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Register a new userThe low-temperature behavior of the quark-meson model
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We revisit the phase diagram of strong-interaction matter for the two-flavor quark-meson model using the Functional Renormalization Group. In contrast to standard mean-field calculations, an unusual phase structure is encountered at low temperatures and large quark chemical potentials. In particular, we identify a regime where the pressure decreases with increasing temperature and discuss possible reasons for this unphysical behavior.
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We study the thermodynamic geometry of the Quark-Meson model, focusing on the curvature, $R$, around the chiral crossover at finite temperature and baryon chemical potential. We find a peculiar behavior of $R$ in the crossover region, in which the sign changes and a local maximum develops; in particular, the height of the peak of $R$ in the crossover region becomes large in proximity of the critical endpoint and diverges at the critical endpoint. The appearance of a pronounced peak of $R$ close to the critical endpoint supports the idea that $R$ grows with the correlation volume around the phase transition. We also analyze the mixed fluctuations of energy and baryon number, $langleDelta UDelta Nrangle$, which grow up substantially in proximity of the critical endpoint: in the language of thermodynamic geometry these fluctuations are responsible for the vanishing of the determinant of the metric, which results in thermodynamic instability and are thus related to the appearance of the second order phase transition at the critical endpoint.
We obtain the in-medium effective potential of the three-flavor Polyakov-Quark-Meson model as a real function of real variables in the Polyakov loop variable, to allow for the study of all possible minima of the model. At finite quark chemical potential, the real and imaginary parts of the effective potential, in terms of the Polyakov loop variables, are made apparent, showing explicitly the fermion sign problem of the theory. The phase diagram and other equilibrium observables, obtained from the real part of the effective potential, are calculated in the mean-field approximation. The obtained results are compared to those found with the so-called saddle-point approach. Our procedure also allows the calculation of the surface tension between the chirally broken and confined phase, and the chirally restored and deconfined phase. The values of surface tension we find for low temperatures are very close to the ones recently found for two-flavor chiral models. Some consequences of our results for the early Universe, for heavy-ion collisions, and for proto-neutron stars are briefly discussed.
In-medium properties of the low-lying baryons are studied in the quark-meson coupling (QMC) model, focusing on the $Sigma_b$ and $Xi_b$ baryons. It is predicted that the Lorentz-scalar effective mass of $Sigma_b$ becomes smaller than that of $Xi_b$ at moderate nuclear matter density, and as the density increases, namely, $m^*_{Sigma_b} < m^*_{Xi_b}$, although in vacuum $m_{Sigma_b} > m_{Xi_b}$. We also study the effects of the repulsive Lorentz-vector potentials on the excitation energies of these bottom baryons.
The nonanalyticity and the sign problem in the Z3-symmetric heavy quark model at low temperature are studied phenomenologically. For the free heavy quarks, the nonanalyticity is analyzed in the relation to the zeros of the grand canonical partition function. The Z3-symmetric effective Polyakov-line model (EPLM) in strong coupling limit is also considered as an phenomenological model of Z3-symmetric QCD with large quark mass at low temperature. We examine how the Z3-symmetric EPLM approaches to the original one in the zero-temperature limit. The effects of the Z3-symmetry affect the structure of zeros of the microscopic probability density function at the nonanalytic point. The average value of the Polyakov line can detect the structure, while the other thermodynamic quantities are not sensible to the structure in the zero-temperature limit. The effect of the imaginary quark chemical potential is also discussed. The imaginary part of the quark number density is very sensitive to the symmetry structure at the nonanalytical point. For a particular value of the imaginary quark number chemical potential, large quark number may be induced in the vicinity of the nonanalytical point.
Temperature dependence of pion and sigma-meson screening masses is evaluated by the Polyakov-loop extended Nambu--Jona-Lasinio (PNJL) model with the entanglement vertex. We propose a practical way of calculating meson screening masses in the NJL-type effective models. The method based on the Pauli-Villars regularization solves the well-known difficulty that the evaluaton of screening masses is not easy in the NJL-type effective models.The PNJL model with the entanglement vertex and the Pauli-Villars regularization well reproduces lattice QCD results on temperature dependence of the chiral condensate and the Polyakov loop. The method is applied to analyze temperature dependence of pion screening mass calculated with state-of-the-art lattice simulations with success in reproducing the lattice QCD results.
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