The finite temperature phase transition of strongly interacting matter is studied within a nonlocal chiral quark model of the NJL type coupled to a Polyakov loop. In contrast to previous investigations which were restricted to the mean-field approximation, mesonic correlations are included by evaluating the quark-antiquark ring sum. For physical pion masses, we find that the pions dominate the pressure below the phase transition, whereas above T_c the pressure is well described by the mean-field approximation result. For large pion masses, as realized in lattice simulations, the meson effects are suppressed.
We study the impact of higher order quark-meson scattering processes on the chiral phase structure of two-flavour QCD at finite temperature and quark density. Thermal, density and quantum fluctuations are included within a functional renormalisation group approach to the quark-meson model. We present results on the chiral phase boundary, the critical endpoint, and the curvature of the phase transition line at vanishing density.
In this article, we assume that the two quarks have unequal masses and calculate the next-to-leading order contributions to the spectral densities of the mesonic two-point correlation functions of the vector, axialvector, scalar and pseudoscalar currents. We take dimensional regularization to regularize both the ultraviolet and infrared divergences, and use optical theorem to obtain the spectral densities directly, furthermore, we present some necessary technical details for readers convenience. The analytical expressions are applicable in many phenomenological analysis besides the QCD sum rul…
Lattice studies of QCD at high temperature has investigated the so called ``screening masses", corresponding to quark-antiquark states propagating in $spatial$ (rather than time) direction. Thirty years ago we pointed out that those should correspond to states of 2+1 dimensional quarkonia, and in this work we show that this correspondence provide quantitative description of the lattice data.
We study the nontrivial dispersion relation of mesons resulting from the splitting of the transversal and longitudinal mesonic wave function renormalizations, and its influences on the QCD phase transition, equation of state, and the fluctuations of baryon number. The calculations are performed in a two-flavor low energy effective model within the functional renormalization group approach. We find that influences of the splitting mesonic wave function renormalizations on the equilibrium thermodynamical bulk properties are mild. Furthermore, we have compare the fixed and running expansion for t…
We investigate the soft mode at the QCD critical point (CP) on the basis of the functional renormalization group. We calculate the spectral functions in the meson channels in the two-flavor quark--meson model. Our result shows that the energy of the peak position of the particle--hole mode in the sigma channel becomes vanishingly small as the system approaches the QCD CP, which is a manifestation of the softening of the phonon mode. We also extract the dispersion curves of the mesonic and the phonon mode, a hydrodynamic mode which leads to a finding that the dispersion curve of the sigma-meson…
Scale factor matrices relating mesonic fields in chiral Lagrangians and quark-level operators of QCD sum-rules are shown to be constrained by chiral symmetry, resulting in universal scale factors for each chiral nonet. Built upon this interplay between chiral Lagrangians and QCD sum-rules, the scale factors relating the $a_0$ isotriplet scalar mesons to their underlying quark composite field were recently determined. It is shown that the same technique when applied to $K_0^*$ isodoublet scalars reproduces the same scale factors, confirming the universality property and further validating this …
We study the correlations between quark-antiquark pairs in different quantum number channels in a deconfined plasma by using an effective model of QCD. Using the three flavour PNJL model, the finite temperature spectral functions for different mesonic states are studied at zero and nonzero quark chemical potentials. It is found that in the $η$ channel resonance structures survive above the chiral transition temperature $\tc$, while the kaonic states seem to get washed off just above $\tc$. The sensitivity of the structures to the anomaly term are carefully investigated.
A consistency check for any UV complete model for large N QCD should be, among other things, the existence of a well-defined vector and scalar mesonic spectra. In this paper, we use our UV complete model in type IIB string theory to study the IR dynamics and use this to predict the mesonic spectra in the dual type IIA side. The advantage of this approach is two-fold: not only will this justify the consistency of the supergravity approach, but it will also give us a way to compare the IR spectra and the model with the ones proposed earlier by Sakai and Sugimoto. Interestingly, the spectra comin…
We investigate the high-temperature phase of QCD using lattice QCD simulations with $N_f = 2$ dynamical Möbius domain-wall fermions. On generated configurations, we study the axial $U(1)$ symmetry, overlap-Dirac spectra, screening masses from mesonic correlators, and topological susceptibility. We find that some of the observables are quite sensitive to lattice artifacts due to a small violation of the chiral symmetry. For those observables, we reweight the Möbius domain-wall fermion determinant by that of the overlap fermion. We also check the volume dependence of observables. Our data near t…
We study the effects of pion and sigma meson backcoupling on the chiral order parameters and the QCD phase diagram and determine their effect on the location of the chiral critical endpoint. To this end, we solve a coupled set of truncated Dyson--Schwinger equations for Landau gauge quark and gluon propagators with $N_f=2+1$ dynamical quark flavors and explicitly backcoupled mesons. The corresponding meson bound-state properties and the quark-meson Bethe--Salpeter vertices are obtained from their homogeneous Bethe--Salpeter equation. We find chiral-restoration effects of the pion and/or sigma …
We elaborate on how to incorporate mesonic correlators into the worldline formalism. We consider possible applications to QCD-like theories in various dimensions. We focus on large-N_c two dimensional QCD (the 't Hooft model) and relate it to a single harmonic oscillator. We also discuss the dependence of the Peskin S-parameter on the number of massless flavors and their representation and compare our expression to the corresponding expression obtained at weak coupling. Finally, we use the worldline formalism to discuss how the Veneziano limit of QCD is realized in holography in the limit of s…
It is shown how a chiral Lagrangian framework can be used to derive relationships connecting quark-level QCD correlation functions to mesonic-level two-point functions. Crucial ingredients of this connection are scale factor matrices relating each distinct quark-level substructure (e.g., quark-antiquark, four-quark) to its mesonic counterpart. The scale factors and mixing angles are combined into a projection matrix to obtain the physical (hadronic) projection of the QCD correlation function matrix. Such relationships provide a powerful bridge between chiral Lagrangians and QCD sum-rules that …
Mesonic and nucleon fluctuation effects are investigated in medium. We couple the nucleon field to the $2+1$ flavor meson model and investigate the finite temperature and density behavior of the system, in particular, the axial anomaly function. Somewhat contrary to earlier expectations we find that it tends to strengthen at finite density. At lower temperatures nucleon density fluctuations can cause a relative difference in the $U_A(1)$ axial anomaly of about $20\%$. This has important consequences on the mesonic spectra, especially on the $η-η'$ system, as we observe no drop in the $η'$ mass…
We determine the leading order mesonic~($B_0$ and $F_0$) and baryonic~($m_0$, $D$ and $F$) SU(3) chiral perturbation theory low energy constants from lattice QCD. We employ gauge ensembles with $N_f=3$ (i.e., $m_u=m_d=m_s$) non-perturbatively improved Wilson fermions at six distinct values of the lattice spacing in the range $a\approx (0.039 - 0.098)$ fm, which constitute a subset of the Coordinated Lattice Simulations (CLS) gauge ensembles. The pseudoscalar meson mass $M_π$ ranges from around $430$ MeV down to $240$ MeV and the linear spatial lattice extent $L$ from $6.4\,M_π^{-1}$ to $3.3\,M…
Chiral Lagrangian mesonic fields can be connected to QCD quark operators via matrix operators containing scale factors. These scale factor matrices are shown to be constrained by chiral symmetry, resulting in a universal scale factor for each Chiral Lagrangian nonet. QCD sum-rules, combined with mixing angles from Chiral Lagrangian analyses, are used to determine the scale factors for the $a_0$ isotriplet and $K_0^*$ isodoublet scalar mesons. The resulting scale factors verify the universality property, providing a validation of the scale factor matrices connecting Chiral Lagrangian mesonic fi…
Studies of the QCD phase diagram must properly include nucleonic degrees of freedom and their thermodynamics in the range of baryon chemical potentials characteristic of nuclear matter. A useful framework for incorporating relevant nuclear physics constraints in this context is a chiral nucleon-meson effective Lagrangian. In the present paper, such a chiral nucleon-meson model is extended with systematic inclusion of mesonic fluctuations using the functional renormalization group approach. The resulting description of the nuclear liquid-gas phase transition shows a remarkable agreement with th…
Properties of the scale-factor matrices forming a bridge between the mesonic fields of chiral Lagrangians and quark-level structures of QCD sum-rules are reviewed. The scale-factor matrices combined with mixing angles provide a physical projection of a QCD correlation function matrix that disentangles the mesonic states. This methodology is illustrated for the isotriplet $a_0(980)$-$a_0(1450)$ system, and the scale factors are determined from the combined inputs of QCD sum-rules and chiral Lagrangians. The resulting scale factors are shown to be in good agreement with the vacuum expectation va…
We first review the method to calculate the spectral functions in the functional renormalization group (FRG) approach, which has been recently developed. We also provide the numerical stability conditions given by the present authors for a generic nonlinear evolution equation that are necessary for obtaining the accurate effective potential from the flow equation in the FRG. As an interesting example, we report the recent calculation of the spectral functions of the mesonic and particle-hole excitations using a chiral effective model of Quantum Chromodynamics (QCD); we extract the dispersion r…
We investigate the distance and temperatures scale for which the string in baryonic quark configuration approaches the limiting behavior of mesonic strings in pure Yang-Mills SU(3) lattice gauge theory. We calculate and compare the numerical values of the Polyakov loop correlators and the width profile of both diquark-quark $(QQ)Q$ and mesonic $Q\bar{Q}$ strings. We find the diquark-quark configuration to exhibit an identical behavior to the mesonic string for the potential and energy-density width profile for temperature near the end of QCD plateau. In the vicinity of the deconfinement point;…
We study the asymmetric nuclear matter using a holographic QCD model by introducing a baryonic charge in the infrared boundary. We first show that, in the normal hadron phase, the predicted values of the symmetry energy and it's slope parameter are comparable with the empirical values. We find that the phase transition from the normal phase to the pion condensation phase is delayed compared with the pure mesonic matter: The critical chemical potential is larger than the pion mass which is obtained for the pure mesonic matter. We also show that, in the pion condensation phase, the pion contribu…
Within a formulation of a Dynamical AdS/QCD model we calculate the spectrum of light flavored mesons. The background fields of the model correspond to an IR deformed Anti de Sitter metric coupled to a dilaton field. Confinement comes as a consequence of the dilaton dynamics coupled to gravity. Additionally to the Regge-like spectrum of light- scalar, vector and higher spin mesons, we obtain the decay width of scalar mesons into two pions.
The derivative of the grand potential in mean field approximation, non-strange and strange condensates and deconfinement phase-transition in thermal and dense hadronic medium are verified in extended SU(3) linear sigma-model (eLSM). In determining the chiral phase-transition, the chiral condensates sigma_x and sigma_y are analysed. The chiral mesonic phase-structures in temperature- and density-dependence are taken as free parameters to be fitted. These parameters are classified corresponding to scalar meson nonets; (pseudo)-scalar and (axial)-vector. For deconfinement phase-transition, effect…
We present a novel relativistic density-functional approach to modeling quark matter with a mechanism to mimic confinement. The quasiparticle treatment of quarks provides their suppression due to large quark selfenergy already at the mean-field level. We demonstrate that our approach is equivalent to a chiral quark model with medium-dependent couplings. The dynamical restoration of the chiral symmetry is ensured by construction of the density functional. Beyond the mean field, quark correlations in the pseudoscalar channel are described within the Gaussian approximation. This explicitly introd…
In order to study the fate of mesons in thermal QCD at finite baryon chemical potential, we consider light mesonic correlation functions using the Taylor expansion to ${\cal O}((μ/T)^2)$, in both the hadronic and quark-gluon plasma phases. We use the FASTSUM anisotropic fixed-scale lattices with $N_f = 2+1$ flavours of Wilson fermion. We find that mesonic correlators are sensitive to finite-density corrections and that the second-order terms indicate the chiral crossover in the vector and axial-vector channels.
We present a strategy based on the step-scaling technique to study non-perturbatively thermal QCD up to very high temperatures. As a first concrete application, we compute the flavour non-singlet meson screening masses at 12 temperatures covering the range from $T \sim 1$ GeV up to $\sim 160$ GeV in the theory with three massless quarks. The calculation is carried out by Monte Carlo simulations on the lattice by considering large spatial extensions in order to have negligible finite volume effects. For each temperature we have simulated 3 or 4 values of the lattice spacing, so as to perform th…
We investigate the relation between the physical pion pole and screening masses and the mesonic fluctuation scale in low-energy QCD, which relates to the curvature of the mesonic effective potential. This relation is important for the correct relative weight of quantum, thermal and density fluctuations. Hence, it governs the location of phase boundaries as well as the phase structure of QCD. The identification of the correct physics scales is also primarily important for the correct adjustment of the parameters of effective models for low-energy QCD. It is shown that subject to an appropriate …
This paper scrutinizes the dynamical QCD effects influence on mesons, namely, the mean-square root radius of a pion in the holographic light-front wave function setup, in the context of the AdS/QCD. The nuclear configurational entropy, associated to mesonic holographic light-front wave functions, is shown to have a critical point that optimizes the two parameters of the spin-improved light-front wave function. The mean-square root pion radius and its cross-section, computed upon these derived values, match the exact existing experimental data to the precision of 0.14\%, below the experimental …
The meson family of $η$ pseudoscalars is studied in the context of the AdS/QCD correspondence and the differential configurational entropy (DCE). For it, two forms of configurational-entropic Regge-like trajectories are engendered, relating the $η$ mesonic states excitation number to both their experimental mass spectrum in the Particle Data Group (PDG) and the DCE as well. Hence, the mass spectrum of $η$ pseudoscalar mesonic states, beyond the already detected states $η(550)$, $η'(958)$, $η(1295)$, $η(1405)$, $η(1475)$, $η(1760)$, $η(2225)$, and $η(2320)$, is derived for any excitation number…
The existing theory of hard exclusive QCD processes is based on two assumptions: (i) $factorization$ into a $hard\,block$ times light front distribution amplitudes (DA's); (ii) use of perturbative gluon exchanges within the hard block. However, unlike DIS and jet physics, the characteristic momentum transfer $Q$ involved in the factorized block is not large enough for this theory to be phenomenologically successful. In this work, we revisit the latter assumption (ii), by explicitly calculating the $instanton-induced$ contributions to the hard block, and show that they contribute substantially …
In the present work, higher-order mesonic interactions are included in the linear sigma model at a finite temperature. The effective potential is minimized in the calculations of the sigma and pion effective masses. The field equations have been solved in the mean-field approximation, by using the extended iteration method at a finite temperature. The order of chiral phase transition, the effective sigma and pion masses, and the effective mesonic potential are investigated as functions of the temperature. We find that the chiral phase transition satisfies the Goldstone theorem below the critic…
In this work, we calculate leading-order anomalous dimension matrices for dimension-6 four-quark operators which appear in the operator product expansion of flavour non-diagonal and diagonal vector and axial-vector two-point correlation functions. The infrared renormalon structure corresponding to four-quark operators is reviewed and it is investigated how the eigenvalues of the anomalous dimension matrices influence the singular behaviour of the $u=3$ infrared renormalon pole. It is found that compared to the large-$β_0$ approximation where at most quadratic poles are present, in full QCD at …
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 …
We model the observed $J^{++}$ mesonic mass spectrum in terms of energies for tightly knotted and linked chromoelectric QCD flux tubes. The data is fit with one and two parameter models. We predict a possible new state at approximately 1190 MeV and a plethora of new states above 1690 MeV.
We present a recent development towards a unified description of quark-hadron matter in the QCD phase diagram that is based on a cluster decomposition of the generalized Beth-Uhlenbeck approach to quark matter, selfconsistently coupled to Polyakov-loop and mesonic background fields. The Mott dissociation of hadrons under extreme conditions of temperature and density is triggered by chiral symmetry restoration and confining aspects are modeled by the coupling to the background mean fields. First results for the QCD phase diagram with the capability to describe critical endpoints as well as cros…
We study the two-flavor quark-meson (QM) model with the functional renormalization group (FRG) to describe the effects of collective mesonic fluctuations on the phase diagram of QCD at finite baryon and isospin chemical potentials, $μ_B$ and $μ_I$. With only isospin chemical potential there is a precise equivalence between the competing dynamics of chiral versus pion condensation and that of collective mesonic and baryonic fluctuations in the quark-meson-diquark model for two-color QCD at finite baryon chemical potential. Here, finite $μ_B=3μ$ introduces an additional dimension to the phase di…
We consider a holographic model of QCD, obtained by a very simple modification of the original construction, which describes at the same time the pion mass, the QCD anomalies and the baryons as topological solitons. We study in detail its phenomenological implications in both the mesonic and baryonic sectors and compare with the observations.
A nonlocal chiral quark model is consistently extended beyond mean field using a strict 1/Nc expansion scheme. The parameters of the nonlocal model are refitted to the physical values of the pion mass and the weak pion decay constant. The size of the 1/Nc correction to the quark condensate is carefully studied in the nonlocal and the usual local Nambu-Jona-Lasinio models. It is found that even the sign of the corrections can be different. This can be attributed to the mesonic cut-off of the local model. It is also found that the 1/Nc corrections lead to a lowering of the temperature of the chi…
We investigate pion and sigma meson correlations in hot quark matter within a modified NJL model. Special emphasis is on the transformation of mesonic bound states to resonances (Mott dissociation) when due to the partial chiral symmetry restoration with increasing temperature the threshold of quark-antiquark continuum states drops below the meson mass at the corresponding Mott temperature. The description is based on evaluating the polarization functions for quark-antiquark (meson) correlations as a function of the temperature and the results can be represented by introducing modulus and phas…
We modify the mesonic wavefunction by using a short distance scale r0 in analogy with Hydrogen atom and estimate the values of masses and decay constants of the open flavour charm mesons D, Ds and Bc within the framework of a QCD Potential Model. We also calculate leptonic decay widths of these mesons to study branching ratios and life time. The results are in good agreement with experimental and other theoretical values.
