Properties of a scalar $σ$-meson are investigated in the two-flavor Nambu-Jona-Lasinio model with the Polyakov loop. Model analysis of the phase diagram of strong interacting matter is performed. The temperature dependence of the $σ\rightarrowππ$ decay width is studied at the zero chemical potential and near the critical end-point. The calculated strong coupling constant $g_{σππ}$ and the decay width are compared with available experimental data and other model results. Nonthermal enhancement of the total decay width is noted for the $σ$ meson near the critical end-point when the condition $m_σ\geq2m_π$ is broken.
We study D meson resonances in hot, dense quark matter within the NJL model and its Polyakov-loop extension. We show that the mass splitting between D^+ and D^- mesons is moderate, not in excess of 100 MeV. When the decay channel into quasifree quarks opens (Mott effect) at densities above twice saturation density, the decay width reaches rapidly the value of 200 MeV which entails a spectral broadening sufficient to open J/psi dissociation processes. Contrary to results from hadronic mean-field theories, the chiral quark model does not support the scenario of a dropping D meson masses so that …
We study the equation of state of QCD using an improved version of the three-flavor Polyakov-Nambu-Jona-Lasinio model beyond the mean-field approximation. It incorporates the effects of unquenched quarks into the Polyakov-loop effective potential, as well as mesonic contributions to the grand-canonical potential. We study in full detail the calculation of the thermodynamical potential in this approach and compare the resulting pressure and entropy density with the most-recent lattice-QCD calculations at zero baryochemical potential. Finally, we present some exploratory results at finite chemic…
Quark-hadron matter at finite temperature and density is studied using a two-flavor, color SU(2) (P)NJL model. The hadronic effective Lagrangian, derived by bosonization of the quark fields and renormalized using the Eguchi method, emerges in the form of an extended linear sigma model with meson and diquark-baryon fields. Chiral and diquark condensates are studied as functions of temperature and baryon density. Masses of mesons and diquark-baryons are calculated with and without the Polyakov loop effect. We investigate the equation of state of quark-hadron matter by taking into account the con…
Recent consensus on the $N_f=2+1$ equation of state at vanishing chemical potential from different lattice-QCD groups has spoiled the previous agreement with the outcome from the mean-field Polyakov-Nambu-Jona-Lasinio model. In this letter we review the thermodynamics of the PNJL model introducing two important aspects needed to describe the pressure computed in the lattice QCD. First, we consider the thermodynamics of the model beyond the mean-field approach to include pseudoscalar and scalar mesonic-like fluctuations into the grand-canonical potential. This accounts for the hadronic pressure…
We compute the equation of state of hadronic matter at finite temperature with zero net baryon density by the Nambu-Jona-Lasinio model for interacting quarks in uniform background temporal color gauge fields. In the low temperature confining phase, unphysical thermal quark-antiquark excitations which would appear in the mean field approximation, are eliminated by enforcing vanishing expectation value of the "Polyakov-loop" of the background gauge field, while in the high temperature confining phase this expectation value is taken as close to unity allowing thermal excitations of free quarks an…
We study chiral symmetry restoration and quark deconfinement beyond mean field approximation in a magnetized PNJL model. The feedback from mesons to quarks modifies the quark coupling constant and Polyakov potential. As a result, the separate critical temperatures for the two phase transitions at mean field level coincide and the magnetic catalysis becomes inverse magnetic catalysis, when the meson contribution is included.
Various thermodynamic quantities and the phase diagram of strongly interacting hot and dense magnetized quark matter are obtained with the $ 2 $-flavour Nambu-Jona-Lasinio model with Polyakov loop considering finite values of the anomalous magnetic moment (AMM) of the quarks. Susceptibilities associated with constituent quark mass and traced Polyakov loop are used to evaluate chiral and deconfinement transition temperatures. It is found that, inclusion of the AMM of the quarks in presence of the background magnetic field results in a substantial decrease in the chiral as well as deconfinement …
The behavior of strange matter in the frame of the SU(3)Polyakov-loop extended Nambu-Jona-Lasinio model including $U_A(1)$ anomaly is considered. We discuss the appearance of a peak in the ratio of the number of strange mesons to non-strange mesons known as the "horn". The PNJL model gives a schematic description of the chiral phase transition and meson properties at finite temperature and density. Using the model, we can show that the splitting of kaon and anti-kaon masses appears as a result of introduction of density. This may explain the difference in the $K^+/π^+$ ratio and $K^-/π^-$ rati…
The properties of the vector meson current-current correlation function and its spectral representation are investigated in details with and without isoscalar-vector interaction within the framework of effective QCD approach, namely Nambu-Jona-Lasinio (NJL) model and its Polyakov Loop extended version (PNJL), at finite temperature and finite density. The influence of the isoscalarvector interaction on the vector meson correlator is obtained using the ring resummation known as the Random Phase Approximation (RPA). The spectral as well as the correlation function in PNJL model show that the vect…
We provide a novel calculation of the Mott effect in non-local PNJL models. We find that the "deconfinement" transition temperature in these models is lower than the Mott temperature. Furthermore, the mass and the width of the $σ$ and the $π$ meson modes is calculated with the result that the width in nonlocal models is in general reduced as compared to local models. Difficulties encountered while attempting to "Wick rotate" covariant models are carefully discussed.
Within the three-flavor PNJL and EPNJL chiral quark models we have obtained pseudoscalar meson properties in quark matter at finite temperature $T$ and baryochemical potential $μ_B$. We compare the meson pole (Breit-Wigner) approximation with the Beth-Uhlenbeck (BU) approach that takes into account the continuum of quark-antiquark scattering states when determining the partial densities of pions and kaons. We evaluate the kaon-to-pion ratios along the (pseudo-)critical line in the $T-μ_B$ plane as a proxy for the chemical freezeout line, whereby the variable $x=T/μ_B$ is introduced that corres…
In this paper we detail the thermodynamics of two flavor nonlocal Polyakov-Nambu-Jona-Lasinio models for different parametrizations of the quark interaction regulators. The structure of the model is upgraded in order to allow for terms in the quark selfenergy which violate Lorentz invariance due to the presence of the medium. We examine the critical properties, the phase diagram as well as the equation of state. Furthermore, some aspects of the Mott effect for pions and sigma mesons are discussed explicitly within a nonlocal Polyakov-Nambu-Jona-Lasinio model. In particular, we continued the me…
We have studied the vector meson spectral function (VMSF) in a hot and dense medium within an effective QCD model namely the Nambu-Jona-Lasinio (NJL) and its Polyakov Loop extended version (PNJL) with and without the effect of isoscalar vector interaction (IVI). The effect of the IVI has been taken into account using the ring approximation. We obtained the dilepton production rate (DPR) using the VMSF and observed that at moderate temperature it is enhanced in the PNJL model as compared to the NJL and Born rate due to the suppression of color degrees of freedom.
In this work we have re-explored our earlier study on the vector meson spectral function and its spectral property in the form of dilepton rate in a two-flavour Polyakov loop extended Nambu-Jona-Lasinio (PNJL) model in presence of a strong entanglement between the chiral and Polyakov loop dynamics. The entanglement considered here is generated through the four-quark scalar type interaction in which the coupling strength depends on the Polyakov loop and runs with temperature and chemical potential. The entanglement effect is also considered for the four-quark vector type interaction in the same…
The crucial points of physics of light scalar mesons are discussed. The special attention is given to the chiral shielding of lightest scalar mesons and the production of the well established light scalar mesons in the ϕradiative decays. Arguments in favor of the four-quark model of the a0(980) and f0(980) mesons are given.
The following topics are considered. 1. Confinement, chiral dynamics and light scalar mesons. 2. $ϕ$-meson radiative decays about nature of light scalar resonances. Arguments in favor of the four-quark model of the $a_0(980)$ and $f_0(980)$ mesons are given.
The structure of the scalar mesons has been a subject of debate for many decades. In this work we look for $\bar{q}q$ states among the physical resonances using an extended Linear Sigma Model that contains scalar, pseudoscalar, vector, and axial-vector mesons both in the non-strange and strange sectors. We perform global fits of meson masses, decay widths and amplitudes in order to ascertain whether the scalar $\bar{q}q$ states are below or above 1 GeV. We find the scalar states above 1 GeV to be preferred as $\bar{q}q$ states.
For the first time, as far as we know, in field theory are found explicit forms of propagators satisfying the Källen -- Lehmann representation. To be exact, it is shown that scalar meson propagators, taking into account a virtual intermediate state contribution to the resonance self-energy, satisfy the Källen -- Lehmann representation in the wide domain of coupling constants of the light scalar mesons with the two-particle states. It is proposed to use these propagators in routine fitting data about light scalar mesons to reveal physics underlying the light scalar mesons.
Decays of hidden-charm scalar tetra-quark mesons as the partners of D_{s0}(2317) which has successfully been assigned to the iso-triplet scalar tetra-quark [c,n][sbar,nbar]_{I=1} meson are studied. Because OZI-rule allowed strong decays are kinematically limited, their radiative decays are expected to be important.
We investigate chemical-potential ($μ$) and temperature ($T$) dependence of scalar and pseudo-scalar meson masses for both real and imaginary $μ$, using the Polyakov-loop extended Nambu--Jona-Lasinio (PNJL) model with three-flavor quarks. A three-flavor phase diagram is drawn in $μ^2$-$T$ plane where positive (negative) $μ^2$ corresponds to positive (imaginary) $μ$. A critical surface is plotted as a function of light- and strange-quark current mass and $μ^2$. We show that $μ$-dependence of the six-quark Kobayashi-Maskawa-'t Hooft (KMT) determinant interaction originated in $U_\mathrm{A}(1)$ a…
Despite the apparent simplicity of meson spectroscopy, light scalar mesons cannot be accommodated in the usual $q\bar q$ structure. We study the description of the scalar mesons below 2 GeV in terms of the mixing of a chiral nonet of tetraquarks with conventional $q\bar q$ states. A strong diquark-antidiquark component is found for several states. The consideration of a glueball as dictated by quenched lattice QCD drives a coherent picture of the isoscalar mesons.
The following topics are considered. 1) Confinement, chiral dynamics, and light scalar mesons. 2) Chiral shielding of the σ(600) 3)The ϕmeson radiative decays about nature of light scalar resonances. 4) The J/ψdecays about nature of light scalar resonances. 5) The a0(980)\toγγand f0(980)\toγγdecays about nature of light scalar resonances. 6) New round in γγ\toπ^+π^-, the Belle data. 7) The a0(980)-f0(980) mixing: theory and experiment. Arguments in favor of the four-quark model of the a0(980) and f0(980) mesons are given.
We study the semileptonic decays of $D_{s}^{+}$, $D^{+}$, and $D^{0}$ mesons into the light scalar mesons [$f_{0} (500)$, $K_{0}^{\ast} (800)$, $f_{0} (980)$, and $a_{0}(980)$] and the light vector mesons [$ρ(770)$, $ω(782)$, $K^{\ast} (892)$, and $ϕ(1020)$]. With the help of a chiral unitarity approach in coupled channels, we compute the branching fractions for scalar meson processes of the semileptonic $D$ decays in a simple way. Using current known values of the branching fractions, we make predictions for the branching fractions of the semileptonic decay modes with other scalar and vector …
We study the effects of light scalar mesons on the skyrmion properties by constructing and examining a mesonic model including pion, rho meson, and omega meson fields as well as two-quark and four-quark scalar meson fields. In our model, the physical scalar mesons are defined as mixing states of the two- and four-quark fields. We first omit the four-quark scalar meson field from the model and find that when there is no direct coupling between the two-quark scalar meson and the vector mesons, the soliton mass is smaller and the soliton size is larger for lighter scalar mesons; when direct coupl…
In this work, I studied the spectrum of scalar mesons and axial-vector mesons via Dyson-Schwinger equation and Bethe-Salpeter equation approach in the rainbow-ladder approximation. An interaction model with a repulsive term added to the one used for the pseudoscalar and vector mesons is proposed. My results are consistent with the experiment data and other model results, which shows that this interaction model is effective for all the heavy, heavy-light, and light scalar and axial-vector mesons.
For some experimental guidelines of the next millenium, I review the determinations of the masses, decays and mixings of the gluonia, scalar and hybrid mesons from QCD spectral sum rules and low-energy theorems, and compare them with the lattice.
We estimate the rates for radiative transitions of the lightest scalar mesons f_0(980) and a_0(980) to the vector mesons rho and omega. We argue that measurements of the radiative decays of those scalar mesons can provide important new information on their structure.
We study the possibility that the light scalar mesons are (qbar qbar q q) states rather than (qbar q). We perform a lattice QCD calculation of pseudoscalar meson scattering amplitudes, ignoring quark loops and quark annihilation, and find indications that for sufficiently heavy quarks there is a stable four-quark bound state with J^{PC}=0^{++} and non-exotic flavor quantum numbers.
The light scalar mesons, discovered over forty years ago, became a challenge for the naive quark-antiquark model from the outset. At present the nontrivial nature of these states is no longer denied practically anybody. Two-photon physics has made a substantial contribution to understanding the nature of the light scalar mesons. Recently, it entered a new stage of high statistics measurements. We review the results concerning two-photon production mechanisms of the light scalars, based on the analysis of current experimental data.
The following topics are considered. 1) Confinement, chiral dynamics, and light scalar mesons. 2) Chiral shielding of the $σ(600)$. 3) The $ϕ$ meson radiative decays about nature of light scalar resonances. 4) The $J/ψ$ decays about nature of light scalar resonances. 5) The $a_0(980)\toγγ$ and $f_0(980)\toγγ$ decays about nature of light scalar resonances. 6) New round in $γγ\toπ^+π^-$, the Belle data. Arguments in favor of the four-quark model of the $a_0(980)$ and $f_0(980)$ mesons are given.
We study the two point-function for the scalar mesons $σ, κ, f_0(980)$ and $a_0(980)$ as diquak-antidiquark states. We also study the decays of these mesons into $ππ$, $Kπ$ and $K\bar{K}$. We found that the couplings are consistent with existing experimental data, pointing in favor of the four-quark structure for the light scalar mesons.
We consider chiral perturbation theory with an explicit broad $σ$-meson and study its contribution to the scalar form factors of the pion and the nucleon. Our goal is to learn more about resonance saturation in the scalar sector.
The scalar mesons $σ(600)$, $κ(800)$, $f_0(980)$ and $a_0(980)$ together with the pseudo Goldstone bosons $π$, $K$, and $η$ may be considered as the Higgs sector of strong interaction. After a long time of uncertainty about the internal structure of the scalar mesons there now seems to be consistency which is in line with the major parts of experimental observations. Great progress has been made by introducing the unified model of Close and Törnqvist. This model states that mesons below 1 GeV may be understood as $q^2\bar{q}^2$ in S-wave with some $q\bar{q}$ in P-wave in the center, further ou…
We discuss the electroproduction of pseudoscalar ($0^{-+}$) or scalar ($0^{++}$) meson production off the scalar target. The most general formulation of the differential cross section for the $0^{-+}$ or $0^{++}$ meson production process involves only one or two hadronic form factors, respectively, on a scalar target. The Rosenbluth-type separation of the differential cross section provides the explicit relation between the hadronic form factors and the different parts of the differential cross section in a completely model-independent manner. The absence of the beam spin asymmetry for the pse…
The masses of the low-lying scalar mesons are investigated in the three-flavor Nambu Jona-Lasinio (NJL) model by treating the scalar mesons as composite objects of a quark and an antiquark. It is known that a simple $\bar qq$ picture fails to reproduce so-called inverse mass ordering for the scalar mesons. Recently a new mechanism to reproduce the observed mass spectrum of the scalar mesons was proposed in a linear sigma model by introducing flavor symmetry breaking induced by the U(1) axial anomaly. Motivated by this proposal, we examine whether this new mechanism works also in the NJL model.…
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.
In this work we shall investigate the mass modifications of scalar mesons $\left( D_{0}, B_{0}\right)$,vector mesons $\left( D^{\ast}, B^{\ast}\right)$ and axial-vector mesons $\left(D_{1}, B_{1}\right)$ at finite density and temperature of the nuclear medium. The above mesons are modified in the nuclear medium through themodification of quark and gluon condensates. We shall find the medium modification of quark and gluon condensates within chiral SU(3) model through the medium modification of scalar-isoscalar fields $σ$ and $ζ$ at finite density and temperature. These medium modified quark an…
We study the photoproduction of scalar mesons close to the threshold of f_0(980) and a_0(980) using a unitary chiral model. Peaks for both resonances show up in the invariant mass distributions of pairs of pseudoscalar mesons. A discussion is made on the photoproduction of these resonances in nuclei, which can shed light on their nature, a subject of continuous debate.
I review a proposed pattern of the light scalar mesons with q\bar{q} mesons and glueball above 1 GeV and tetraquark mesoniums below 1 GeV. Several challenges and caveats of calculating these light scalar mesons with dynamical fermions are discussed.
We discuss in detail the extraction of hadronic mixing strengths from lattice studies. We apply this to the mixing of a scalar glueball and a scalar meson in the quenched approximation. We also measure correlations appropriate for flavour-singlet scalar mesons using dynamical quark configurations from UKQCD. This enables us to compare the results from the quenched study of the mixing with the direct determination of the mixed spectrum. Improved methods of evaluating the disconnected quark diagrams are also presented.
Combining the recent lattice calculation of $a_0(1450)$ and $σ(600)$ mesons with the overlap fermion in the chiral regime with the pion mass less than $300 {\rm MeV}$, the quenched lattice calculation of the scalar glueball, and the phenomenological study of the mixing of isoscalar scalar mesons $f_0(1710)$, $f_0(1500)$, $f_0(1370)$ through their decays, a simple pattern for the light scalar mesons begins to emerge. Below 1 GeV, the scalar mesons form a nonet of tetraquark mesoniums. Above 1 GeV, the nonent $q\bar{q}$ mesons are made of an octet with largely unbroken SU(3) symmetry and a fairl…
After presenting the motivations to explore the low-lying scalar mesons such as the $σ$, $a_0$ and $κ$ in the unquenched as well as quenched lattice QCD, we review the works done by our collaboration (SCALAR Collaboration) with a what-to-do-next list. We briefly mention the imporatance to explore the $N_c$ dependence of and possible effects of the $U_A(1)$ anomaly to the properties the low-lying scalar mesons.
The propagation of the scalar (σand δ) and vector (ωand ρ) mesons in an iso-asymmetric nuclear matter is studied in detail, using the Walecka model. We calculate the invariant masses and spectral functions of the mesons, including the effect of meson mixing. At finite density, the mixing effect is quite important in the propagation of the scalar and (longitudinal) vector mesons. In the σchannel, we find a three-peak structure in the spectral function, caused by the mixing effect.
We derive the QCD sum rules for the vector and scalar meson mixing in nuclear medium, using a two quark interpolating field for both mesons. Modeling the mixing via a nucleon hole contribution with known coupling constant, the sum rule can be used to determine the overlap of the interpolating field and the scalar meson. In the I=0 channel, we find a stable Borel curve and an overlap that is about 10% of the corresponding value in the pseudo scalar or vector channel. The sum rule in the I=1 channel is less reliable but also consistent with a small value for the overlap. These results suggest th…
We study the effects of isovector-scalar ($δ$)-meson on neutron star. Influence of $δ$-meson on both static and rotating neutron star is discussed. Inclusion of $δ$-meson in a neutron star system consisting of proton, neutron and electron, make the equation of state stiffer in higher density and consequently increases the maximum mass of the star. But induction of $δ$-meson in the hyperon star decreases the maximum mass of the hyperon star. This is due to the early evolution of hyperons in presence of $δ-$meson.
Employing QCD sum rules the in-medium modifications of scalar charm mesons in a cold nuclear matter environment are estimated. The mass splitting of D*-D*-bar is quantified.
We determine the mass and strength of the scalar meson from NN scattering data by renormalizing the One Boson Exchange Potential. This procedure provides a great insensitivity to the unknown short distance interaction making the vector mesons marginally important and allowing for SU(3) couplings in the 1S0 channel. The scalar meson parameters are tightly constrained by low energy np. We discuss whether this scalar should be compared to the recent findings based on the Roy equations analysis of pipi scattering.
It is shown that recently proposed RMF model with $σ$ and $δ$ meson interaction agrees with the observational data and presents an interesting structure with phase transition in the outer part of neutron star core.
