We formulate a kinetic theory of self-interacting meson fields with an aim to describe the freezeout stage of the space-time evolution of matter in ultrarelativistic nuclear collisions. Kinetic equations are obtained from the Heisenberg equation of motion for a single component real scalar quantum field taking the mean field approximation for the non-linear interaction. The mesonic mean field obeys the classical non-linear Klein-Gordon equation with a modification due to the coupling to mesonic quasi-particle excitations which are expressed in terms of the Wigner functions of the quantum fluctuations of the meson field, namely the statistical average of the bilinear forms of the meson creation and annihilation operators. In the long wavelength limit, the equations of motion of the diagonal components of the Wigner functions take a form of Vlasov equation with a particle source and sink which arises due to the non-vanishing off-diagonal components of the Wigner function expressing coherent pair-creation and pair-annihilation process in the presence of non-uniform condensate. We show that in the static homogeneous system, these kinetic equations reduce to the well-known gap equation in the Hartree approximation, and hence they may be considered as a generalization of the Hartree approximation method to non-equilibrium systems. As an application of these kinetic equations, we compute the dispersion relations of the collective mesonic excitations in the system near equilibrium.
We propose an analog of the familiar gap equation for the case of four-quark condensates at finite temperature. The condensates of interest correspond to scalar, vector, psudoscalar, axial vector, and tensor Dirac structures. Working with correlators at zero chemical potential without factorization, we arrive at coupled equations for these four-quark condensates and the masses of certain light-quark mesons. We study the temperature dependence of the four-quark condensates and masses; in one of our models, factorization of the four-quark condensates is shown to be increasingly violated as the t…
Wilson coefficients of light four-quark condensates in QCD sum rules are evaluated for pseudo-scalar $D$ mesons, thus, pushing the sum rules toward mass dimension six. Contrary to the situation for $\bar{q}q$ mesons the impact of the four-quark condensates for vacuum as well as in-medium situations is found to be rather small within the Borel window used in previous analyses. The complete four-quark condensate contributions enable to identify candidates for an order parameter of spontaneous chiral symmetry breaking/restoration as well as to evaluate stability criteria of operator product expan…
Using the quark-meson coupling (QMC) model, we study the density dependence of the quark and gluon condensates in nuclear matter. We show that the change of the quark condensate is mainly driven by the scalar field in the medium and that the reduction of the quark condensate is suppressed at high density, even in the mean-field approximation. The gluon condensate decreases by 4 - 6 % at nuclear saturation density. We also give a simple relationship between the change of the quark condensate and that of a hadron mass in the medium.
We evaluate the nucleon sigma term and in-medium quark condensate in the modified quark-meson coupling model which features a density-dependent bag constant. We obtain a nucleon sigma term consistent with its empirical value, which requires a significant reduction of the bag constant in the nuclear medium similar to those found in the previous works. The resulting in-medium quark condensate at low densities agrees well with the model independent linear order result. At higher densities, the magnitude of the in-medium quark condensate tends to increase, indicating no tendency toward chiral symm…
QCD sum rules for $D$ and $B$ mesons in a strongly interacting environment require the decomposition of Gibbs averaged operators related to tensor structures. We present a procedure to decompose these operators into vacuum and medium-specific parts, thus defining plain medium-specific condensates with coefficients vanishing in vacuum. Our decomposition allows for an identification of potential elements of order parameters for chiral restoration, in particular for higher mass-dimension quark-condensates which would be masked otherwise if operators with uncontracted Lorentz indices would be link…
We develop a quantum kinetic theory of the chiral condensate and meson quasi-particle excitations using the O(N) linear sigma model which describe the chiral phase transition both in and out of equilibrium in a unified way. A mean field approximation is formulated in the presence of mesonic quasi-particle excitations which are described by generalized Wigner functions. It is shown that in equilibrium our kinetic equations reduce to the gap equations which determine the equilibrium condensate amplitude and the effective masses of the quasi-particle excitations, while linearization of transport …
The study of light pseudoscalar quark-antiquark bound states in the Dyson-Schwinger approach with the effective QCD coupling enhanced by the interplay of the dimension 2 gluon condensate <A^2> and dimension 4 gluon condensate <F^2>, is extended to the eta-eta' complex. We include the effects of the gluon axial anomaly into the Dyson-Schwinger approach to mesons. The calculated masses, mixing and two-photon decay widths of eta and eta' mesons are in agreement with experiment. Also, in a model-independent way, we give the modification of the Gell-Mann--Okubo and Schwinger nonet relations due to …
We explore the effect of including quantum fluctuations in the two flavor Nambu$-$Jona-Lasinio model at finite temperature. This is accomplished, in a symmetry preserving way, by including collective and noncollective modes in the one-meson-loop gap equation which originate from poles and branch cuts in the complex plane, respectively. The inclusion of a boson cutoff, $Λ_b$, is necessary to regularize the meson-loop momenta. This new parameter is used to study the influence of going beyond the usual mean field approximation in the quark condensate. As the temperature increases, chiral symmetry…
In this talk we review results from studies with unconventional many hadron systems containing mesons: systems with two mesons and one baryon, three mesons, some novel systems with two baryons and one meson, and finally systems with many vector mesons, up to six, with their spins aligned forming states of increasing spin. We show that in many cases one has experimental counterparts for the states found, while in some other cases they remain as predictions, which we suggest to be searched in BESIII, Belle, LHCb, FAIR and other facilities.
Recent developments provided evidence that the dimension 2 gluon condensate <A^2> is important for the nonperturbative regime of Yang-Mills theories (quantized in the Landau gauge). We show that it may be relevant for the Dyson-Schwinger approach to QCD. In order that this approach leads to a successful hadronic phenomenology, an enhancement of the effective quark-gluon interaction seems to be needed at intermediate (p^2 \sim 0.5 GeV^2) momenta. It is shown that the gluon condensate <A^2> provides such an enhancement. It is also shown that the resulting effective strong running coupling leads …
D mesons serve as excellent probes of hot and/or dense strongly interacting matter. They can provide insight into the restoration of chiral symmetry. The chiral condensate as well as other chirally odd condensates, such as certain four-quark condensates, are linked to order parameters of spontaneous chiral symmetry breaking. Thus, the evaluation of these higher order condensate contributions in the framework of QCD sum rules is of high interest. We present a general method for projecting Lorentz indices of ground state expectation values providing a crucial step towards a comprehensive calcula…
The modification of the $ϕ$ meson spectrum in nuclear matter is studied in an updated QCD sum rule analysis, taking into account recent improvements in properly treating the chiral invariant and breaking components of four-quark condensates. Allowing both mass and decay width to change at finite density, the QCD sum rule analysis determines certain combinations of changes for these parameters that satisfy the sum rules equally well. A comprehensive error analysis, including uncertainties related to the behavior of various condensates at linear order in density, the employed renormalization sca…
We compute cross sections for incoherent and coherent diffractive J/$Ψ$ and $Ψ(2S)$ production in ultraperipheral heavy ion collisions. The dipole models used in these calculations are obtained by fitting the HERA deep inelastic scattering data and compared with available electron-proton diffraction measurements. We obtain a reasonably good description of the available ALICE data. We find that the normalization of the ultraperipheral cross section has large model dependence, but the rapidity dependence is more tightly constrained.
We study the properties of the light vector mesons ($ρ$, $ω$ and $ϕ$) in strange hadronic matter using the QCD sum rule approach. The in-medium masses of the vector mesons are calculated from the modifications of the light quark condensates and the gluon condensates in the hadronic medium. The light quark condensates in the hadronic matter are obtained from the values of the non strange and strange scalar fields of the explicit chiral symmetry breaking term in a chiral SU(3) model. The in-medium gluon condensate is calculated through the medium modification of a scalar dilaton field, which is …
The QCD sum rule approach to the in-medium behavior of hadrons is discussed for omega meson, nucleon and D meson. Emphasis is devoted to the impact of four-quark condensates and to order parameters of spontaneous symmetry breaking.
We derive the effective coarse-grained field equation for the scalar condensate of the linear sigma model in a simple and straightforward manner using linear response theory. The dissipative coefficient is calculated at tree level on the basis of the physical processes of sigma-meson decay and of thermal sigma-mesons and pions knocking sigma-mesons out of the condensate. The field equation is solved for hot matter undergoing either one or three dimensional expansion and cooling in the aftermath of a high energy nuclear collision. The results show that the time constant for returning the scalar…
The mass modifications of the light vector mesons ($ω$, $ρ$ and $ϕ$) are investigated in asymmetric nuclear matter in the presence of strong magnetic fields, using a QCD sum rule approach. These are computed from the medium modifications of the non-strange and strange light quark condensates as well as scalar gluon condensate. The quark and gluon condensates are calculated from the medium changes of the scalar fields (non-strange and strange) and a scalar dilaton field in the magnetized nuclear matter, within a chiral SU(3) model. The scalar dilaton field within the model breaks the scale inva…
We analyze the properties of four-quark condensates and scalar susceptibilities in the meson gas, within finite temperature Chiral Perturbation Theory (ChPT). The breaking of the factorization hypothesis does not allow for a finite four-quark condensate and its use as an order parameter, except in the chiral limit. This is rigorously obtained within ChPT and is therefore a model-independent result. Factorization only holds formally in the large $N_c$ limit and breaks up at finite temperature even in the chiral limit. Nevertheless, the factorization breaking terms are precisely those needed to …
The in-pseudoscalar-meson condensate can be represented through the pseudoscalar-meson's scalar form factor at zero momentum transfer. With the aid of a mass formula for scalar mesons, revealed herein, the analogue is shown to be true for in-scalar-meson condensates. The concept is readily extended to all hadrons so that, via the zero momentum transfer value of any hadron's scalar form factor, one can readily extract the value for a quark condensate in that hadron which is a measure of dynamical chiral symmetry breaking.
A scaled SU(3) Nambu - Jona-Lasinio Lagrangian is used to compute the mass of the nine scalar mesons in the vacuum and the mass of the gluball. It is shown that a suitable choice of the vacuum gluon condensate allows to reproduce the experimental masses of the scalar mesons except for the {$K^*_{0}$}(1430). This choice corresponds to a weak coupling between the gluon and quark condensates, giving a {$f_{0}$}(1500) or a {$f_{J}$}(1710) which is nearly a pure glueball.
We evaluate equal time point to point spatial correlation functions of mesonic currents at finite temperature. For this purpose we consider the QCD vacuum structure in terms of quark antiquark condensates and their fluctuations in terms of an irreducible four point structure of the vacuum. The temperature dependence of quark condensates is modeled using chiral perturbation theory for low temperatures and lattice QCD simulations near the critical temperature.We first consider the propagation of quarks in a condensate medium at finite temperature. We then determine the correlation functions in a…
We study the effect of a non-zero strange quark mass on the color-flavor-locked (CFL) phase of high density quark matter. We have previously shown that for a strange quark mass $m_s\sim m_u^{1/3}Δ^{2/3}$ the CFL state becomes unstable toward the formation of a neutral kaon condensate. Recently, several authors discovered that for $m_s\sim (2Δp_F)^{1/2}$ the CFL state contains gapless fermions, and that the gapless modes lead to an instability in current-current correlation functions. Using an effective theory of the CFL state we demonstrate that this instability is resolved by the formation of…
QCD sum rules are used to compute the first few moments of the mesonic quark momentum. Transverse, longitudinal and mixed transverse-longitudinal components are examined. The transverse size of the pion is shown to be dictated by the gluon condensate, even though the mass and the longitudinal distribution are dominated by the quark condensate. The implications of our results for color transparency physics and finite temperature QCD are discussed.
We consider the rate at which energy is emitted by neutrinos from the dense interior of neutron stars containing a Bose condensate of pions or kaons. The rates obtained are larger, by a factor of 2, than those found earlier, and are consistent with those found for the direct Urca processes.
We have determined the relation between the in-medium $ω$ meson mass and quark condensate in the framework of a Nambu Jona-Lasinio model constrained by some recent experimental data on the meson properties in nuclei. In addition to the usual four-quark interactions, we have included eight-quark terms in the Lagrangian. The parameters of this model have been determined using the meson properties in the vacuum as well as in the medium. More particularly, we have constrained both the in-medium pion decay constant to the value measured in experiments on deeply bound pionic atoms and the in-medium …
Masses and decay constants of scalar $D_0$ and $D_{s0}$ mesons in isospin asymmetric strange hadronic matter at finite temperature are evaluated using QCD sum rules and chiral SU(3) model. In-medium light quark condensates, $\left\langle \bar{u}u\right\rangle_{ρ_{B}}$ and $\left\langle \bar{d}d\right\rangle_{ρ_{B}}$, the strange quark condensates, $\left\langle \bar{s}s\right\rangle_{ρ_{B}}$, and the gluon condensates, $\left\langle \frac{α_{s}}π {G^a}_{μν} {G^a}^{μν} \right\rangle_{ρ_{B}}$, needed in QCD sum rule calculations are evaluated using chiral SU(3) model. As an application, we calcu…
QCD sum rules predict that the change of the strange quark condensate $<\bar s s>$ in hadron matter at finite baryon density causes a shift of the peak position of the di-electron spectra from $ϕ$ meson decays. Due to the expansion of hadron matter in heavy-ion collisions, the $ϕ$ peak suffers a smearing governed by the interval of density in the expanding fireball, which appears as effective broadening of the di-electron spectrum in the $ϕ$ region. The emerging broadening is sensitive to the in-medium change of $<\bar s s>$. This allows to probe directly in-medium modifications of $<\bar s s>…
We point out that chiral condensates at nonzero temperature and magnetic fields are in strict connection to the space-time integral of corresponding two-point neutral meson correlation functions in the pseudoscalar channel via the Ward-Takahashi identity. Screening masses of neutral pseudoscalar mesons, which are defined as the exponential decay of the corresponding spatial correlation functions in the long distance, thus are intrinsically connected to (inverse) magnetic catalysis of chiral condensates. To study this we performed lattice simulations of $(2+1)$-flavor QCD on $32^3\times N_t$ la…
In this letter we update our predictions for exclusive $J/Ψ$ and $Υ$ photoproduction in proton-proton and nucleus - nucleus collisions at the Run 2 LHC energies obtained with the color dipole formalism and considering the impact parameter Color Glass Condensate model (bCGC) for the forward dipole - target scattering amplitude. A comparison with the LHCb data on rapidity distributions and photon - hadron cross sections is presented. Our results demonstrate that the current data can be quite well described by the bCGC model, which takes into account nonlinear effects in the QCD dynamics and repr…
Pseudo-scalar and scalar $D$ mesons are considered within the QCD sum rule approach. We present an analysis of the mass splitting of the pseudo-scalar D - D-bar mesons and the relation to QCD condensates. Weinberg type sum rules are derived for chiral partners which highlight the role of the chiral condensate.
The Sakai-Sugimoto model provides a holographic description for chiral symmetry breaking. We use this model to investigate chirally broken phases in an external magnetic field at finite isospin and baryon chemical potentials. The equations of motion for the bulk gauge fields are solved analytically and the free energy is computed from the Yang-Mills and Chern-Simons contributions to the D8 brane action. In the case of a neutral pion condensate, a magnetic field is found to induce nonzero gradients of the Goldstone boson fields corresponding to meson supercurrents. A charged pion condensate, on…
QCD sum rules are evaluated at finite nucleon densities and temperatures to determine the change of mass parameters for the lightest vector mesons $ρ$, $ω$ and $ϕ$ in a strongly interacting medium. For conditions relevant for the starting experiments at HADES we find that the in-medium mass shifts of the $ρ$ and $ω$ mesons are governed, within the Borel QCD sum rule approach, by the density and temperature dependence of the four-quark condensate. In particular, the variation of the strength of the density dependence of the four-quark condensate reflects directly the decreasing mass of the $ρ$ …
A detailed analysis of the lowest two moments of the $ϕ$ meson spectral function in vacuum and nuclear matter is performed. The consistency is examined between the constraints derived from finite energy QCD sum rules and the spectra computed within an improved vector dominance model, incorporating the coupling of kanonic degrees of freedom with the bare $ϕ$ meson. In the vacuum, recent accurate measurements of the $e^+ e^- \to K^+ K^-$ cross section allow us to determine the spectral function with high precision. In nuclear matter, the modification of the spectral function can be described by …
QCD sum rules for D and B mesons embedded in cold nuclear matter are evaluated. We quantify the mass splitting of D - D-bar and B - B-bar mesons as a function of the nuclear matter density; extrapolated to saturation density it is in the order of 60 and 130 MeV driven essentially by the condensates <q-adjoint q>, <q-adjoint g sigma G q> and <q-bar q>. The genuine chiral condensate <q-bar q>, amplified by heavy-quark masses, enters the Borel transformed sum rules for the mass splitting beyond linear density dependence. Including strange quark condensates reveals a umerically smaller and opposit…
An updated investigation of QCD sum rules for the first two moments of rho meson spectral functions, both in vacuum and in-medium, is performed with emphasis on the role of the scale related to spontaneous chiral symmetry breaking in QCD. It is demonstrated that these lowest moments of vector current spectral distributions do permit an accurate sum rule analysis with controlled input including QCD condensates of the lowest dimensions, whereas higher moments are subject to uncertainties from higher dimensional condensates. Possible connections with Brown-Rho scaling are discussed. The factoriza…
The recent measurement of the mass of neutron stars (PSR J1614 - 2230, PSR J0348 + 0432, MSP J0740 + 6620) restricts the lower limit $\sim 2M_{\odot}$ of the maximum mass of such compact stars, making it possible for dense matter to exist in massive stars. The relativistic mean field theory with parameter sets FSUGold including Kaon condensation is used to describe the properties of neutron stars in $β$ equilibrium. Through careful choice of the parameter of the $σ$-cut $c_σ$, we are able to produce a maximum mass neutron star with Kaon condensation heavier than $2M_{\odot}$, and we find that …
Previously the quark and meson properties in a many quark system at finite temperature have been studied within effective QCD approaches in the Hartree approximation. In the present paper we consider the influence of the mesonic correlations on the quark self-energy and on the quark propagator within a systematic $1/N_c$- expansion. Using a general separable ansatz for the nonlocal interaction, we derive a selfconsistent equation for the $1/N_c$ correction to the quark propagator. For a separable model with cut-off formfactor, we obtain a decrease of the condensate of the order of 20\% at zero…
We propose a quantization procedure for the nucleon-scalar meson system, in which an arbitrary mean scalar meson field $ϕ$ is introduced. The equivalence of this procedure with the usual ones is proven for any given value of $ϕ$. By use of this procedure, the scalar meson field in the Walecka's RMFT and in Chin's RHA are quantized around the mean field. Its corrections on these theories are considered by perturbation up to the second order. The arbitrariness of $ϕ$ makes us free to fix it at any stage in the calculation. When we fix it in the way of Walecka's RMFT, the quantum corrections are …
Based on QCD sum rules we explore the consequences of a pure chiral restoration scenario for the rho meson, where all chiral symmetry breaking condensates are dropped whereas the chirally symmetric condensates remain at their vacuum values. This pure chiral restoration scenario causes the drop of the rho spectral moment by about 120 MeV. The complementarity of mass shift and broadening is discussed. A simple parametrization of the rho spectral function leads to a width of about 600 MeV if no shift of the peak position is assumed.
Open charm mesons (pseudo-scalar and scalar as well as axial-vector and vector) propagating or resting in nuclear matter display an enhanced sensitivity to the chiral condensate. This offers new prospects to seek for signals of chiral restoration, in particular in p-A and p-bar-A reactions as envisaged in first-round experiments by the CBM and PANDA collaborations at FAIR. Weinberg type sum rules for charming chiral partners are presented, and the distinct in-medium modifications of open-charm mesons are discussed. We also address the gluon condensates near Tc and their impact on QCD sum rules…
The effect of narrow dibaryon resonances to nuclear matter and structure of neutron stars is investigated in the mean-field theory (MFT) and in the relativistic Hartree approximation (RHA). The existence of massive neutron stars imposes constraints to the coupling constants of the omega- and sigma-mesons with dibaryons. We conclude that the experimental candidates to dibaryons d1(1920) and d'(2060) if exist form in nuclear matter a Bose condensate stable against compression. This proves stability of the ground state for nuclear matter with a Bose condensate of the light dibaryons.
