Recursive method for opacity expansion at finite temperature

Using a reaction operator approach, we derive the multiple-scattering induced gluon number distribution function to all orders in powers of opacity at finite temperature. The detailed balance effect is analyzed by taking into account both gluon emission and absorption in a thermal medium. We also calculate virtual corrections and show that the infrared divergence cancels out in the gluon distribution function at finite temperature.     

Gluon condensates at finite baryon densities and temperature

We derive here the equation of state for quark matter with a nontrivial vacuum structure in QCD at finite temperature and baryon density. Using thermofield dynamics, the parameters of thermal vacuum and the gluon condensate function are determined through minimisation of the thermodynamic potential, along with a self-consistent determination of the effective gluon and quark masses. The scale parameter for the gluon condensates is related to the SVZ parameter in the context of QCD sum rules at zero temperature. With inclusion of quarks in the thermal vacuum the critical temperature at which the gluon condensate vanishes decreases as compared to that containing only gluons. At zero temperature, we similarly obtain the critical baryon density for the same to be about 0.36 fm^?3.     

The three-gluon condensates at finite (low) temperature

The three-gluon condensates at finite temperature are found to be of two types. It turns out that these two types of gluon condensates differ only in sign. The value of these condensates is investigated in the framework of the grand partition function for a dilute instanton medium at finite (low) temperature, and found to decrease slowly with the temperature even for very low temperature and vanish nearly atT=240 MeV.     

有限温度下胶子场三圈真空图中的红外发散

用热传播子的实时形式对有限温度下胶子场的三圈真空图进行了详细的计算，在维数正规化方案下把真空图中的红外发散全部孤立出来了.     

Regge behaviour of distribution functions and evolution of gluon distribution function in next-to-leading order at low-x

Evolution of gluon distribution function from Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equation in next-to-leading order (NLO) at low-x is presented assuming the Regge behaviour of quark and gluon at this limit. We compare our results of gluon distribution function with MRST2004, GRV98LO and GRV98NLO parametrizations and show the compatibility of Regge behaviour of quark and gluon distribution functions with perturbative quantum chromodynamics (PQCD) at low-x.      

Heavy quark potential and quarkonia dissociation rates

Quenched lattice data for the interaction (in terms of heavy quark free energies) in the color-singlet channel at finite temperatures are fitted and used within the non-relativistic Schrödinger equation formalism to obtain binding energies and scattering phase shifts for the lowest eigenstates in the charmonium and bottomonium systems in a hot gluon plasma. The partial dissociation rate due to the Bhanot-Peskin process is calculated using different assumptions for the gluon distribution function, including free massless gluons, massive gluons, and massive damped gluons. It is demonstrated that a temperature dependent gluon mass has an essential influence on the heavy quarkonia dissociation, but that this process alone is insufficient to describe the heavy quarkonia dissociation rates.Arrival of the final proofs: 8 July 2005PACS: 12.38.Gc, 12.38.Mh, 14.40.GxD. Blaschke: Present address: GSI mbH, 64291 Darmstadt, Germany     

Infrared Divergences of Three-Loop Vacuum Graghs of Gluon Field at Finite Temperature

The kinds of infrared divergent integrals in three-loop vacuum graghs of gluon field at finite temperature are pointed out and their regularization is discussed. All of the infrared divergences in three-loop vacuum graghs of gluon field are isolated.     

Gravity’s Rainbow induces topology change

In this paper the Gribov gap equation at finite temperature is analyzed. The solutions of the gap equation (which depend explicitly on the temperature) determine the structure of the gluon propagator within the semi-classical Gribov approach. The present analysis is consistent with the standard confinement scenario for low temperatures, while for high enough temperatures, deconfinement takes place and a free gluon propagator is obtained. An intermediate regime in between the confined and free phases can be read off from the resulting gluon propagator, which appears to be closely related to partial deconfinement.     

Thermal Mass of the Gluon and the Disociation of J/ψ and ψ′in QGP Environment

Using thermo-field edynamics method,we calculate the efective mass and Debye screening mass of the gluon at finite temperature and finite density.The critical temperature and density for the dissociation of J/ψ and ψ′are obtained.     

Regge behaviour of structure function and gluon distribution at low-x in leading order

We present a method to find the gluon distribution from the proton structure function data at low-x assuming the Regge behaviour of the gluon distribution function at this limit. We use the leading order (LO) Altarelli–Parisi (AP) evolution equation in our analysis and compare our result with those of other authors. We also discuss the limitations of the Taylor expansion method in extracting the gluon distribution from the structure function used by those authors. Received: 2 January 2000 / Revised version: 23 February 2000 / Published online: 6 July 2000     

Renormalization of the Mass Gap

We have explicitly shown that QCD is the color gauge invariant theory at non-zero mass gap as well. It has been defined as the value of the regularized full gluon self-energy at some finite point. The mass gap is mainly generated by the nonlinear interaction of massless gluon modes. All this allows one to establish the structure of the full gluon propagator in the explicit presence of the mass gap. In this case, the two independent general types of formal solutions for the full gluon propagator as a function of the regularized mass gap have been found. The nonlinear iteration solution at which the gluons remain massless is explicitly present. The existence of the solution with an effective gluon mass is also demonstrated.     

Hadron resonance gas and nonperturbative QCD vacuum at finite temperature

Nonperturbative QCD vacuum with two light quarks at finite temperature was studied in a hadron resonance-gas model. Temperature dependences of the quark and gluon condensates in the confined phase were obtained. It is shown that the quark condensate and one-half (chromoelectric component) of the gluon condensate are evaporated at the same temperature corresponding to the quark-hadron phase transition. With allowance for the temperature shift of hadron masses, the critical temperature was found to be T _c ?190 MeV.     

An Analysis of the Proton Structure Function and the Gluon Distributions at Small x

Recently, we reported an analysis of Proton structure function at small x based on Taylor approximated DGLAP equations assuming a plausible relationship between the singlet and the gluon distributions. In this paper, we report a generalised version of the previous work. A corresponding study of the suggested gluon distribution is also made.The present generalised version of the model for the structure function results in a wider x range of phenomenological validity than the earlier one. A comparison of both the models of the proton structure function and the gluon distribution is made with exact result as well as with the Froissart saturated models of Block, Durand and Mckay.     

Analytic approach to the approximate solution of the independent DGLAP evolution equations with respect to the hard-Pomeron behavior

We show that it is possible to use hard-Pomeron behavior to the gluon distribution and singlet structure function at low x. We derive a second-order independent differential equation for the gluon distribution and the singlet structure function. In this approach, both singlet quarks and gluons have the same high-energy behavior at small x. These equations are derived from the next-to-leading order DGLAP evolution equations. All results can be consistently described in the framework of perturbative QCD, which shows an increase of gluon distribution and singlet structure functions as x decreases.     

One-loop factorization for inclusive hadron production in p-A collisions in the saturation formalism

We demonstrate the QCD factorization for inclusive hadron production in p-A collisions in the saturation formalism at one-loop order, with explicit calculation of both real and virtual gluon radiation diagrams. In particular, we find that the cross section can be written into a factorization form in the coordinate space at the next-to-leading order, while the naive form of the convolution in the transverse momentum space does not hold. The collinear divergences associated with the incoming parton distribution of the nucleon and the outgoing fragmentation function of the final-state hadron, as well as the rapidity divergence with small-x dipole gluon distribution of the nucleus are factorized into the splittings of the associated parton distribution and fragmentation functions and the energy evolution of the dipole gluon distribution function. The hard coefficient function is evaluated at one-loop order, and contains no divergence.     

The temporal axial gauge at finite temperature explored using the real time formalism

The temporal axial gauge is discussed at zero temperature and extended to finite temperature. A set of Feynman rules is determined within the real-time formalism which allows one to do perturbation theory at finite temperature using the temporal gauge. As a demonstration of the Feynman rules derived we do a simple linear response analysis for the gluon plasma at high temperature. This analysis yields a positive damping constant to one loop order in the long-wavelength limit. The problem of the imaginary-time formalism is discussed.     

On finite lattice corrections to gauge field thermodynamics

We consider the ideal gas limit of lattice Yang-Mills with fermions. Recently, such a system has been considered in great detail in the literature. We discuss possible finite lattice corrections to the energy density of the quarks and gluons due to the constraint of the quark-gluon gas being in colour singlet state. In the case of pure Yang-Mills theory at finite temperature, we find that Monte Carlo data agree very well with the asymptotically free gluon gas being a colour singlet. In the presence of quarks, in the quenched approximation, we find that Monte Carlo data seem to agree with a distribution where the quarks themselves form a colour singlet.     

化学非平衡夸克–胶子等离子体中的双轻子产生

研究了正在进行化学平衡的具有有限重子密度的夸克–胶子等离子体系统的演化和双轻子产生.结果发现由于夸克相的寿命随初始夸克化学势的增加而增加,以及其他一些因素,如较高的初始温度、较大的胶子密度和较大的胶子聚变和夸克湮没反应截面,导致热粲夸克对双轻子产生提供了占统治的贡献.这个效应造成中等质量双轻子的重大增强.     

Regge behaviour of distribution functions and t and x-evolutions of gluon distribution function at low-x

In this paper, t and x-evolutions of gluon distribution function from Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equation in leading order (LO) at low-x are presented assuming the Regge behaviour of quarks and gluons at this limit. We compare our results of gluon distribution function with MRST 2001, MRST 2004 and GRV 1998 parametrizations and show the compatibility of Regge behaviour of quark and gluon distribution functions with perturbative quantum chromodynamics (PQCD) at low-x. We also discuss the limitations of Taylor series expansion method used earlier to solve DGLAP evolution equations in the Regge behaviour of distribution functions.      

Lattice QCD calculations for the physical equation of state

In this report we consider the numerical simulations at finite temperature using lattice QCD data for the computation of the thermodynamical quantities including the pressure, energy density and the entropy density. These physical quantities can be related to the equation of state for quarks and gluons. We shall apply the lattice data to the evaluation of the specific structure of the gluon and quark condensates at finite temperature in relation to the deconfinement and chiral phase transitions. Finally we mention the quantum nature of the phases at lower temperatures.