Proper time regularization and the QCD chiral phase transition

Abstract

We study the QCD chiral phase transition at finite temperature and finite quark chemical potential within the two flavor Nambu–Jona-Lasinio (NJL) model, where a generalization of the proper-time regularization scheme is motivated and implemented. We find that in the chiral limit the whole transition line in the phase diagram is of second order, whereas for finite quark masses a crossover is observed. Moreover, if we take into account the influence of quark condensate to the coupling strength (which also provides a possible way of how the effective coupling varies with temperature and quark chemical potential), it is found that a CEP may appear. These findings differ substantially from other NJL results which use alternative regularization schemes, some explanation and discussion are given at the end. This indicates that the regularization scheme can have a dramatic impact on the study of the QCD phase transition within the NJL model.

Dependence of the crossover zone on the regularization method in the two-flavor Nambu–Jona-Lasinio model

“…For the UV (C), PTR and PV schemes, the chiral susceptibility is a regular function for the entire chemical potential range and there is no CEP. These PTR results are in agreement with the one found by Cui et al [56], who did not find a CEP for finite current quark mass. In a similar vein to PTR, no CEP is found in PV nor in UV for the set of parameters (C) as reported by Kohyama et al [29].…”

Effects of Superstatistics on the Location of the Effective QCD Critical End Point

“…From the theoretical side, efforts to locate the CEP employing several techniques [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] were recently carried out. In all of these cases, the full thermalization over the whole reaction volume has been assumed.…”

New algorithm to study the pseudo-Wigner solution of the quark gap equation in the framework of the ( 2+1 )-flavor NJL model

“…As we know, the QCD phase diagram contains rich information: the upper left region of the diagram corresponds to the domain of the thermal QCD where the temperature is very high, and the features of the early universe as well as its expansion can be addressed here [15,16]; the lower right region of the diagram corresponds to the domain of the dense QCD where the chemical potential is very large, and the study of the neutron star is implemented here [17][18][19][20][21][22][23]. At present, a popular scenario is in favor of the existence of the critical endpoint (CEP) [24][25][26][27][28][29]: for the chemical potential smaller (larger) than this point, as the temperature increases, the QCD system will confront a crossover (first order phase transition). Analogously, in the case of chiral limit where the current quark mass m ¼ 0, the tricritical point (TCP) is favored: for the chemical potential smaller (larger) than this point, as the temperature increases, the QCD system will experience a second order phase transition (first order phase transition).…”