Theoretical Study Of The Phase Transition Of The 2+1 Flavor QCD Within Functional Renormalization Group

Studies of the phase structure of Quantum Chromodynamics（QCD）at finite tem-perature and density,especially to search for the critical end point（CEP）,have attracted lots of attention from both the experimental and theoretical sides.In this work,we em-ploy the functional renormalization group（fRG）approach,which encodes the quantum and thermal fluctuations of different scales by running the flow equations.In this thesis,we have studied the QCD phase structure,the equation of state,fluctuations of conserved charges,etc.We employ a low energy effective model,the 2+1 flavor Polyakov-loop improved quark-meson model.The quark and meson masses,and the meson decay constants as functions of temperature and chemical potential have been studied,and the phase diagram of the low energy effective model has been investigated.The equation of states,such as the pressure,trace anomaly,and the baryon number fluctuations have been calculated.It is found that our results agree well with the lattice QCD results at small baryon chemical potentials,and the relevant results at high baryon chemical potentials are predicted.Moreover,we consider the two constraints,i.e.strangeness neutrality（n_S=0）and a fixed ratio of the electric charge to the baryon number density（n_Q/n_B=r）.With these constraints,the correlations of conserved charges are calculated as functions of the collision energy,and a non-monotonic dependence ofχ₃₁^BS/χ₂^Sandχ₂₂^BS/χ₂^Son the collision energy is found.The low energy effective model is also extended to imaginary chemical potentials.Through a closed-loop integration in the complex plane,we calculate the net baryon num-ber probability distribution.The Z（3）symmetry of the gluon background field（Polyakov loop）and the Roberge-Weiss periodicity,and their relations with the confinement-deconfinement phase transition have been investigated.The Roberge-Weiss periodicity results in that,only states of the net baryon number N_B=N（N∈Z）are possible,while N_B=N±1/3 are prohibited.Furthermore,we also study the reliability region of a newly proposed expansion scheme based on lattice calculations in imaginary chemical potentials,and compare it with conventional Taylor expansions.The fRG approach is also applied to the 2+1 flavor first-principle QCD at finite temperature and densities.With the technique of the dynamical hadronization,degrees of freedom are transferred from the quarks and gluons at the high energy scale to composite hadrons,e.g.,the mesons at the low energy scale.Various flow equations of propagators and vertices are derived,which allow us to calculate observables at finite temperature and densities,e.g.,the quark chiral condensate.It is found that our calculated results within the 2+1 flavor fRG-QCD approach are in excellent agreement with the lattice QCD results at vanishing baryon chemical potential.The QCD phase diagram for the2+1 flavor QCD within the fRG approach is obtained,and the location for the CEP is estimated at(T_CEP=108Me V,μ_B,CEP=650Me V).Moreover,we also calculate the QCD equations of state,i.e.the pressure,the entropy density,trace anomaly and the speed of sound,at finite temperature and baryon chemical potentials.The relevant results are compared with the lattice QCD results at vanishing and small baryon chemical potentials withμ_B/T（?）2.5.Within the errors our results are in good agreement with the lattice results,and the equation of state at large baryon chemical potentials are also obtained.The baryon number fluctuations are calculated within the 2+1 flavor fRG-QCD approach,which are consistent with lattice results at vanishing baryon chemical potentials.We study the dependence of the baryon number fluctuations on the collision energy in heavy-ion collisions,and a non-monotonic behavior is found.