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Register a new userQuark-mass dependence of the three-flavor QCD phase diagram at zero and imaginary chemical potential: Model prediction
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We draw the three-flavor phase diagram as a function of light- and strange-quark masses for both zero and imaginary quark-number chemical potential, using the Polyakov-loop extended Nambu-Jona-Lasinio model with an effective four-quark vertex depending on the Polyakov loop. The model prediction is qualitatively consistent with 2+1 flavor lattice QCD prediction at zero chemical potential and with degenerate three-flavor lattice QCD prediction at imaginary chemical potential.
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Phase transitions in the imaginary chemical potential region are studied by the Polyakov loop extended Nambu-Jona-Lasinio (PNJL) model that possesses the extended Z3 symmetry. The extended Z3 invariant quantities such as the partition function, the chiral condensate and the modifed Polyakov loop have the Roberge-Weiss (RW) periodicity. There appear four types of phase transitions; deconfinement, chiral, Polykov-loop RW and chiral RW transitions. The orders of the chiral and deconfinement transitions depend on the presence or absence of current quark mass, but those of the Polykov-loop RW and chiral RW transitions do not. The scalar-type eightquark interaction newly added in the model makes the chiral transition line shift to the vicinity of the deconfiment transition line.
Properties of QCD at finite imaginary chemical potential are revisited to utilize for the model building of QCD in low energy regimes. For example, the electric holonomy which is closely related to the Polyakov-loop drastically affects thermodynamic quantities beside the Roberge-Weiss transition line. To incorporate several properties at finite imaginary chemical potential, it is important to introduce the holonomy effects to the coupling constant of effective models. This extension is possible by considering the entanglement vertex. We show justifications of the entanglement vertex based on the derivation of the effective four-fermi interaction in the Nambu--Jona-Lasinio model and present its general form with the local approximation. To discuss how to remove model ambiguities in the entanglement vertex, we calculate the chiral condensate with different $mathbb{Z}_3$ sectors and the dual quark condensate.
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.
We present the phase diagram and the fluctuations of different conserved charges like quark number, charge and strangeness at vanishing chemical potential for the 2+1 flavor Polyakov Loop extended Nambu--Jona-Lasinio model with eight-quark interaction terms using three-momentum cutoff regularisation. The main effect of the higher order interaction term is to shift the critical end point to the lower value of the chemical potential and higher value of the temperature. The fluctuations show good qualitative agreement with the lattice data.
We study properties of 2+1-flavor QCD in the imaginary chemical potential region by using two approaches. One is a theoretical approach based on QCD partition function, and the other is a qualitative one based on the Polyakov-loop extended Nambu--Jona-Lasinio (PNJL) model. In the theoretical approach, we clarify conditions imposed on the imaginary chemical potentials $mu_{f}=itheta_{f}T$ to realize the Roberge-Weiss (RW) periodicity. We also show that the RW periodicity is broken if anyone of $theta_{f}$ is fixed to a constant value. In order to visualize the condition, we use the PNJL model as a model possessing the RW periodicity, and draw the phase diagram as a function of $theta_{u}=theta_{d}equiv theta_{l}$ for two conditions of $theta_{s}=theta_{l}$ and $theta_{s}=0$. We also consider two cases, $(mu_{u},mu_{d},mu_{s}) =(itheta_{u}T,iC_{1}T,0)$ and $(mu_{u},mu_{d},mu_{s})=(iC_{2}T,iC_{2}T,itheta_{s}T)$; here $C_{1}$ and $C_{2}$ are dimensionless constants, whereas $theta_{u}$ and $theta_{s}$ are treated as variables. For some choice of $C_{1}$ ($C_{2}$), the number density of up (strange) quark becomes smooth in the entire region of $theta_{u}$ ($theta_{s}$) even in high $T$ region.
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