Current quark mass effects on the chiral phase transition of QCD in the improved ladder approximation

Abstract

Current quark mass effects on the chiral phase transition of QCD is studied in the improved ladder approximation. An infrared behavior of the gluon propagator is modified in terms of an effective running coupling. The analysis is based on a composite operator formalism and a variational approach. We use the Schwinger-Dyson equation to give a "normalization condition" for the Cornwall-Jackiw-Tomboulis effective potential and to isolate the ultraviolet divergence which appears in an expression for the quark-antiquark condensate. We study the current quark mass effects on the order parameter at zero temperature and density. We then calculate the effective potential at finite temperature and density and investigate the current quark mass effects on the chiral phase transition. We find a smooth crossover for T > 0, µ = 0 and a first-order phase transition for µ > 0, T = 0. Critical exponents are also studied and our model gives the classical mean-field values. We also study the temperature dependence of masses of scalar and pseudoscalar bosons. A critical end point in the T -µ plane is found at T ∼ 100 MeV, µ ∼ 300 MeV.

Three flavor Nambu–Jona-Lasinio model with Polyakov loop and competition with nuclear matter

“…For any value of the quark chemical potential, the critical temperature is identified with the temperature at which the up quark chiral condensate σ u has a jump (first order transition), or the derivative of σ u with respect to the temperature is maximum (second order transition). The phase The numerical values of the cross-over temperatures at µ = 0 are in the same range of the results found in QCD-like theories [24,25,26] or in lattice QCD [27]. On the other hand, the CEPs are located at values of µ much higher than the respective values found in QCD/like theories [24,25,26], lattice QCD [27] and empirical analysis of the ratio of shear viscosity to entropy density [28], which suggest there is a CEP at T ≈ 165 MeV and µ ≈ 50 MeV.…”

“…The critical endpoints (CEPs) separating the cross-over from the first-order lines are located, for the three cases, at (µ E , T E ) ≈ (300, 140) MeV (highest curve), (µ E , T E ) ≈ (300, 115) MeV (middle curve) (µ E , T E ) ≈ (310, 68) MeV (lowest curve). At µ = 0 we find for the three cases the cross-over temperatures T χ (µ = 0) ≈ 223 MeV (highest curve), T χ (µ = 0) ≈ 200 MeV (middle curve), T χ (µ = 0) ≈ 189 MeV (lowest curve).The numerical values of the cross-over temperatures at µ = 0 are in the same range of the results found in QCD-like theories[24,25,26] or in lattice QCD[27]. On the other hand, the CEPs are located at values of µ much higher than the respective values found in QCD/like theories[24,25,26], lattice QCD[27] and empirical analysis of the ratio of shear viscosity to entropy density[28], which suggest there is a CEP at T ≈ 165 MeV and µ ≈ 50 MeV.…”

“…At µ = 0 we find for the three cases the cross-over temperatures T χ (µ = 0) ≈ 223 MeV (highest curve), T χ (µ = 0) ≈ 200 MeV (middle curve), T χ (µ = 0) ≈ 189 MeV (lowest curve).The numerical values of the cross-over temperatures at µ = 0 are in the same range of the results found in QCD-like theories[24,25,26] or in lattice QCD[27]. On the other hand, the CEPs are located at values of µ much higher than the respective values found in QCD/like theories[24,25,26], lattice QCD[27] and empirical analysis of the ratio of shear viscosity to entropy density[28], which suggest there is a CEP at T ≈ 165 MeV and µ ≈ 50 MeV. Clearly the details of the models matter; in relation to this problem, in Ref [12].…”

Phase Structure of Hot and/or Dense QCD with the Schwinger-Dyson Equation

“…7), 8) In the SDE analysis, the phase structure of QCD in the finite temperature and finite chemical potential region have been investigated, concentrating on the chiral symmetry restoration. 9), 10), 11), 12), 13), 14) In a previous work, 15) solving the SDE with the full momentum dependence included, we studied the phase transition from the hadron phase to the two-flavor color superconducting (2SC) phase in the region of finite quark chemical potential at zero temperature. It was shown that the phase transition is of first order and the existence of the 2SC phase decreases the critical chemical potential at which the chiral symmetry is restored.…”

Critical endpoint in the Polyakov-loop extended NJL model

“…In the original NJL model that includes scalar and pseudo-scalar type four-quark interactions, it was found that there exists a CEP in the phase diagram [5,6]. However, the CEP is located at a lower temperature (T ) and a higher µ compared with the one predicted by a lattice QCD simulation [2] and by the QCD-like theory [7,8]. Moreover, recent empirical analysis [9] of η/s, the ratio of shear viscosity to entropy density, suggest there is a CEP at T e ∼ 165 MeV and µ e ∼ 50 − 60 MeV that is much higher T and lower µ than the NJL model predictions.…”