Diquark condensate and quark interaction with an instanton liquid

The interaction of light quarks with an instanton liquid is considered at nonzero density of quark/baryon matter in a phase where the diquark condensate is nonzero. It is shown that the inclusion of the relevant perturbation of the instanton liquid leads to an increase in the quark chemical potential μ_c. This in turn induces a considerable growth of the threshold quark-matter density at which one expects the emergence of color superconductivity.     

Properties of lightest mesons at finite temperature and quark/baryon chemical potential in the instanton model of the QCD vacuum

The paper is focused on calculating the finite temperature and quark/baryon chemical potential dependencies of the quark condensate and the π-and σ-meson masses in the subcritical region in the instanton model of the QCD vacuum. The impact of phononlike excitation of instanton liquid on the characteristics of the σ meson in such an environment is also examined.     

Vacuum Condensates from the Modification of Global Color Symmetry Model

Based on the quark propagator in the instanton dilute liquid approximation, we have determined the quark condensate , the mixed quark gluon condensate g,μνσ^μνq) and the four-quark condensate at the mean-field level in the framework of global color symmetry model. The numerical calculation shows that our result is compatible with the range obtained within other nonperturbative approaches. In particular, we have found that even at the mean-field level the naive vacuum saturation approximation is not a good approximation when we consider nonlocal four-quark condensate.     

Instanton liquid at finite temperature and chemical potential of quarks

Instanton liquid in heated and strongly interacting matter is studied using the variational principle. The dependence of the instanton liquid density (gluon condensate) on the temperature and the quark chemical potential is determined under the assumption that, at finite temperatures, the dominant contribution is given by an ensemble of calorons. The respective one-loop effective quark Lagrangian is used.     

Instantons and meson correlation functions in QCD

Various QCD correlators are calculated in the instanton liquid model in zeromode approximation and 1/N _c expansion. Previous works are extended by including dynamical quark loops. In contrast to the original “perturbative” 1/N _c approximation, not all quark loops are suppressed. Renormalization of the instanton density allows the identification of the density with the gluon condensate even in presence of dynamical quark loops. In the flavor singlet meson correlators a chain of quark bubbles survives the N _c → ∞ limit causing a massive η′ in the pseudoscalar correlator while keeping massless pions in the triplet correlator. The correlators are plotted and meson masses and couplings are obtained from a spectral fit. They are compared to the values obtained from numerical studies of the instanton liquid and to experimental results.     

Evidence for instanton-induced dynamics from lattice QCD

We perform a study of the nonperturbative dynamics of the light-quark sector of QCD, based on some recent results of lattice simulations with chiral fermions. We analyze some correlators that are designed to probe the Dirac structure of the quark-quark interaction at different scales. We show that, in the nonperturbative regime, such an interaction contains very large scalar and pseudoscalar components. We observe quantitative agreement between lattice QCD results and the predictions of the instanton liquid model. Moreover, we study how the quark-quark interaction is modified, when quark loops are suppressed. We observe a dramatic effect related to the loss of unitarity, which is naturally explained in the instanton picture. Such an effect cannot be explained in a Dyson-Schwinger equations (DSE) approach, if one assumes a vector quark-gluon coupling.     

Four-fermion interaction in relativistic heavy ion collisions

A (nearly) perfect liquid discovered in experiments with ultrarelativistic heavy ion collisions is investigated by studying the quark ensembles with four-fermion interaction considered as a fundamental theoretical approach. A comparative analysis of several quantum liquid models is performed, allowing one to conclude that the presence of gas-liquid phase transition is a characteristic feature of those models. The problem of the instability of the quark droplets with the small number of quarks, related with a possible formation of a chiral soliton, is discussed. A mixed phase of vacuum and baryon matter, as a possible scenario of its stability, is studied. Some aspects of the color superconductivity are considered. In addition, a recently proposed nontrivial thermodynamic state, called the fermion condensate, is studied. An analysis of unexpected opportunity to link the bare and effective coupling constants is performed within the framework of a simple model. It is pointed out that a simple subtraction procedure leads to the finite result without a typical logarithmic singularity for the observed coupling constant as a function of the transferred energy.     

Solution of the Schwinger-Dyson Equation Involving the Gluon condensate Kernel

The form of the quantum chromodynamic Schwinger-Dyson (SD) equation modified by the nonperturbative kernel associated with the gluon condensate is obtained. It is shown that the eolution for the renormalisation group invariant quark condensate from the SD equation is in agreement with that obtained from the consistent equation for quark condensate when the leading behavior of the dynamical quark mass is concerned^[1]. It is also found that the gluon condensate kernel makes the critical coupling constant above which the chiral symmetry breaks smaller and increases the value of the quark condensate.     

Monopoles, instantons and chiral condensate in lattice QCD

We analyze the interplay of topological objects in four-dimensional QCD at finite temperature on the lattice. The distributions of color magnetic monopoles in the maximum abelian gauge are computed around instantons. Studies are performed in both pure and full QCD and in both the confinement and deconfinement phase. We find an enhanced probability for monopoles inside the core of an instanton on gauge field average. This is independent of the topological charge definition used. For specific gauge field configurations we visualize the situation graphically. Moreover the correlation of monopole loops and instantons with the chiral condensate is investigated. Strong evidence is found that clusters of the quark condensate and topological objects coexist locally on individual configurations.     

非微扰QCD真空中夸克真空凝聚的结构(英文)

基于Dyson-Schwinger方程(DSEs)所确定的夸克传播子和算符成积展开(OPE),在彩虹近似下,预言了QCD真空中非定域夸克真空凝聚的结构。这种结构由夸克自能函数Af和Bf决定,通过数值求解DSEs就可以得到这些自能函数。但是,直接数值求解DSEs方程非常复杂,这里采用Roberts和Williams提出的参数化方法,用参数化的夸克传播函数σf v(p2)和σf s(p2)计算夸克自能函数。同时,也计算了定域的夸克真空凝聚值,夸克胶子混合的真空凝聚值,以及夸克的虚度。理论预言和计算结果均与标准QCD求和定则、格点QCD和瞬子模型的理论结果大致相符。和这些模型的结果相比,参数化方法得到的轻夸克(u,d,s)的定域真空凝聚偏大,这主要是由于模型依赖导致的。与u,d夸克相比,s夸克的真空凝聚比较大,这是因为s夸克自身质量较大的缘故。当然,Roberts-Williams参数化的夸克传播子只是一个经验公式,只能近似描述夸克的传播。     

Off-diagonal quark distributions in pions in the effective single-instanton approximation

Nonperturbative functions that parametrize off-diagonal hadronic matrix elements of the light-cone leading-twist quark operators are considered. These functions are calculated within the proposed relativistic quark model allowing for the nontrivial structure of the QCD vacuum, special attention being given to gauge invariance. Hadrons are treated as bound states of quarks; strong-interaction quark-pion vertices are described by effective interaction Lagrangians generated by instantons. The parameters of the instanton vacuum, such as the effective radius of the instanton and the quark mass, are related to the vacuum expectation values of the quark-gluon operators of the lowest dimension and to low-energy pion observables.     

Instanton vacuum in thermal QCD

The effects of instanton-anti-instanton interactions in high-temperature QCD with colour SU(2) are studied with and without quarks. The instanton potential proves to have no repulsive core, thus creating troubles with the definition of nonperturbative contributions to physical quantities. Also the chiral condensate is calculated, and it is shown to vanish if number of quark flavoursN _f≧2, whereas forN _f=1 it is nonzero for the arbitrary high temperature.     

Nonperturbative contribution to the quark form factor within the instanton model

The nonperturbative effects in the quark form factor are considered in the Wilson loop formalism, within the framework of the instanton liquid model. For the integration path corresponding to this form factor, the explicit expression for the vacuum expectation value of the Wilson operator is found to the leading order. It is shown that the instantons produce the power-like corrections to the perturbative result, which are comparable in magnitude with the perturbative part at the scale of order of the inverse average instanton size. It is demonstrated that the instanton contributions to the quark form factor are exponentiated to high orders in the small instanton density parameter.Received: 30 September 2002, Published online: 22 October 2003PACS: 12.38.-t Quantum chromodynamics - 11.15.Tk Other nonperturbative techniques     

Studying pion effects in the quark propagator

Within the framework of Schwinger-Dyson and Bethe-Salpeter equations we investigate the importance of pions for the quark-gluon interaction. To this end we choose a truncation for the quark-gluon vertex that includes intermediate pion degrees of freedom and adjust the interaction such that unquenched lattice results for various current quark masses are reproduced. After extrapolation to the physical point we find a considerable contribution of the pion back reaction to the quark mass function as well as to the chiral condensate.     

Nonlocal Four-Quark Condensate and Vacuum Susceptibilities

Based on the quark propagator in the instanton dilute liquid approximation, we have determined the nonlocal four-quark condensate at the mean-field level in the framework of global color symmetry model. By making use of this formula, the vacuum susceptibility (pionsusceptibility) was calculated in this paper. The theoretical analysis and numerical calculation show that even at the mean-field level the naive vacuum saturation approximation is not a good approximation when we consider nonlocal four-quark condensate.     

Possible pseudogap phase in QCD

Thermal pion fluctuations, in principle, can completely disorder the phase of quark condensate and thus restore chiral symmetry. If this happens before the quark condensate melts, strongly interacting matter will be in the pseudogap state just above the chiral phase transition. The quark condensate does not vanish locally, and quarks acquire constituent masses in the pseudogap phase, despite the fact that chiral symmetry is restored.     

ΔS = 0 effective weak chiral Lagrangianfrom the instanton vacuum

We investigate the ΔS = 0 effective chiral Lagrangian from the instanton vacuum. Based on the ΔS = 0 effective weak Hamiltonian from the operator product expansion and renormalization group equations, we derive the strangeness-conserving effective weak chiral Lagrangian from the instanton vacuum to order and the next-to-leading order in the 1/N_c expansion at the quark level. We find that the quark condensate and a dynamical term which arise from the QCD and electroweak penguin operators appear in the next-to-leading order in the 1/N_c expansion for the ΔS = 0 effective weak chiral Lagrangian, while they are in the leading order terms in the ΔS = 1 case. Three different types of form factors are employed and we find that the dependence on the different choices of the form factor is rather insensitive. The low-energy constants of the Gasser-Leutwyler type are determined and discussed in the chiral limit. Arrival of the final proofs: 2 December 2005 PACS: 12.40.-y, 14.20.Dh     

Chiral and deconfinement transition from correlation functions: SU(2) vs. SU(3)

We study a gauge-invariant order parameter for deconfinement and the chiral condensate in SU(2) and SU(3) Yang–Mills theory in the vicinity of the deconfinement phase transition using the Landau gauge quark and gluon propagators. We determine the gluon propagator from lattice calculations and the quark propagator from its Dyson–Schwinger equation, using the gluon propagator as input. The critical temperature and a deconfinement order parameter are extracted from the gluon propagator and from the dependency of the quark propagator on the temporal boundary conditions. The chiral transition is determined using the quark condensate as order parameter. We investigate whether and how a difference in the chiral and deconfinement transition between SU(2) and SU(3) is manifest.     

Sigma meson and phonon-like excitations of the instanton vacuum

The possible nature of two experimentally observed scalar mesons that are widely spaced in mass and whose special features may be caused by the excitations of the instanton liquid considered as a model of the QCD vacuum. It is shown that mass changes in the scalar sector may prove to be unexpectably large, even though the scale of such corrections to the dynamical quark mass is relatively small.