Lattice simulations along with studies in continuum QCD indicate that non-perturbative quantum fluctuations lead to an infrared regularisation of the gluon propagator in covariant gauges in the form of an effective mass-like behaviour. In the present work we propose an analytic understanding of this phenomenon in terms of gluon condensation through a dynamical version of the Higgs mechanism, leading to the emergence of color condensates. Within the functional renormalisation group approach we compute the effective potential of covariantly constant field strengths, whose non-trivial minimum is related to the color condensates. In the physical case of an SU(3) gauge group this is an octet condensate. The value of the gluon mass obtained through this procedure compares very well to lattice results and the mass gap arising from alternative dynamical scenarios.
We establish a novel method of obtaining the gauge-invariant bilocal condensate of gluon fields from the solutions of the Dyson--Schwinger equations (DSE) which works in the infrared and ultraviolet limits. We present explicit results for SU(3) case in four dimensions, and compare to other related analytical and lattice results.
The aim of this work is to study the holographic dual to the gauge theory with a nonzero gluon condensate. We check for consistency the holographic way of describing the condensate and calculate the expectation value of a small Wilson loop in the presence of the gluon condensate, thus obtaining the relevant coefficient in the operator product expansion of the small loop in different holographic models. We also study the effect of the condensate on the Gross-Ooguri phase transition in the correlator of two circular Wilson loops in parallel and concentric configurations. In the numerical study o…
We study the spectra of light mesons as well as the dissociation of a quarkonium and monopole-anti monopole bound state in a gluon condensate background. In order to describe the confining phase we introduce an IR cutoff in two ways, namely the hard wall and the braneless approaches. We find that the meson spectra strongly depend on the gluon condensate in the braneless approach, while they do not in the hard wall model. The latter result appears to be a more probable feature of QCD.
We derive recently obtained relations, relating the logarithmic gauge coupling derivative of the hadron mass and the cosmological constant to the matter and vacuum gluon condensates, within a Hamiltonian framework. The key idea is a canonical transformation which brings the relevant part of the Hamiltonian into a suitable form. Furthermore we illustrate the relations within the Schwinger model and ${\cal N}=2$ super Yang Mills theory (Seiberg-Witten theory).
We derive a holographic prediction of the deconfinement temperature $T_c$ at vanishing chemical potential within a simplest AdS/QCD model with dynamical dilaton. Our analysis leads to a linear relation between $T_c^4$ and the gluon condensate. After normalizing this relation to the lattice data for $SU(3)$ pure gauge theory, the standard phenomenological value of gluon condensate from QCD sum rules leads to the prediction $T_c=156$ MeV which is in a perfect agreement with the modern lattice results and freeze-out temperature measured by the ALICE Collaboration.
We discuss application of formalism of small-$x$ effective action for reggeized gluons, \cite{Gribov,LipatovEff,BFKL}, for the calculation of classical gluon field of relativistic color charge, similarly to that done in CGC approach of \cite{Venug,Kovner}. The equations of motion with the reggeon fields are solved in LO and NLO approximations and new solutions are found. The results are compared to the calculations performed in the CGC framework and it is demonstrated that the LO CGC results for the classical field are reproduced in our calculations. Possible applications of the NLO solution i…
In a scalar approximation the distribution of a gluon condensate in a glueball is calculated. In this approximation the SU(3) gauge fields are separated on two parts: (1) is the $SU(2) \subset SU(3)$ subgroup, (2) is the coset $SU(3) / SU(2)$. Using an approximate nonperturbative quantization technique two scalar fields are applied for the description of the SU(2) and coset degrees of freedom. In this approach 2-point Green's functions are a bilinear combination of scalar fields and 4-point Green's functions are the product of 2-points Green's functions.
We propose a clear definition of the gluon condensate within the large-$β_0$ approximation as an attempt toward a systematic argument on the gluon condensate. We define the gluon condensate such that it is free from a renormalon uncertainty, consistent with the renormalization scale independence of each term of the operator product expansion (OPE), and an identical object irrespective of observables. The renormalon uncertainty of $\mathcal{O}(Λ^4)$, which renders the gluon condensate ambiguous, is separated from a perturbative calculation by using a recently suggested analytic formulation. The…
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.
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 test gauge/string duality by evaluating expectation values of small Wilson loops in pure Yang-Mills theories. On the gauge-theory side, there exists rich phenomenology. The dual formulation provides with a universal language to evaluate the gluon condensate and quadratic correction in terms of the metric in the fifth coordinate. Quantitatively, the estimated value of the gluon condensate is approximately 0.010 GeV^4.
We propose a new reformulation of Yang-Mills theory in which three- and four-gluon self-interactions are eliminated at the price of introducing a sufficient number of auxiliary fields. We discuss the validity of this reformulation in the possible applications such as dynamical gluon mass generation, color confinement and glueball mass calculation. We emphasize the transverse-gluon pair condensation as the basic mechanism for dynamical mass generation. The confinement is realized as a consequence of a fact that the auxiliary fields become dynamical in the sense that they acquire the kinetic ter…
We demonstrate that a clear physical content and relevance can be attributed to the on-shell BRST-invariant mixed gluon--ghost condensate of mass dimension two which was recently proposed by the author. We argue that a gauge invariant observable is associated with the mixed condensate.
We determine the non-perturbative gluon condensate of four-dimensional SU(3) gauge theory in a model independent way. This is achieved by carefully subtracting high order perturbation theory results from non-perturbative lattice QCD determinations of the average plaquette. No indications of dimension two condensates are found. The value of the gluon condensate turns out to be of a similar size as the intrinsic ambiguity inherent to its definition.
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.
After making some critical comments about the traditional method of extracting the gluon condensate from lattice QCD data, I present an alternative analysis. The result is more than a factor of five larger than the phenomenological value. Two closely related subjects, the effects of the infrared renormalons on the extraction and the Lepage and Mackenzie improvement on a lattice perturbation series, are also discussed.
We derive the set of kinetic equations that control the evolution of gluons in the presence of a condensate. We show that the dominant singularities remain logarithmic when the scattering involves particles in the condensate. This allows us to define a consistent small angle approximation.
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 structure of the confining string in Yang-Mills theory using the method of the field strength correlators. The method allows us to demonstrate that both the local fluctuations of the topological charge and the gluon condensate are suppressed in the vicinity of the string axis in agreement with results of lattice simulations.
We study the binding energy of a heavy quark-antiquark ($q\bar{q}$) pair using the first-order path integral formalism. This makes the Yang-Mills constraint equation explicit, and highlights that it is valid without relying on a semiclassical approximation. A generalized gauge-covariant Coulomb gauge is chosen to allow for a decomposition of the chromoelectric field into a gauge-covariant generalization of transverse and longitudinal parts. This decomposition makes it clear that the $q\bar{q}$ binding energy is determined solely by the solution to the constraint equation. Assuming that the low…
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.
Within a self-consistent proper-time Renormalization Group (RG) approach we investigate an effective QCD trace anomaly realization with dilatons and determine the finite-temperature behavior of the gluon condensate. Fixing the effective model at vanishing temperature to the glueball mass and the bag constant a possible gluonic phase transition is explored in detail. Within the RG framework the full non-truncated dilaton potential analysis is compared with a truncated potential version.
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.
A calculation of the thermal quark propagator is presented taking the gluon condensate above the critical temperature into account. The quark dispersion relation following from this propagator is derived.
The gluon condensate as a function of temperature and baryon density in a nucleon medium is obtained from an effective dilaton Lagrangian. It is shown that, at a normal nuclear density of nucleons, n_0 = 0.17 fm^{-3} the gluon condensate decreases by about 10%.
We present a calculation of the thermal quark propagator taking the gluon condensate above the critical temperature into account. The quark dispersion relation following from this propagator, describing two massive modes, is discussed.
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…
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…
An expression for the photon condensate in quantum electrodynamics is presented and generalized to deduce a simple relation between the gluon condensate and the running coupling constant of quantum chromodynamics (QCD). Ambiguities in defining the condensates are discussed. The values of the gluon condensate from some Ansätze for the running coupling in the literature are compared with the value determined from QCD sum rules.
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…
We give the hyperasymptotic expansion of the plaquette with a precision that includes the terminant associated to the leading renormalon. Subleading effects are also considered. The perturbative series is regulated using the principal value prescription for its Borel integral. We use this analysis to give a determination of the gluon condensate in SU(3) pure gluodynamics that is independent of the scale and renormalization scheme used for the coupling constant: $\langle G^2 \rangle_{\rm PV} (n_f=0)=3.15(18)\; r_0^{-4}$.
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.
A calculation of the thermal quark propagator is presented taking the gluon condensate above the critical temperature into account. The quark dispersion relation and the dilepton production following from this propagator are derived.
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…
We study the operator product expansion of the plaquette (gluon condensate) and the self-energy of an infinitely heavy quark. We first compute their perturbative expansions to order $α^{35}$ and $α^{20}$, respectively, in the lattice scheme. In both cases we reach the asymptotic regime where the renormalon behavior sets in. Subtracting the perturbative series, we obtain the leading non-perturbative corrections of their respective operator product expansions. In the first case we obtain the gluon condensate and in the second the binding energy of the heavy quark in the infinite mass limit. The …
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 $Λ_{QCD}=0.28$.
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…
Concerning the trace anomaly in field theory a nonvanishing vacuum energy breaks the scale symmetry as well, in addition to the usual beta function dependent term, requiring a unit operator in the trace anomaly. This additional term is also necessary in quantum chromodynamics (QCD) to cancel the inherent ambiguity in the gluon condensate. The inseparability of the gluon condensate effect from the perturbative contribution to the vacuum energy renders it impossible to isolate the gluon condensate effect on the cosmological constant.
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 co…
