Intensive search for a proper and realistic equations of state (EOS) is still continued for studying the phase diagram existing between quark gluon plasma (QGP) and hadron gas (HG) phases. Lattice calculations provide such EOS for the strongly interacting matter at finite temperature ($T$) and vanishing baryon chemical potential ($μ_{B}$). These calculations are of limited use at finite $μ_{B}$ due to the appearance of notorious sign problem. In the recent past, we had constructed a hybrid model description for the QGP as well as HG phases where we make use of a new excluded-volume model for HG and a thermodynamically-consistent quasiparticle model for the QGP phase and used them further to get QCD phase boundary and a critical point. Since then many lattice calculations have appeared showing various thermal and transport properties of QCD matter at finite $T$ and $μ_{B}=0$. We test our hybrid model by reproducing the entire data for strongly interacting matter and predict our results at finite $μ_{B}$ so that they can be tested in future. Finally we demonstrate the utility of the model in fixing the precise location, the order of the phase transition and the nature of CP existing on the QCD phase diagram. We thus emphasize the suitability of the hybrid model as formulated here in providing a realistic EOS for the strongly interacting matter.
A first attempt to accommodate the chiral and deconfining phase transitions of QCD in the bottom-up holographic framework is given. We constrain the relation between dilaton field $ϕ$ and metric warp factor $A_e$ and get several reasonable models in the Einstein-Dilaton system. Using the potential reconstruction approach, we solve the corresponding gravity background. Then we fit the background-related parameters by comparing the equation of state with the two-flavor lattice QCD results. After that we study the temperature dependent behavior of Polyakov loop and chiral condensate under those b…
Ambiguities regarding the physics and the existence of the critical point (CP) on the QCD phase boundary still exist and the mist regarding the conjectured QCD phase boundary has not yet cleared. In this paper we extend our earlier study where we constructed a deconfining phase boundary using Gibbs' equilibrium conditions after using a quasiparticle equation of state (EOS) for quark gluon plasma (QGP) and an excluded volume EOS for the hadron gas (HG) and find the presence of a critical point on this phase boundary where the first order phase transition terminates. In this paper, we plot the d…
We consider an improved soft-wall AdS/QCD model coupled to an Einstein-dilaton system, which offers a way to study the deconfining and chiral transitions simultaneously. The correlation between these two transitions has been investigated in detail in the Einstein-dilaton-scalar system with the bulk scalar field representing the vacuum of matters in the flavor sector of the model. We find that the effects of the scaling dimension $Δ$ of the dual operator of the dilaton manifest in chiral transitions, although the equation of state can all be matched with the two-flavor lattice results for $Δ=2.…
We review the influence of a magnetic background on the phase diagram of strong interactions and how the chiral and deconfining transitions can be affected. First we summarize results for both transitions obtained in the framework of the linear sigma model coupled to quarks and to the Polyakov loop, and how they compare to other effective model approaches and to lattice QCD. Then we discuss the outcome of the magnetic MIT bag model that yields a behavior for the critical deconfining temperature which is compatible with recent lattice results and magnetic catalysis. The qualitative success of t…
We discuss the effects of rotation on confining properties of gauge theories focusing on compact electrodynamics in two spatial dimensions as an analytically tractable model. We show that at finite temperature, the rotation leads to a deconfining transition starting from a certain distance from the rotation axis. A uniformly rotating confining system possesses, in addition to the usual confinement and deconfinement phases, a mixed inhomogeneous phase which hosts spatially separated confinement and deconfinement regions. The phase diagram thus has two different deconfining temperatures. The fir…
I review our current understanding of the properties of strongly interacting matter at high temperatures, based upon numerical calculations in lattice QCD. I discuss the chiral and deconfining aspects of the QCD transition, the equation of state, fluctuations of conserved charges, color screening, meson correlation functions, and the determination of some transport coefficients.
Location of critical point and mapping the QCD phase boundary still exists as one of the most interesting and studied problems of heavy-ion physics. A new equation of state (EOS) for a gas of extended baryons and pointlike mesons is presented here which accounts for the repulsive hard-core interactions arising due to the geometrical size of the baryons. A first order deconfining phase transition is obtained using Gibbs' equilibrium criteria and a bag model EOS for the weakly interacting quark matter. It is interesting to find that the phase transition line ends at a critical point beyond which…
We study the finite density phase transition in the lattice QCD at real chemical potential. We adopt canonical approach and the canonical partition function is constructed for Nf=2 QCD. After derivation of the canonical partition function we calculate observables like the pressure, the quark number density, its second cumulant and the chiral condensate as a function of the real chemical potential. We covered a wide range of temperature region starting from the confining low to the deconfining high temperature. We observe signals for the deconfinement and the chiral restoration phase transition…
The physics regarding the existence of the critical end point (CEP) on the QCD phase boundary still remains unclear and its precise location is quite uncertain. In this paper we propose that the hard-core size of the baryons used in the description of the hot and dense hadron gas (HG) plays a decisive role in the existence of CEP. Here we construct a deconfining phase transition using Gibbs' equilibrium conditions after using a quasiparticle equation of state (EOS) for QCD plasma and excluded-volume EOS for the HG. We find that the first order transition results only when we assign a hard-core…
We review recent results on the phase structure of QCD and bulk QCD thermodynamics. In particular we discuss how universal critical scaling related to spontaneous breaking of the chiral symmetry manifests itself in recent lattice QCD simulations and how the knowledge on non-universal scaling parameter can be utilized in the exploration of the QCD phase diagram. We also show how various (generalized) susceptibilities can be employed to characterize properties of QCD matter at low and hight temperatures, related to deconfining aspects of the QCD transition. Finally, we address the input these la…
We use the available two different self-consistent formulations of quasiparticle models and extend their applications for the description of quark gluon plasma (QGP) at non-vanishing baryon chemical potentials. The thermodynamical quantities calculated from these models are compared with the values obtained from lattice simulations and a good agreement between theoretical calculations and lattice QCD data suggests that the values of the parameters used in the paper are consistent. A new equation of state (EOS) for a gas of extended baryons and pointlike mesons is presented here which incorpora…
In this paper, we re-analyze the $1^{-+}$ and $0^{++}$ light hybrids from QCD sum rules with a Monte-Carlo based uncertainty analysis. With $30\%$ uncertainties in the accepted central values for QCD condensates and other input parameters, we obtain a prediction on $1^{-+}$ hybrid mass of $1.71 \pm 0.22$\,GeV, which covers the mass of $π_1(1600)$. However, the $0^{++}$ hybrid mass prediction is more than 4\,GeV, which is far away from any known $a_0$ meson. We also study the correlations between the input and output parameters of QCD sum rules.
We study the phase structure of lattice QCD with heavy quarks at finite temperature and density by a histogram method. We determine the location of the critical point at which the first-order deconfining transition in the heavy-quark limit turns into a crossover at intermediate quark masses through a change of the shape of the histogram under variation of coupling parameters. We estimate the effect of the complex phase factor which causes the sign problem at finite density, and show that, in heavy-quark QCD, the effect is small around the critical point. We determine the critical surface in 2+…
We study the spectra of the hybrid mesons containing one heavy quark ($q\bar{Q}g$) within the framework of QCD sum rules in the heavy quark limit. The derived sum rules are stable with the variation of the Borel parameter within their corresponding working ranges. The extracted binding energy for the heavy hybrid doublets $H^h(S^h)$ and $M^h(T^h)$ is almost degenerate. We also calculate the pionic couplings between these heavy hybrid and the conventional heavy meson doublets using the light-cone QCD sum rule method. The extracted coupling constants are rather small as a whole. With these coupl…
QCD Laplace sum-rules are used to calculate axial vector $(J^{PC}=1^{++})$ charmonium and bottomonium hybrid masses. Previous sum-rule studies of axial vector heavy quark hybrids did not include the dimension-six gluon condensate, which has been shown to be important in the $1^{--}$ and $0^{-+}$ channels. An updated analysis of axial vector heavy quark hybrids is performed, including the effects of the dimension-six gluon condensate, yielding mass predictions of 5.13 GeV for hybrid charmonium and 11.32 GeV for hybrid bottomonium. The charmonium hybrid mass prediction disfavours a hybrid interp…
The masses of $1^{--}$ charmonium and bottomonium hybrids are evaluated in terms of QCD sum rules. We find that the ground state hybrid in charm sector lies in $m_{H_c}=4.12\sim 4.79$ GeV, while in bottom sector the hybrid may situated in $m_{H_b} = 10.24\sim 11.15$ GeV. Since the numerical result on charmonium hybrid mass is not compatible with the charmonium spectra, including structures newly observed in experiment, we tempt to conclude that such a hybrid does not purely exist, but rather as an admixture with other states, like glueball and regular quarkonium, in experimental observation. H…
Search of a proper and realistic equations of state (EOS) for strongly interacting matter used in the study of QCD phase diagram still appears as a challenging task. Recently, we have constructed a hybrid model description for the quark gluon plasma (QGP) as well as hadron gas (HG) phases where we use a new excluded-volume model for HG and a thermodynamically-consistent quasiparticle model for the QGP phase. We attempt to use them to get a QCD phase boundary and a critical point. We test our hybrid model by reproducing the entire lattice QCD data for strongly interacting matter at zero baryon …
Recent theoretical investigations have unveiled a rich structure in the quantum chromodynamics (QCD) phase diagram which consists of quark gluon plasma (QGP) and the hadronic phases but also supports the existence of a cross-over transition ending at a critical end point (CEP). We find a too large variation in determination of the coordinates of the CEP in the temperature (T), baryon chemical potential ($μ_{B}$) plane and, therefore, its identification in the current heavy-ion experiments becomes debatable. Here we use an equation of state (EOS) for a deconfined QGP using a thermodynamically c…
Hybrid mesons with exotic quantum numbers $J^{PC}=1^{-+}$ are examined in soft-wall AdS/QCD. The predicted mass spectrum is compared to the measured values of the candidates $π_1(1400)$, $π_1(1600)$ and $π_1(2015)$. Thermal effects are analysed through the spectral function in the AdS-Black Hole model, and the differences with the Hawking-Page description are discussed.
We propose and test a new approach to computation of canonical partition functions in lattice QCD at finite density. We suggest a few steps procedure. We first compute numerically the quark number density for imaginary chemical potential $iμ_{qI}$. Then we restore the grand canonical partition function for imaginary chemical potential using fitting procedure for the quark number density. Finally we compute the canonical partition functions using high precision numerical Fourier transformation. Additionally we compute the canonical partition functions using known method of the hopping parameter…
We investigate the properties of the deconfining/chiral restoring transition for two flavor QCD in presence of a uniform background magnetic field. We adopt a standard staggered discretization of the fermion action and a lattice spacing of the order of 0.3 fm. We explore different values of the bare quark mass, corresponding to pion masses in the range 200 - 480 MeV, and magnetic fields up to |e|B ~ 0.75 GeV^2. The deconfinement and chiral symmetry restoration temperatures remain compatible with each other and rise very slightly (< 2 % for our largest magnetic field) as a function of the magne…
We use QCD Laplace sum-rules to study meson-hybrid mixing in vector ($1^{--}$) heavy quarkonium. We compute the QCD cross-correlator between a heavy meson current and a heavy hybrid current within the operator product expansion. In addition to leading-order perturbation theory, we include four- and six-dimensional gluon condensate contributions as well as a six-dimensional quark condensate contribution. We construct several single and multi-resonance models that take known hadron masses as inputs. We investigate which resonances couple to both currents and so exhibit meson-hybrid mixing. Compa…
We use QCD Laplace sum-rules to explore mixing between conventional mesons and hybrids in the heavy quarkonium vector $J^{PC}\!=\!1^{--}$ channel. Our cross-correlator includes perturbation theory and contributions proportional to the four-dimensional and six-dimensional gluon condensates. We input experimentally determined charmonium and bottomonium hadron masses into both single and multi-resonance models in order to test them for conventional meson and hybrid components. In the charmonium sector we find evidence for meson-hybrid mixing in the $J/ψ$ and a $\approx4.3$ GeV resonance. In the b…
Axial vector $(J^{PC}=1^{++})$ charmonium and bottomonium hybrid masses are determined via QCD Laplace sum-rules. Previous sum-rule studies in this channel did not incorporate the dimension-six gluon condensate, which has been shown to be important for $1^{--}$ and $0^{-+}$ heavy quark hybrids. An updated analysis of axial vector charmonium and bottomonium hybrids is presented, including the effects of the dimension-six gluon condensate. The axial vector charmonium and bottomonium hybrid masses are predicted to be 5.13 GeV and 11.32 GeV, respectively. We discuss the implications of this result…
In this paper, we study instanton contributions to the correlator of the hybrid current $g\bar q σ_{μν}G^a_{νμ}T^a q$. These contributions are then included in a QCD sum-rule analysis of the isoscalar $0^{++}$ hybrid mass. We find a mass at 1.83 GeV for the $(\bar uug+\bar ddg)/\sqrt{2}$ hybrid. However, for the $\bar ssg$ hybrid, we find the sum rules are unstable. We also study non-zero width effects, which affect the mass prediction. The mixing effects between these two states are studied and we find QCD sum rules support the existence of a flavor singlet hybrid with mass at around 1.9 GeV.…
We calculate the coefficients of the dimension-8 quark and gluon condensates in the current-current correlator of $1^{-+}$ light hybrid current $g\bar{q}(x)γ_νiG_{μν}(x)q{(x)}$. With inclusion of these higher-power corrections and updating the input parameters, we re-analyze the mass of the $1^{-+}$ light hybrid meson from Monte-Carlo based QCD sum rules. Considering the possible violation of factorization of higher dimensional condensates and variation of $\langle g^3G^3\rangle$, we obtain a conservative mass range 1.72--2.60\,GeV, which favors $π_{1}(2015)$ as a better hybrid candidate compa…
Within QCD, colourless states may be constructed corresponding to exotic matter outside of the traditional quark model. Experiments have recently observed tetraquark and pentaquark states, but no definitive hybrid meson signals have been observed. With the construction of the PANDA experiment at FAIR, and with full commissioning of the GlueX experiment at JLab expected to be completed this year, the opportunity for the observation of hybrid mesons has greatly increased. However, theoretical calculations are necessary to ascertain the identity of any experimental resonances that may be observed…
Masses of the pseudoscalar $(J^{PC}=0^{-+})$ charmonium and bottomonium hybrids are determined using QCD Laplace sum-rules. The effects of the dimension-six gluon condensate are included in our analysis and result in a stable sum-rule analysis, whereas previous studies of these states were unable to optimize mass predictions. The pseudoscalar charmonium hybrid is predicted to have a mass of approximately 3.8 GeV and the corresponding bottomonium prediction is 10.6 GeV. Calculating the full correlation function, rather than only the imaginary part, is shown to be necessary for accurate formulat…
QCD sum-rules are employed to determine whether the X(3872) can be described as a mixed state that couples to $J^{PC}=1^{++}$ charmonium hybrid and $\bar D D^*$ molecular currents. After calculating the mixed correlator of hybrid and molecular currents, we formulate the sum-rule in terms of a mixing parameter that interpolates between the pure molecular and hybrid scenarios. As the mixing parameter is increased from the pure molecular case, the predicted mass increases until it reaches a maximum value in good agreement with the X(3872) and the resulting sum-rule analysis appears more robust th…
