Real-time evolution of critical modes in the QCD phase diagram

Abstract

A QCD-assisted relaxation dynamic model for the critical mode of the critical end point (CEP) in the QCD phase diagram is developed, which allows us to investigate the critical slowing down effect quantitatively in the QCD phase diagram, especially in the proximity of the CEP, without any phenomenological parameters. The relaxation time from nonequilibrium to equilibrium in the QCD phase diagram is extracted from the Langevin simulations of the QCD-assisted relaxation dynamic model. It is found that in a narrow region along the phase boundary radiated from the CEP, the relaxation time is enhanced significantly. Outside this narrow region, the relaxation time drops drastically, which implies that the dynamic critical region is small in the QCD phase diagram. We also find that the effects of critical slowing down are mild on the chemical freeze-out curves.

Figures (13)

• Figure 1: Left panel: Heatmap of the reduced relaxation time $\tau/\tau_0$ in the QCD phase diagram. The relaxation time is normalized by the maximal relaxation time $\tau_0$ in this plane, which is located at a point near the CEP, denoted by the red dot. Three typical chemical freeze-out curves used also in Fu:2021oaw are shown. The black dot-dashed line denotes the phase boundary of crossover obtained in QCD within the fRG Fu:2019hdw. The black dotted line stands for the line of the maximal relaxation time along the temperature direction at a fixed baryon chemical potential. Right panel: 3D plot of the left panel.
• Figure 2: Relaxation time as a function of the baryon chemical potential along the phase boundary and the three chemical freeze-out curves, respectively, as shown in Fig. \ref{['fig:relaxtime']}.
• Figure 3: Diagrammatic representation of the flow of two-point correlation functions for mesons, where the gray blobs denote the one-particle-irreducible (1PI) vertices. The derivative $\tilde{\partial}_t$ only hits the $k$-dependence of the regulators, which in fact results in an insert of one regulator for each inner propagator of the diagrams on the r.h.s. Here, $t=\ln(k/\Lambda)$ denotes the RG time, with $k$ and $\Lambda$ being the RG scale and an ultraviolet cutoff scale, respectively.
• Figure 4: Renormalized temporal wave function $\bar{Z}_\phi^{(t)}$ in \ref{['eq:barZt']} in the QCD phase diagram calculated from the fRG approach to QCD at finite temperature and densities, where $\bar{Z}_\phi^{(t)}$ is rescaled with the maximal value $\bar{Z}_{\phi, \mathrm{max}}^{(t)}$ in the phase diagram shown in this plot. The blue solid line denotes the position of the maximal value of $|\partial \bar{Z}_\phi^{(t)}/\partial T|$ along the temperature direction at different baryon chemical potentials. The magenta dashed line stands for the position of the maximal value of $\bar{Z}_\phi^{(t)}$ along the temperature direction at different baryon chemical potentials. The black dot-dashed line denotes the phase boundary.
• Figure 5: Imaginary part of the retarded two-point correlation function of sigma mode as a function of the frequency, where contributions from different parts are presented separately. The spatial momentum is chosen to be $|\bm{p}|=10$ MeV. Results with $\mu_B=0$, 630 MeV for several different values of $T$ are presented in the panels of the first and second rows, respectively.