N-Midpoint Rule for Calculating the Effective Mesonic Potential at Finite Temperature

The temperature dependence of meson properties is studied by using the effective potential formalism. The effective mesonic potential is numerically calculated using the n-midpoint rule at finite temperature. The meson masses, the phase transition, and the energy density are investigated as functions of temperature. The obtained results are compared with those from other works. The present technique is compared with the Hartree approximation and the imaginary time formalism. We conclude that the calculated effective potential successfully predicts the meson properties, the phase transition, and the critical temperature in comparison with other models and avoid the difficulty that found in the Hartree approximation which depends on cutoff technique.     

The equation of state of quarks and mesons in a renormalization group flow picture

Non-perturbative flow equations within an effective linear sigma model coupled to constituent quarks for two quark flavours are derived and solved. A heat kernel regularization is employed for a renormalization group improved effective potential. We determine the initial values of the coupling constants in the effective potential at zero temperature. Solving the evolution equations with the same initial values at finite temperature in the chiral limit, we find a second-order phase transition at T_c≈150 MeV. Due to the smooth decoupling of massive modes, we can directly link the low-temperature four-dimensional theory to the three-dimensional high-temperature theory. We calculate the equation of state in the chiral limit and for finite pion masses and determine universal critical exponents.     

Meson Properties at Finite Temperature in the Linear Sigma Model

The meson masses are investigated at finite temperature in the framework of the linear sigma model with an explicit chiral symmetry breaking term. The imaginary-time thermo-field dynamics and effective potential have been used for the calculation of the meson masses. We found that the behavior of the sigma and pion masses at finite temperature is in agreement with previous works. The critical temperature, the order of the phase transition, and the dependence of the meson fields on the temperature are discussed.     

The extended quark sigma model at finite temperature and baryonic chemical potential

An extended quark sigma model which includes higher-order mesonic interactions is studied at the finite baryonic chemical potential u _B and temperature T. The field equations have been solved in the mean-field approximation by using the modified iteration method at finite baryonic chemical potential u _B and temperature T. The Goldstone theorem is satisfied below a critical temperature in the chiral limit for u _B = 0. As expected from general universality, the chiral phase transition is second-order. By including the higher-order mesonic interactions, the critical temperature is reduced compared to that found in recent works and is in good agreement with lattice QCD results. The nucleon mass is examined in the (u _B , T) plane, showing a strong dependence on u _B and T. We find that an increase in both the baryonic chemical potential u _B and the temperature T leads to an increase in the values of the nucleon mass. This is evidence for the quark-gluon deconfinement phase transition at higher values of temperature.     

Effect of Logarithmic Mesonic Potential on Nucleon Magnetic Moments and Hedgehog Mass

The logarithmic mesonic potential is proposed for computing some nucleon properties. The logarithmic potential is based on some aspects of QCD. The field equations have been solved in mean-field approximation. Good results are obtained for the nucleon magnetic moment and the hedgehog mass in comparison with the Skyrmion model. In particular, nucleon properties are calculated for sigma and quark masses which are computed recently.     

Eight-quark interactions as a chiral thermometer

A NJL Lagrangian extended to six [1–3] and eight quark interactions [4] is applied to study temperature effects [5] (SU(3) flavor limit, massless case), and [6] (realistic massive case). The transition temperature can be considerably reduced as compared to the standard approach, in accordance with recent lattice calculations [7]. The mesonic spectra built on the spontaneously broken vacuum induced by the’ t Hooft interaction strength, as opposed to the commonly considered case driven by the four-quark coupling, undergoes a rapid crossover to the unbroken phase, with a slope and at a temperature which is regulated by the strength of the OZI violating eight-quark interactions. This strength can be adjusted in consonance with the four-quark coupling and leaves the spectra unchanged, except for the sigma meson mass, which decreases. A first order transition behavior is also a possible solution within the present approach.     

On the phase structure of QCD in a finite volume

The chiral phase transition in QCD at finite chemical potential and temperature can be characterized for small chemical potential by its curvature and the transition temperature. The curvature is accessible to QCD lattice simulations, which are always performed at finite pion masses and in finite simulation volumes. We investigate the effect of a finite volume on the curvature of the chiral phase transition line. We use functional renormalization group methods with a two flavor quark-meson model to obtain the effective action in a finite volume, including both quark and meson fluctuation effects. Depending on the chosen boundary conditions and the pion mass, we find pronounced finite-volume effects. For periodic quark boundary conditions in spatial directions, we observe a decrease in the curvature in intermediate volume sizes, which we interpret in terms of finite-volume quark effects. Our results have implications for the phase structure of QCD in a finite volume, where the location of a possible critical endpoint might be shifted compared to the infinite-volume case.     

Nuclear Matter in a Chiral SU(3) Quark Mean-Field Model

A quark meson coupling model based on SU(3)_L×SU(3)_R symmetry and scale invariance is proposed. The quarks and mesons get masses through symmetry broken. We apply this SU(3) chiral constituent quark model to investigating the nuclear matter at finite temperature and density. The effective baryon masses, compression modulus and hyperon potentials are all reasonable. The critical temperature of liquid-gas phase transition is also calculated in this model.     

NN potential with a six-quark core from the constituent quark model

A mesonic nucleon-nucleon potential from an effective quark interchange mechanism for non-overlapping nucleons is obtained from the constituent quark model. This is supplemented at short range by a phenomenological, non-mesonic potential describing the transition to a six-quark core with a discrete energy spectrum. NN phase shifts and low energy parameters are calculated and compared with data and phase shift analyses. Core parameters are extracted from the fits.     

On the QCD phase structure from effective models

Some recent theoretical developments of the QCD phase diagram are summarized. Chiral symmetry restoration and the confinement/deconfinement transition at nonzero temperature and quark densities are analyzed in the framework of an effective linear sigma model with three light quark flavors. The sensitivity of the chiral transition as well as the existence of a critical end point in the phase diagram on the value of the sigma mass is explored. The influence of the axial anomaly on the chiral critical surface is addressed. Finally, the modifications by the inclusion of the Polyakov loop on the phase structure are investigated.     

Application of the heat-kernel method to the constituent quark model at finite temperature

The heat-kernel method is applied to the constituent quark model. We calculate the effect of thermal quark fluctuations on the meson action and the resulting quark condensate and ππ-scattering amplitude at finite temperature. The quarks produce a chiral phase transition only by their effect on the mesonic coupling constants. The s-wave isospin zero ππ-scattering amplitude diverges near the phase transition showing the necessity for a more sophisticated treatment of meson fluctuations.     

Effects of mesonic correlations in the QCD phase transition

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. The text was submitted by the authors in English.     

Nonlocal PNJL model beyond mean field

A nonlocal chiral quark model is consistently extended beyond mean field using a strict 1/N _c expansion scheme. It is found that the 1/N _c corrections lead to a lowering of the temperature of the chiral phase transition in comparison with the mean-field result. On the other hand, near the phase transition the 1/N _c expansion breaks down and a nonperturbative scheme for the inclusion of mesonic correlations is needed in order to describe the phase transition region.     

Cross sections for charmonia dissociation in collisions with pions, rhos and kaons

We calculate the unpolarized cross sections for dissociation reactions of charmonia in collisions with π,ρ and K in a potential that is derived from QCD.The reactions are governed by the quark-interchange processes.The mesonic quark-antiquark relative-motion wave functions are determined by the central spinindependent terms of the potential.The numerical wave functions and cross sections are parametrized.The difference of transition amplitudes in the prior form and in the post form is explored by deriving and examining the transition amplitudes of the one-gluon-exchange spin-spin term of the potential in the two forms.We find that the post-prior discrepancy in meson-meson elastic scattering that is governed by quark-interchange processes depends on the difierence of quark or antiquark masses and of quark-antiquark spatial distributions ofthe two mesons.     

Phase transition and the nucleon as a soliton in the Nambu-Jona-Lasinio model at finite temperature and density

We study some bulk thermodynamical characteristics, meson properties and the nucleon as a baryon-number-one soliton in hot quark matter in the NJL model as well as in hot nucleon matter in a hybrid NJL model in which the Dirac sea of quarks is combined with a Fermi sea of nucleons. In both cases, working in the mean-field approximation, we find a chiral phase transition from the Goldstone to the Wigner phase. At finite density the chiral order parameter and the constituent quark mass have a non-monotonic temperature dependence — at finite temperatures not close to the critical one they are less affected than in cold matter. Whereas quark matter is rather soft against thermal fluctuations and the corresponding chiral phase transition is smooth, nucleon matter is much stiffer and the chiral phase transition is very sharp. The thermodynamical variables show large discontinuities which is an indication for a first-order phase transition. We solve the B = 1 solitonic sector of the NJL model in the presence of external hot quark and nucleon media. In the hot medium at intermediate temperature the soliton is more bound and less swelled than in the case of cold matter. At some critical temperature, which for nucleon matter coincides with the critical temperature for the chiral phase transition, we find no more a localized solution. According to this model scenario one should expect a sharp phase transition from nucleon to quark matter.     

Quark matter properties and fluctuations of conserved charges in (2+1)-flavored quark model

In this study, the susceptibilities of conserved charges, baryon number, charge number, and strangeness number at zero and low values of chemical potential are presented. Taylor series expansion was used to obtain results for the three-flavor Polyakov quark meson (PQM) model and the Polyakov loop extended chiral quark mean-field (PCQMF) model. Mean-field approximation was used to study quark matter with the inclusion of the isospin chemical potential, as well as the vector interactions. The effects of isospin chemical potential and vector-interactions on phase diagrams were analyzed. A comparative analysis of the two models was completed. Fluctuations of the conserved charges were enhanced in the transition temperature regime and hence provided information about the critical end point (CEP). Susceptibilities of conserved quantities were calculated by using the Taylor series method. Enhancement of fluctuations in the transition temperature neighborhood provided a clear signature of a quantum chromodynamics (QCD) critical-point.     

Quark-gluon plasma diagnostics in a successive equilibrium scenario

The relativistic Fokker-Planck equation has been used to study the evolution of the quark distribution in the quark-gluon phase expected to be formed in ultra-relativistic heavy-ion collisions. The effect of thermal masses for quarks and gluons is incorporated to take account of the in-medium properties. We find that the kinetic equilibrium is achieved before the system reaches the critical temperature of quark-hadron phase transition. We find that chemical equilibrium is not achieved during this time. We have evaluated the electromagnetic probes of quark-gluon plasma from the non-equilibrated quark-gluon phase and compared them with those in completely equilibrated scenario. The hard QCD production rates for the electromagnetic ejectiles as well as the heavy quark production rates are also calculated.     

On the scaling behavior of the chiral phase transition in QCD in finite and infinite volume

We study the scaling behavior of the two-flavor chiral phase transition using an effective quark–meson model. We investigate the transition between infinite-volume and finite-volume scaling behavior when the system is placed in a finite box. We can estimate effects that the finite volume and the explicit symmetry breaking by the current quark masses have on the scaling behavior which is observed in full QCD lattice simulations. The model allows us to explore large quark masses as well as the chiral limit in a wide range of volumes, and extract information about the scaling regimes. In particular, we find large scaling deviations for physical pion masses and significant finite-volume effects for pion masses that are used in current lattice simulations.     

Studying pion effects on the chiral phase transition

We investigate the chiral phase transition at finite temperatures and zero chemical potential with Dyson-Schwinger equations. Our truncation for the quark-gluon interaction includes mesonic degrees of freedom, which allows us to study the impact of the pions on the nature of the phase transition. Within the present scheme we find a 5% change of the critical temperature due to the pion backreaction whereas the mean field character of the transition is not changed.     

Temperature dependence of standard model CP violation

We analyze the temperature dependence of CP violation effects in the standard model by determining the effective action of its bosonic fields, obtained after integrating out the fermions from the theory and performing a covariant gradient expansion. We find nonvanishing CP violating terms starting at the sixth order of the expansion, albeit only in the C-odd-P-even sector, with coefficients that depend on quark masses, Cabibbo-Kobayashi-Maskawa matrix elements, temperature and the magnitude of the Higgs field. The CP violating effects are observed to decrease rapidly with temperature, which has important implications for the generation of a matter-antimatter asymmetry in the early Universe. Our results suggest that the cold electroweak baryogenesis scenario may be viable within the standard model, provided the electroweak transition temperature is at most of order 1 GeV.