Electric and magnetic screenings of the thermal gluons are studied by using the background expansion method in a gluodynamic model with dimension-2 gluon condensate. At low temperature, the electric and magnetic gluons are degenerate. With the increasing of temperature, it is found that the electric and magnetic gluons start to split at certain temperature $T_0$. The electric screening mass changes rapidly with temperature when $T>T_0$, and the Polyakov loop expectation value rises sharply around $T_0$ from zero in the vacuum to a value around 0.8 at high temperature. This suggests that the color electric deconfinement phase transition is driven by electric gluons. It is also observed that the magnetic screening mass keeps almost the same as its vacuum value, which manifests that the magnetic gluons remains confined. Both the screening masses and the Polyakov loop results are qualitatively in agreement with the Lattice calculations.
The electric screening mass of the gluon at finite temperature is estimated by considering the gluon condensate above the critical temperature. We find that the thermal gluons acquire an electric mass of order T due to the gluon condensate.
The effects of a thermalized gas of gluons in a q,q bar plasma is investigated. Then the interplay between Debye screening and confinement is analyzed in a simplified model. While the one-gluon exchange gives results very similar, but not equal, to the electric case, the phenomenological introduction of confinement leads to very different results.
The hadronic screening mass at high temperature ($T$) in QCD$_4$ is examined on the basis of the QCD sum rules in (2+1) dimensions. Due to the magnetic gluon condensate at high $T$ which is expected to be nonvanishing, the screening mass deviates from the asymptotic value $2πT$. Also, the screening mass in the vector (pseudo-vector) channel turns out to be heavier than that in the scalar (pseudo-scalar) channel.
A method to measure the suppression of soft-gluon radiation by a heavy quark ("dead cone") is discussed. We analyse this QCD phenomenon in the framework of the HERA experiment using Monte Carlo simulations.
We construct the effective model based on QCD with gluon condensate. Under the assumption that the gluons are condensed with the sharp momentum peak in the momentum space, we formulate the effective field theory incorporating both the gluon condensate and the chiral condensate, then study the phase transition on temperature and chemical potential plane with respect to two condensates. We find that the condensates decrease with increasing temperature, which is reliable tendency on the condensate being consistent with the argument of the asymptotic behavior.
We calculate the contribution of local gluon condensate into the quadratic theta-term of vacuum energy and discuss its application to the study of axion mass.
We estimate the temperature dependence of the gluon condensate from the Polyakov loop effective potential. It is presented how this analytic approach provides a simple picture for the electric gluon condensate around the deconfinement temperature, showing that it drops to zero in a temperature range which is in good agreement with different pure gauge lattice results.
We discuss how magnetic screening can be systematically included in a self-consistent way for Chromodynamics at high temperatures. The resulting gap equation, which gives the summation of self-energy iterations, is calculated to one-loop order and leads to a nonzero value for the magnetic mass.
The color screening in a QCD plasma, that was studied in a formulation making evident similarities and differences with the electric case, is continued by taking into account the contributions of real gluons. The results, which include a numerical analysis not previously performed, show a damping of the correlation function which, if not exponential, does not differ very much from that form. The role of the temperature, which affect both the population and the dynamics of the quark-gluon system, is found to be relevant.
We investigate the quark-gluon mixed condensate based on an AdS/QCD model. Introducing a holographic field dual to the operator for the quark-gluon mixed condensate, we obtain the corresponding classical equation of motion. Taking the mixed condensate as an additional free parameter, we show that the present scheme reproduces very well experimental data. A fixed value of the mixed condensate is in good agreement with that of the QCD sum rules.
By the use of the gauge/gravity duality, we calculate the imaginary part of heavy quarkonium potential and thermal width with the effect of gluon condensate which is absent in AdS$_{5}$ background. Our results show that the dropping gluon condensate reduces the absolute value of imaginary potential and therefore decreases the thermal width both in "exact" and "approximate" approach implying that the heavy quarkonium has a weaker bound with the increase of gluon condensate. In addition, the thermal width will disappear at a critical condensate value, which indicates the dissociation of quarkoni…
We study the genuine non-perturbative corrections to the Landau gauge ghost-gluon vertex in terms of the non-vanishing dimension-two gluon condensate, and prove these corrections to give account of current SU(2) lattice data for the vertex with different kinematical configurations in the domain of intermediate momenta, roughly above 2-3 GeV. Based on this OPE analysis, we also present a simple model for the vertex, in acceptable agreement with the lattice data also in the IR domain. The necessity of a non-vanishing dimension-two gluon condensate will be also investigated through the analysis o…
The mixed quark-gluon condensate is another chiral order parameter in QCD, which plays an important role in the application of QCD sum rules. In this letter, we study the properties of quark-gluon mixed condensate at finite temperature and quark chemical potential in the framework of global color symmetry model. Using an infrared-dominant model gluon two-point function, we find that the behavior of quark-gluon mixed condensate at finite temperature and chemical potential is similar to that of the quark condensate, and both of them give the same information about chiral phase transition. We als…
Nonlocal gluon condensates are vacuum expectations of the product of gluon field strength tensors. Short-distance expansions of two-, three-, and four-gluon condensates are presented up to dimension-8 local operators. We propose a method for calculating the Wilson coefficients based on the presented expansions and the Feynman diagram technique in the background field approach. The method is demonstrated using the glueball current correlators as examples. Methodological aspects of the background field approach are discussed in relation to glueball studies within QCD sum rules. We confirm the re…
Beyond the deep IR, the analysis of ghost and gluon propagators still keeps very interesting non-perturbative information. The Taylor-scheme coupling can be computed and applied to obtain the $Λ_{\rm QCD}$ parameter from Landau gauge lattice simulations. Furthermore, a dimension-two gluon condensate, that can be understood in the instanton liquid model, plays an important role in the game.
The quark and gluon viscosities are calculated in quark-gluon plasmas to leading orders in the coupling constant by including screening. For weakly interaction QCD and QED plasmas dynamical screening of transverse interactions and Debye screening of longitudinal interactions controls the infrared divergences. For strongly interacting plasmas other screening mechanisms taken from lattice calculations are employed. By solving the Boltzmann equation for quarks and gluons including screening the viscosity is calculated to leading orders in the coupling constant. The leading logarithmic order is ca…
We review briefly and in retrospect the development which brought about the QCD sum rules based on introduction of the gluon condensate (M.A. Shifman, A.I. Vainshtein, and V.I. Zakharov (1978)).
We investigate a connection between a renormalon ambiguity of heavy quark mass and the gluon condensate contribution into the quark dispersion law related with a virtuality defining a displacement of the heavy quark from the perturbative mass-shell, which happens inside a hadron.
One-loop quark contributions to the dimension-four gluon condensate term in the operator product expansion (OPE) of the scalar glueball correlation function are calculated in the MS-bar scheme in the chiral limit of $n_f$ quark flavours. The presence of quark effects is shown not to alter the cancellation of infrared (IR) singularities in the gluon condensate OPE coefficients. The dimension-four gluonic condensate term represents the leading power corrections to the scalar glueball correlator and, therein, the one-loop logarithmic contributions provide the most important condensate contributio…
We evaluate the suppression of $J/ψ$ production in an equilibrating quark gluon plasma for two competing mechanisms: Debye screening of colour interaction and dissociation due to energetic gluons. Results are obtained for $S+S$ and $Au+Au$ collisions at RHIC and LHC energies. At RHIC energies the gluonic dissociation of the charmonium is found to be equally important for both the systems while the screening of the interaction plays a significant role only for the larger systems. At LHC energies the Debye mechanism is found to dominate for both the systems. While considering the suppression of …
A new relation between $ρ$-meson mass, weak $π$-meson decay constant, quark and gluon condensates is derived from the QCD sum rules. As a byproduct an explanation for the dominance of $ρρ$-decay for the $f_0(1370)$-meson is proposed.
We apply the effective theory of color glass condensate to the analysis of gluon states in dense quark matter, in which the saturation region of gluons is also present. We find that in the region two point function of gluons shows algebraic long range order. The order is completely the same as the one gluons show in the dense quark matter, which form quantum Hall states. The order leads to the vanishing of massless gluon pole. We also find that the saturation region of gluons extends from small $x$ to even large $x\lesssim 1$ in much dense quark matter. We point out a universality that the col…
We calculate the lowest-dimensional nonlocal quark and gluon condensates within the single instanton approximation of the instanton liquid model. As a result, we determine the values of average virtualities of quarks $λ_q^2$ and gluons $λ_g^2$ in the QCD vacuum and obtain parameterless predictions for the ratio $λ_g^2/λ_q^2 = 12/5$, and for some ratios of different vacuum condensates of higher dimensions. The nonlocal properties of quark and gluon condensates are analyzed, and insufficiency of the single instanton approximation is discussed.
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…
Based on the Dyson-Schwinger Equations (DSEs) with zero- and finite temperature, the two quark condensate, the four quark condensate and quark gluon mixed condensate in non-perturbative QCD state are investigated by solving the DSEs respectively at zero and finite temperature. These condensates are important input parameters in QCD sum rule with zero and finite temperature and properties of hadronic study. The calculated results manifest that the three condensates are almost independent of the temperature below the critical point temperature $T_{c}$. The results also show that the chiral symme…
Motivated by the desire to understand the nucleon mass structure in terms of light-cone distributions, we introduce the twist-four parton distribution function $F(x)$ whose first moment is the gluon condensate in the nucleon. We present the equation of motion relations for $F(x)$ and discuss the possible existence of the delta function (`zero mode') contribution at $x=0$. We also perform one-loop calculations for quark and gluon targets.
There is a good deal of current interest in the condensate A^2 which has been seen to play an important role in calculations which make use of the operator product expansion. That development has led to the publication of a large number of papers which discuss how that condensate could play a role in a gauge-invariant formulation. In the present work we consider gluon propagation in the presence of such a condensate which we assume to be present in the vacuum. We show that the gluon propagator has no on-mass-shell pole and, therefore, a gluon cannot propagate over extended distances. That is, …
The low-energy QCD theorems are generalized in the presence of a constant magnetic field H. Two-loop approximation for the vacuum energy density in the framework of the chiral perturbation theory was obtained and the quark and gluon condensates were found as the functions of H.
The perturbative contribution in the average plaquette is subtracted using Borel summation and the remnant of the plaquette is shown to scale as a dim-4 condensate. A critical review is presented of the renormalon subtraction scheme that claimed a dim-2 condensate. The extracted gluon condensate is compared with the latest result employing high order (35-loop) calculation in the stochastic perturbation theory.
Sum rules for the nonperturbative piece of correlators (specifically, the vector current correlator) are discussed. The sum rule subtracting the perturbative part is of the superconvergent type. Thus it is dominated by the bound states and low energy production cross section. It leads to a determination of the gluon condensate of $<α_s G^2> = 0.048 \pm 0.039 GeV^4$
The quark gluon plasma which has been observed at RHIC is a strongly interacting system and has been called sQGP. This is a system at high temperatures and almost zero baryon chemical potential. A similar system with high chemical potential and almost zero temperature may exist in the core of compact stars. Most likely it is also a strongly interacting system. The strong interactions may be partly due to non-perturbative effects, which survive after the deconfinement transition and which can be related with the non-vanishing gluon condensates in the sQGP. In this work, starting from the QCD La…
The study of the perturbative Odderon at high gluon densities in the color glass condensate requires to take into account states with more than three gluons. We formulate evolution equations for these states in which the number of gluons is not fixed during the evolution. We further determine the coupling of these Odderon states to the gamma to eta_c impact factor for arbitrary numbers of gluons. We find an exact solution of the evolution equation for the four-gluon Odderon state in terms of the three-gluon Odderon state. It is shown that a similar solution exists also for a different class of…
The lowest dimensional gluon condensate $G_2$ is analyzed at finite temperature and chemical potential using a holographic model of QCD with conformal invariance broken by a background dilaton. Starting from the free energy of the model, the thermodynamical quantities needed to determine the $T$ and $μ$ dependence of the gluon condensate are evaluated. At high temperature the gluon condensate is independent of chemical potential. Moreover, at $μ=0$ and in the string frame, the temporal and spatial Wilson loops at low temperature are computed; they are related to the (chromo) electric and magne…
We compute the quark and gluon condensates in $QCD$ with $N$ colors and $N_f$ flavors based on the renormalization group equations and on the knowledge of a single scale $Λ_{QCD}$. For $N=3$ and $N_f=3$ our findings are in the good range for $0.2\leqΛ_{QCD}\leq 0.36$ and in excellent agreement with the results in the literature from sum rules for a value $Λ_{QCD}=0.28$.
The Debye screening mass for a quark-gluon plasma at high temperature is calculated to next-to-leading order in the QCD coupling constant from the correlator of two Polyakov loops. The result agrees with the screening mass defined by the location of the pole in the gluon propagator as calculated by Rebhan. It is logarithmically sensitive to nonperturbative effects associated with the screening of static chromomagnetic fields.
We consider here chiral symmetry breaking in quantum chromodynamics arising from gluon condensates in vacuum. Through coherent states of gluons simulating a mean field type of approximation, we show that the off-shell gluon condensates of vacuum generate a mass-like contribution for the quarks, giving rise to chiral symmetry breaking. We next note that spontaneous breaking of global chiral symmetry links the four component quark field operator to the pion wave function. This in turn yields many hadronic properties in the light quark sector in agreement with experiments, leading to the conclusi…
We discuss how the presence of a squeezed gluon vacuum might lead to quark confinement in the framework of the global colour model of QCD. Using reduced phase space quantization of massive vector theory we construct a Lorentz invariant and colourless squeezed gluon condensate and show that it induces a permanent, nonlocal quark interaction (delta-function in 4-momentum space), which according to Munczek and Nemirovsky might lead to quark confinement. Our approach makes it possible to relate the strength of this effective confining quark interaction to the strength of the physical gluon condens…
The Color Glass Condensate is a universal state of matter which can manifest itself in hadronic processes involving small-x partons, like DIS and pp, pA and AA collisions at high energy. Observables are given in terms of multi-gluon correlators, whose ensemble evolves according to a RG equation, the JIMWLK equation. We focus on recent progress towards its solution which lead to quasi-exact, analytic expressions for the multi-gluon correlators at high energy.
There is considerable freedom in setting boundary conditions to perturbation theory at $t=\pm\infty$. The standard PQED and PQCD expansions are based on the (empty) perturbative vacuum. Since the true QCD ground state is expected to have a condensate of low momentum gluons, I propose studying expansions around states containing free particles. A specific boundary condition (the `Perturbative Gluon Condensate'), which implies a freezing of low momentum gluons, could be a candidate for describing confinement physics. The modified perturbative series has a number of new features, although it is f…
The operator-product expansion(OPE) could be employed to obtain the lowest-order, nonlocal quark scalar condensate component of gluon vacuum polarization. In particular, nonlocal quark scalar condensate can be calculated by solving Dyson-Schwinger Equation(DSE) of QCD. Then, field-theoretic aspects of the gluon vacuum polarization and nonperturbative gluon propagator will be considered in the Landau gauge of the Lorentz gauge fixing. The gluon propagator we obtained is finite in the infrared domain where the single gluon mass $m_g$ can be determined. Our results of the ratio $m_{g}/Λ_{QCD}$ th…
The flavour dependence of the mixed quark-gluon condensate is studied through the analysis of correlators of the hybrid current $a_μ=g\bar sγ_ργ_5 G_{ρμ}d$. The flavour symmetry breaking for this type of condensates is found to be less than that for the quark condensates. For the ratio of strange to nonstrange condensates we obtain \mbox{$R=0.95\pm 0.15$}. For the kaon coupling to the current $a_μ$ we find $δ'^2=(0.020\pm0.005)GeV^2$, which is an order of magnitude smaller than analogous chirally unsuppressed coupling.
The dimension two gluon condensate has been used previously within a simple phenomenological model to describe power corrections from available lattice data for the renormalized Polyakov loop and the heavy quark-antiquark free energy in the deconfined phase of QCD (hep-ph/0505215,hep-ph/0702055). The QCD trace anomaly of gluodynamics also shows unequivocal inverse temperature power corrections which may be encoded as dimension two gluon condensate. We analyze lattice data of the trace anomaly and compare with other determinations of the condensate from previous references, yielding roughly sim…
In a recent work we described the form taken by the Minkowski-space gluon propagator in the presence of an A^2 condensate. This condensate has been seen to play an important role in calculations which make use of the operator product expansion. The latter work has led to the publication of a large number of papers which discuss how the A^2 condensate could play a role in a gauge-invariant formulation. In the present work we discuss the properties of both the Euclidean-space and Minkowski-space gluon propagator. In the case of the Euclidean-space propagator we can make contact with the results …
The charmonium sum rules for the axial-vector current are considered. The three-loop perturbative corrections, operators up to 8 dimension and perturbative corrections to the lowest dimension operator are accounted. The contribution of the operators of 6 and 8 dimensions is computed in the framework of factorization hypothesis and instanton model. For the value of gluon condensate the following result is obtained: (0.005+0.001-0.004)GeV^4 (for the charm quark mass 1.275 GeV).
We interpret lattice data for the equation of state of pure gauge $SU(3)_c$ by an evaporation model. At low temperatures gluons are frozen inside the gluon condensate, whose dynamics is described in terms of a dilaton lagrangian. Above the critical temperature quasi-free gluons evaporate from the condensate: a first order transition is obtained by minimizing the thermodynamical potential of the system. Within the model it is possible to reproduce lattice QCD results at finite temperature for thermodynamical quantities such as pressure and energy. The gluonic longitudinal mass can also be evalu…
The lowest dimensional gluon condensate $G_2$ is analysed at finite temperature and chemical potential using a bottom/up holographic model of QCD. Starting from the free energy of the model, pressure, entropy and quark density are obtained. Moreover, at zero chemical potential, the temporal and spatial Wilson loops at low temperature are computed; they are related to the (chromo-)electric and magnetic components of $G_2$, respectively.
The purpose of these lectures is to provide an introduction to the physics issues which are being studied in the RHIC heavy ion program. These center around the production of new states of matter. The Quark Gluon Plasma is thermal matter which once existed in the big bang which may be made at RHIC. The Color Glass Condensate is a universal form of matter which controls the high energy limit of strong interactions. Both such forms of matter might be produced and probed at RHIC.
I propose that the properties of QCD perturbation theory should be investigated when the boundary state (`perturbative vacuum') at $t= \pm\infty$ includes gluons. Any boundary state that has an overlap with the true QCD ground state generates a perturbative series that (when summed to all orders) is formally exact. Through an analogy with the boundary condition corresponding to a fermion condensate, I propose an explicit form for a `perturbative gluon condensate' that suppresses low momentum gluon production, thus generating an effective mass gap. Standard perturbative calculations are modifie…
The quark <\barψψ> and gluon <F_{μν}F^{μν}> vacuum expectation values are non-vanishing at low orders in α_s when the perturbative ground state includes quark and gluon pairs. This offers possibilities of studying the effects of a non-trivial vacuum using formally exact perturbative methods. The QCD Feynman rules are modified only for the free, on-shell quark and gluon propagators at zero four-momentum. Gauge and lorentz invariance is maintained, while chiral symmetry is spontaneously broken by the ground state.
A feasible mechanism of unitarization of amplitudes of deep inelastic scattering at small values of Bjorken $x$ is the gluon fusion. However, its efficiency depends crucially on the vacuum color screening effect which accompanies the multiplication and the diffusion of BFKL gluons from small to large distances. From the fits to lattice data on field strength correlators the propagation length of perturbative gluons is $R_c\simeq 0.2-0.3$ fermi. The probability to find a perturbative gluon with short propagation length at large distances is suppressed exponentially. It changes the pattern of (d…
We begin with the discussion of the relationship between the trace of the energy momentum tensor and the gluon condensate at finite temperatures. Using the recent numerical data from the simulations of lattice gauge theory for quantum chromodynamics(QCD) we present the computational evaluations for the gluon condensate. A short discussion of the properties of deconfinement and the implications on the high temperature limit are included. We also mention the case of the massive quarks where some of the properties of the condensate appear to change. We put together these results with some ideas r…
A Borel resummation scheme of subtracting the perturbative contribution from the average plaquette is proposed using the bilocal expansion of Borel transform. It is shown that the remnant of the average plaquette, after subtraction of the perturbative contribution, scales as a dim-4 condensate. A critical review of the existing procedure of renormalon subtraction is presented.
After a short description of the currents coming from the known conservation laws in classical physics, we look at some further cases which arise after quantization in relation to quantum chromodynamics (QCD) at finite temperature. In these cases, however, some basic changes appear with the anomalies. First we go into the relationship between the trace of the energy momentum tensor and the gluon condensate at finite temperature. Using the recent numerical data from the simulations of lattice guage theory we present the computational evaluations for the gluon condensates at finite temperature. …
Charmonium sum rules are analyzed with the primary goal to obtain the restrictions on the value of dimension 4 gluon condensate. The moments M_n(Q^2) of the polarization operator of vector charm currents are calculated and compared with experimental data. The 3-loop (alpha_s^2) perturbative corrections, the gluon condensate contribution with alpha_s corrections and dimension 6 operator G^3 contribution are accounted. It is shown that the sum rules for the moments do not work at Q^2=0, where the perturbation series diverges and G^3 contribution is large. The domain in the plane (n, Q^2), where …
Under assumption of singular behavior of alpha_s(q^2) at q^2 sim 0 and of large q^2 behavior, corresponding to the perturbation theory up to four loops, a procedure is considered of matching the beta-function at a boundary of perturbative and non-perturbative regions. The contribution of the non-perturbative region to the gluon condensate is calculated with varying normalization condition alpha_s(m_tau^2) = 0.29, 0.30,..., 0.36 for two different ways of definition of the non-perturbative invariant charge in the infrared region. We obtain quite consistent results for values of the gluon condens…
Central exclusive Higgs boson production, pp -> p+H+p, at the LHC can provide important complementary contribution to the comprehensive study of the Higgs sector in a remarkably clean topology. The bb(bar) Higgs decay mode is especially attractive, and for certain BSM scenarios may even become the discovery channel. Obvious requirements for the success of such exclusive measurements are strongly suppressed and controllable backgrounds. One potential source of background comes from additional gluon radiation which leads to a three-jet bb(bar)g final state. We perform an explicit calculation of …
Taking into account the gluon condensate contributions, the form factors of the semileptonic $B_c^- \to D^{*0}\ellν$ transition with $l=τ, e$ are calculated in the framework of the three point QCD sum rules. The heavy quark effective theory limit of the form factors are also computed. The relevant total decay width as well as the branching ratio are evaluated and compared with the predictions of the other non-perturbative approaches.
The screening length in a quark-gluon plasma, the dispersion relations of thermal gluon self-energy and the quark potential at high temperature are studied within thermo field dynamics framework. By calculation of the real and imaginary parts, of the gluon self-energy in one-loop order in thermo field dynamics, we obtain an expression for the screening length in a quark-gluon plasma and the dispersion relation between the real and imaginary parts. At high temperature, using photon exchange between electron-positron in a skeleton expansion and ladder approximation, the screened Coulomb potentia…
