Critical behaviors of the $O(4)$ and $Z(2)$ symmetries in the QCD phase diagram

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.

16 pages, 8 figures, 2 tables

References in corpus (34)

• Exact evolution equation for the effective potential
• The order of the quantum chromodynamics transition predicted by the standard model of particle physics
• The equation of state in (2+1)-flavor QCD
• The nonperturbative functional renormalization group and its applications
• The Phase Structure of the Polyakov--Quark-Meson Model
• The QCD crossover at finite chemical potential from lattice simulations
• The QCD phase structure at finite temperature and density
• Bootstrapping Mixed Correlators in the 3D Ising Model
• Chiral symmetry breaking in continuum QCD
• The phase structure of the Polyakov--quark-meson model beyond mean field
• The phase boundary for the chiral transition in (2+1)-flavor QCD at small values of the chemical potential
• Non-monotonic energy dependence of net-proton number fluctuations
• Susceptibilities near the QCD (tri)critical point
• Skewness, kurtosis and the 5th and 6th order cumulants of net baryon-number distributions from lattice QCD confront high-statistics STAR data
• The renormalization group and quark number fluctuations in the Polyakov loop extended quark-meson model at finite baryon density
• QCD phase structure from functional methods
• Renormalization Group Approach towards the QCD Phase Diagram
• Improved Polyakov-loop potential for effective models from functional calculations
• Exact flow equation for composite operators
• Precision calculation of critical exponents in the $O(N)$ universality classes with the nonperturbative renormalization group
• The QCD Phase Boundary from Quark-Gluon Dynamics
• Baryon number fluctuations at finite temperature and density
• Correlation functions of Landau gauge Yang-Mills theory
• Correlated Dirac Eigenvalues and Axial Anomaly in Chiral Symmetric QCD
• On the scaling behavior of the chiral phase transition in QCD in finite and infinite volume
• Chiral Susceptibility in (2+1)-flavour QCD
• Towards quantitative precision in the chiral crossover: masses and fluctuation scales
• Towards finite density QCD with Taylor expansions
• Modeling Finite-Volume Effects and Chiral Symmetry Breaking in Two-Flavor QCD Thermodynamics
• Energy Dependence of Moments of Net-Proton and Net-Charge Multiplicity Distributions at STAR
• Shocks and quark-meson scatterings at large density
• Scaling functions for the O(4)-model in d=3 dimensions
• Exact solutions and residual regulator dependence in functional renormalisation group flows
• Field dependence of the Yukawa coupling in the three flavor quark-meson model

Cited by in corpus (6)

• QCD at finite temperature and density within the fRG approach: An overview
• Critical lensing and kurtosis near a critical point in the QCD phase diagram in and out-of-equilibrium
• Phase structure of 2+1-flavour QCD and the magnetic equation of state
• Real-time dynamics of the $O(4)$ scalar theory within the fRG approach
• Regulator scheme dependence of the chiral phase transition at high densities
• Functional renormalization group study of neutral and charged pion under magnetic fields in the quark-meson model