arXiv subjects
Publications and source records attributed to Hong-shi Zong.
We re-investigate the vector and axial-vector vacuum susceptibilities by taking advantage of the vector and axial-vector Ward-Takahashi identities. We show analytically that, in the chiral limit, the vector vacuum susceptibility is zero and the axial-vector vacuum susceptibility equals three fourths of the square of the pion decay constant. Besides, our analysis reproduces the Weinberg sum rule.
In this paper, we give a direct method for calculating the partition function, and hence the equation of state (EOS) of Quantum Chromodynamics (QCD) at finite chemical potential and zero temperature. In the EOS derived in this paper the pressure density is the sum of two terms: the first term ${\cal P}(μ)|_{μ=0}$ (the pressure density at $μ=0$) is a $μ$-independent constant; the second term, which is totally determined by $G_R[μ](p)$ (the renormalized dressed quark propagator at finite $μ$), contains all the nontrivial $μ$-dependence. By applying a general result in the rainbow-ladder approximation of the Dyson-Schwinger approach obtained in our previous study [Phys. Rev. {\bf C 71}, 015205 (2005)], $G_R[μ](p)$ is calculated from the meromorphic quark propagator proposed in [Phys. Rev. {\bf D 70}, 014014 (2004)]. From this the full analytic expression of the EOS of QCD at finite $μ$ and zero $T$ is obtained (apart from the constant term ${\cal P}(μ)|_{μ=0}$ which can in principle be calculated from the CJT effective action). A comparison between our EOS and the cold, perturbative EOS of QCD of Fraga, Pisarski and Schaffner-Bielich is made. It is expected that our EOS can provide a possible new approach for the study of neutron stars.
Based on the previous work in [Y. Jiang, Y.M. Shi, H.T. Feng, W.M. Sun and H.S. Zong, Phys. Rev. C {\bf 78}, 025214 (2008)] on the quark-meson vertex and pion properties at finite quark chemical potential, we provide an analytical analysis of the weak decay constant of the pion ($f_π[μ]$) and the pion mass ($m_π[μ]$) at finite quark chemical potential using the model quark propagator proposed in [R. Alkofer, W. Detmold, C.S. Fischer and P. Maris, Phys. Rev. D {\bf 70}, 014014 (2004)]. It is found that when $μ$ is below a threshold value $μ_0$ (which equals $0.350 \mathrm{GeV}$, $0.377 \mathrm{GeV}$ and $0.341 \mathrm{GeV}$, for the $\mathrm{2CC}$, $\mathrm{1R1CC}$ and $\mathrm{3R}$ parametrizations of the model quark propagator, respectively.), $f_π[μ]$ and $m_π[μ]$ are kept unchanged from their vacuum values. The value of $μ_0$ is intimately connected with the pole distribution of the model quark propagator and is found to coincide with the threshold value below which the quark-number density vanishes identically. Numerical calculations show that when $μ$ becomes larger than $μ_0$, $f_π[μ]$ exhibits a sharp decrease whereas $m_π[μ]$ exhibits a sharp increase. A comparison is given between the results obtained in this paper and those obtained in previous literatures.
By differentiating the dressed quark propagator with respect to a variable background field, the linear response of the dressed quark propagator in the presence of the background field can be obtained. From this general method, using the vector background field as an illustration, we derive a general formula for the four-quark condensate $<{\tilde 0}|:{\bar q}(0)γ_μq(0){\bar q}(0)γ_μq(0):|{\tilde 0}>$. This formula contains the corresponding fully dressed vector vertex and it is shown that factorization for $<{\tilde 0}|:{\bar q}(0)γ_μq(0){\bar q}(0)γ_μq(0):| {\tilde 0}>$ holds only when the dressed vertex is taken to be the bare one. This property also holds for all other type of four-quark condensate.
Based on the rainbow approximation of Dyson-Schwinger equation and the assumption that the inverse dressed quark propagator at finite chemical potential is analytic in the neighborhood of $μ=0$, a new method for obtaining the dressed quark propagator at finite chemical potential $μ$ from the one at zero chemical potential is developed. Using this method the dressed quark propagator at finite chemical potential can be obtained directly from the one at zero chemical potential without the necessity of numerically solving the corresponding coupled integral equations by iteration methods. A comparison with previous results is given.
A modified method for calculating the pion vacuum susceptibility from an effective quark-quark interaction model is derived. Within this approach it is shown that the pion vacuum susceptibility is free of ultraviolet divergence and is much smaller than the previous estimations.
A modified method for calculating the non-perturbative quark vacuum condensates from the global color symmetry model is derived. Within this approach it is shown that the vacuum condensates are free of ultraviolet divergence which is different from previous studies. As a special, the two-quark condensate and the mixed quark-gluon condensate are calculated. A comparision with the results of the other nonperturbative QCD approaches is given.
A method for obtaining the small current quark mass effect on the dressed quark propagator from an effective quark-quark interaction model is developed. Within this approach both explicit and dynamical chiral symmetry breaking has been analyzed. a comparision with previous results is given.
A method for obtaining the low chemical potential dependence of the dressed quark propagator from an effective quark-quark interaction model is developed. From this the chemical potential dependence of the chiral quark condensate and bag constant are evaluated. It is found that the chiral order parameter decreases with the increasing chemical potential $μ$, which is qualitatively different from the results given by some authors in the literature. The reason for this discrepancy is discussed.
It is shown how the axial vector current of current quarks is related to that of constituent quarks within the framework of the global color symmetry model. Gluon dressing of the axial vector vertex and the quark self-energy functions is described by the inhomogeneous Bethe-Salpeter equation in the ladder approximation and the Schwinger-Dyson equation in the rainbow approximation, respectively.