Abstract
In this work we have studied the QCD phase structure and critical dynamics related to the 3-$d$ $O(4)$ and $Z(2)$ symmetry universality classes in the two-flavor quark-meson low energy effective theory within the functional renormalization group approach. We have employed the expansion of Chebyshev polynomials to solve the flow equation for the order-parameter potential. The chiral phase transition line of $O(4)$ symmetry in the chiral limit, and the $Z(2)$ line of critical end points related to the explicit chiral symmetry breaking are depicted in the phase diagram. Various critical exponents related to the order parameter, chiral susceptibilities and correlation lengths have been calculated for the 3-$d$ $O(4)$ and $Z(2)$ universality classes in the phase diagram, respectively. We find that the critical exponents obtained in the computation, where a field-dependent mesonic nontrivial dispersion relation is taken into account, are in quantitative agreement with results from other approaches, e.g., the conformal bootstrap, Monte Carlo simulations and $d=3$ perturbation expansion, etc. Moreover, the size of the critical regime in the QCD phase diagram is found to be very small.
Highlights
Significant progress has been made in studies of QCD phase structure over the past decade, both from the experimental and theoretical sides; see, e.g., [1,2,3,4,5,6,7,8,9,10]
One of the most prominent features of the QCD phase structure is the probable presence of a second order critical end point (CEP) in the phase diagram spanned by the temperature T and baryon chemical potential μB or densities, which separates the first order phase transition at high μB from the continuous crossover at low μB [1]
QCD phase structure and related critical behaviors have been studied in the two-flavor quark-meson low energy effective theory within the functional renormalization group (fRG) approach in this work
Summary
Significant progress has been made in studies of QCD phase structure over the past decade, both from the experimental and theoretical sides; see, e.g., [1,2,3,4,5,6,7,8,9,10]. We would like to study the QCD phase structure in the chiral limit and finite current quark mass, i.e., with a finite pion mass, in the two-flavor quark-meson low-energy effective field theory (LEFT) within the fRG approach. In this paper we will employ the global effective potential and the high numerical accuracy provided by the Chebyshev expansion to study critical behaviors of the Oð4Þ and Zð2Þ symmetries in the two-flavor LEFT. This computation allows us to determine the Zð2Þ line, i.e., the trajectory of a critical end point moving in the phase diagram with the strength of the explicit chiral symmetry breaking, with a high accuracy. Some threshold functions and anomalous dimensions in the flow equations and some relations for the Chebyshev polynomials are collected in Appendix A and Appendix B, respectively
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