Dressed Gluon Propagator Research Articles

QCD chiral symmetry restoration with a large number of quarks in a model with a confining propagator and dynamically massive gluons

Considering a QCD chiral symmetry breaking model where the gap equation contains an effective confining propagator and a dressed gluon propagator with a dynamically generated mass, we verify that the chiral symmetry is restored for a large number of quarks nf≈7−13. We discuss the uncertainty in the results, that is related to the determination of the string tension (KF), appearing in the confining propagator, and the effective gluon mass (mg) at large nf.

Quark number fluctuations at finite temperature and finite chemical potential via the Dyson-Schwinger equation approach

We investigate the quark number fluctuations up to the fourth order in the matter composed of two light flavor quarks with isospin symmetry and at finite temperature and finite chemical potential using the Dyson-Schwinger equation approach of QCD. In order to solve the quark gap equation, we approximate the dressed quark-gluon vertex with the bare one and adopt both the Marris-Tandy (MT) model and the infrared constant (Qin-Chang) model for the dressed gluon propagator. Our results indicate that the second, third, and forth order fluctuations of net quark number all diverge at the critical end point (CEP). Around the CEP, the second order fluctuation possesses obvious pump while the third and fourth order ones exhibit distinct wiggles between positive and negative. For the MT model and the Qin-Chang model, we give the pseudo-critical temperature at zero quark chemical potential as $T_{c}=146$ MeV and $150$ MeV, and locate the CEP at $({\mu_{E}^{q}}, {T_{E}^{}}) = (120, 124)$ MeV and $(124,129)$ MeV, respectively. In addition, our results manifest that the fluctuations are insensitive to the details of the model, but the location of the CEP shifts to low chemical potential and high temperature as the confinement length scale increases.

Wigner Solution to the Quark Gap Equation in the Nonzero Current Quark Mass

From the graphical representation of the Dyson—Schwinger equation for the dressed gluon propagator it is shown that the gluon propagator in the Wigner phase should be different from that in the Nambu phase. Based on this analysis, we propose a modified gluon propagator to reflect this fact. With such a modified gluon propagator, in the framework of the Nambu—Jona—Lasinio (NJL) model, we obtain the Wigner solution to the quark gap equation at finite current quark mass, which has not been found in literature. This provides a new point of view to study partial restoration of chiral symmetry at finite temperature and chemical potential.

Probing Quark Loop Effects on Dressed Gluon Propagator

We study the quark loop effects on the dressed gluon propagator and also on the quark propagator itself. We find that the gluon propagators are different in two phases. The quark mass effects on the gluon propagator are small but not negligible. We also study the current quark mass dependence on the bag constant.

Chemical Potential Dependence of Vertices

Based on the rainbow-ladder approximation of the Dyson–Schwinger equations and the assumption of the analyticity of the fermion-boson vertex in the neighborhood of zero chemical potential (μ = 0) and neglecting the μ-dependence of the dressed gluon propagator, we apply the method in [Phys. Rev. C 71 (2005) 015205] of studying the dressed quark propagator at finite chemical potential to prove that the general fermion-boson vertex at finite μ can also be obtained from the one at μ = 0 by a simple shift of variables. Using this result we extend the results of [Phys. Lett. B 420 (1998) 267] to the situation of finite chemical potential and show that under the approximations we have taken, the Gell–Mann–Oakes–Renner relation also holds at finite chemical potential.

Quark-meson vertices and pion properties at finite chemical potential

Based on the rainbow-ladder approximation of the Dyson-Schwinger equations and the assumption of the analyticity of the quark-meson vertex in the neighborhood of zero chemical potential ($\ensuremath{\mu}=0$) and neglecting the \ensuremath{\mu}-dependence of the dressed gluon propagator, we use the method of studying the dressed quark propagator at finite chemical potential given in [H. S. Zong, L. Chang, F.Y. Hou, W. M. Sun, and Y. X. Liu, Phys. Rev. C 71, 015205 (2005)] to show that the axial-vector quark-meson vertex at finite \ensuremath{\mu} can be obtained from the corresponding one at $\ensuremath{\mu}=0$ by a shift of variable: ${\ensuremath{\Gamma}}_{5\ensuremath{\nu}}^{j}[\ensuremath{\mu}](k, p)={\ensuremath{\Gamma}}_{5\ensuremath{\nu}}^{j}(\stackrel{~}{k}, p)$, where $k$ and $p$ are the relative and total momentum of the quark-antiquark pair, respectively, and $\stackrel{~}{k}=(\stackrel{\ensuremath{\rightarrow}}{k}, {k}_{4}+i\ensuremath{\mu})$. Similar relations hold for any other type of quark-meson vertex. This feature would facilitate the numerical calculations of the quark-meson vertex function at finite \ensuremath{\mu} considerably. Based on these results and using the dressed quark propagator at $\ensuremath{\mu}=0$ proposed in [R. Alkofer, W. Detmold, C. S. Fischer, and P. Maris, Phys. Rev. D 70, 014014 (2004)], we calculate the pion decay constant ${f}_{\ensuremath{\pi}}$ and the pion mass ${m}_{\ensuremath{\pi}}$ at finite \ensuremath{\mu} and a comparison of our results with those in the literature is made.

Calculation of Equation of State of QCD at Finite Chemical Potential and Temperature

In this paper, using path integral techniques we derive a model-independent formula for the pressure density \U0001d4ab(μ,T) (or equivalently the partition function) of Quantum Chromodynamics (QCD), which gives the equation of state (EOS) of QCD at finite chemical potential and temperature. In this formula the pressure density \U0001d4ab(μ,T) consists of two terms: the first term (\U0001d4ab(μ,T)|T=0) is a μ-independent (but T-dependent) constant; the second term is totally determined by G[μ,T](p⃗,ωn) (the dressed quark propagator at finite μ and finite T), which contains all the nontrivial μ-dependence. Then, in the framework of the rainbow-ladder approximation of the Dyson–Schwinger (DS) approach and under the approximation of neglecting the μ-dependence of the dressed gluon propagator, we show that G[μ,T](p⃗,ωn) can be obtained from G[T](p⃗,ωn) (the dressed quark propagator at μ = 0) by the substitution ωn → ωn + iμ. This result facilitates numerical calculations considerably. By this result, once G[T](p⃗,ωn) is known, one can determine the EOS of QCD under the above approximations (up to the additive term \U0001d4ab(μ,T)|T = 0). Finally, a comparison of the present EOS of QCD and the EOS obtained in the previous literatures in the framework of the rainbow-ladder approximation of the DS approach is given. It is found that the EOS given in the previous literatures does not satisfy the thermodynamic relation .

Numerically Solving Quark-Loop Effects on Dressed Gluon Propagator in Chiral Limit

We do a numerical calculation on the quark-loop effects on the dressed gluon propagator in the chiral limit. It is found that the quark-loop effects on the dressed gluon propagator are significant in solving the quark propagator in the rainbow approximation of the Dyson–Schwinger equation. The approach we used here is quite general and can also be used to calculate both the chemical potential and current quark mass dependence of the dressed gluon propagator.

Running coupling and power corrections in non-linear evolution at the high-energy limit

A main feature of high-energy scattering in QCD is saturation in the number density of gluons. This phenomenon is described by non-linear evolution equations, JIMWLK and BK, which have been derived at leading logarithmic accuracy. In this paper we generalize this framework to include running coupling corrections to the evolution kernel. We develop a dispersive representation of the dressed gluon propagator in the background of Weiszäcker–Williams fields and use it to compute O ( β 0 n − 1 α s n ) corrections to the kernel to all orders in perturbation theory. The resummed kernels present infrared-renormalon ambiguities, which are indicative of the form and importance of non-perturbative power corrections. We investigate numerically the effect of the newly computed perturbative corrections as well as the power corrections on the evolution. We present numerical results for the evolution rate as a function of the saturation scale. We find that running-coupling corrections are necessary for making quantitative predictions even when the saturation scale is very large; at present energies also the power corrections are important.

Quark Loop Effects on Dressed Gluon Propagator inFramework of Global Color Symmetry Model

Based on the global color symmetry model (GCM), a method forobtaining the quark loop effects on the dressed gluon propagatorin GCM is developed. In the chiral limit, it is found that thedressed gluon propagator containing the quark loop effectsin the Nambu–Goldstone and Wigner phases are quite different.In solving the quark self-energy functions in the two differentphases and subsequent study of bag constant one should use the abovedressed gluon propagator as input. The above approach forobtaining the current quark mass effects on the dressedgluon propagator is quite general and can also be used to calculatethe chemical potential dependence of the dressed gluonpropagator.

Approximation of the Schwinger-Dyson and the Bethe-Salpeter equations and chiral symmetry of QCD

The Bethe--Salpeter equation for the pion in chiral symmetric models is studied with a special care to consistency with low-energy relations. We propose a reduction of the rainbow Schwinger--Dyson and the ladder Bethe--Salpeter equations with a dressed gluon propagator. We prove that the reduction preserves the Ward--Takahashi identity for the axial-vector current and the PCAC relation.

COVARIANT MODEL OF CHIRAL SYMMETRY BREAKING IN QCD

With the aim of developing covariant QCD-based models of hadrons we study dynamical chiral symmetry breaking in an ansatz approach to QCD. The quark self-energy is calculated from the Schwinger-Dyson equation using an ansatz for the proper quark-gluon vertex consistent with QCD symmetries. Both asymptotic freedom and behavior consistent with confinement are included in the dressed gluon propagator. With essentially one free parameter we find that we can obtain good results for physically relevant quantities including the pion decay constant fπ, the quark condensate [Formula: see text], the scale parameter ΛQCD, and the constituent quark mass.

Dynamical chiral symmetry breaking in quantum chromodynamics with confinement and asymptotic freedom

We calculate the quark self-energy from dynamical chiral symmetry breaking in quantum chromo-dynamics using an ansatz for the proper quark-gluon vertex and the dressed gluon propagator which is consistent with the Slavnov-Taylor identities in the quark sector. In this way much of the symmetry information of quantum chromodynamics is retained, including, for example, chiral symmetry. Both confinement and asymptotic freedom are included in the gluon propagator. We find that it is straightforward to obtain good results for the pion decay constant ƒ π , the quark condensate 〈q̄q〉, and the scale parameter of quantum chromodynamics Λ QCD.