupling of a dressed-fermion to an Abelian gauge boson, and describe a unified treatment and solution of the familiar longitudinal Ward-Green-Takahashi identity and its less well known transverse counterparts. Novel consequences for the dressed-fermion--gauge-boson vertex are exposed.Comment: 5 pages, 1 figur

Zero mode in a strongly coupled quark gluon plasma

In connection with massless two-flavour QCD, we analyse the chiral symmetry restoring phase transition using three distinct gluon-quark vertices and two different assumptions about the long-range part of the quark-quark interaction. In each case, we solve the gap equation, locate the transition temperature T_c, and use the maximum entropy method to extract the dressed-quark spectral function at T>T_c. Our best estimate for the chiral transition temperature is T_c=(147 +/- 8)MeV; and the deconfinement transition is coincident. For temperatures markedly above T_c, we find a spectral density that is consistent with those produced using a hard thermal loop expansion, exhibiting both a normal and plasmino mode. On a domain T\in[T_c,T_s], with T_s approximately 1.5T_c, however, with each of the six kernels we considered, the spectral function contains a significant additional feature. Namely, it displays a third peak, associated with a zero mode, which is essentially nonperturbative in origin and dominates the spectral function at T=T_c. We suggest that the existence of this mode is a signal for the formation of a strongly-coupled quark-gluon plasma and that this strongly-interacting state of matter is likely a distinctive feature of the QCD phase transition.Comment: 11 pages, 5 figures, 1 tabl

Phase diagram and thermal properties of strong-interaction matter

We introduce a novel procedure for computing the (mu,T)-dependent pressure in continuum QCD; and therefrom obtain a complex phase diagram and predictions for thermal properties of the system, providing the in-medium behaviour of the trace anomaly, speed of sound, latent heat and heat capacity.Comment: 6 pages, 4 figures. Minor amendments in the version accepted for publicatio

Riverine Floodplains of China: Threats and Restoration

Article信州大学山地水環境教育研究センター研究報告 6: 9-9(2010)departmental bulletin pape

Existence and stability of multiple solutions to the gap equation

We argue by way of examples that, as a nonlinear integral equation, the gap equation can and does possess many physically distinct solutions for the dressed-quark propagator. The examples are drawn from a class that is successful in describing a broad range of hadron physics observables. We apply the homotopy continuation method to each of our four exemplars and thereby find all solutions that exist within the interesting domains of light current-quark masses and interaction strengths; and simultaneously provide an explanation of the nature and number of the solutions, many of which may be associated with dynamical chiral symmetry breaking. Introducing a stability criterion based on the scalar and pseudoscalar susceptibilities we demonstrate, however, that for any nonzero current-quark mass only the regular Nambu solution of the gap equation is stable against perturbations. This guarantees that the existence of multiple solutions to the gap equation cannot complicate the description of phenomena in hadron physics.Comment: 14 pages, 15 figure