Polyakov loop fluctuations and deconfinement in the limit of heavy quarks

We explore the influence of heavy quarks on the deconfinement phase transition in an effective model for gluons interacting with dynamical quarks in color SU(3). With decreasing quark mass, the strength of the explicit breaking of the Z(3) symmetry grows, and the first-order transition ends in a critical end point. The nature of the critical end point is examined by studying the longitudinal and transverse fluctuations of the Polyakov loop, quantified by the corresponding susceptibilities. The longitudinal susceptibility is enhanced in the critical region, while the transverse susceptibility shows a monotonic behavior across the transition point. We investigate the dependence of the critical end point on the number of quark flavors at vanishing and finite quark density and relate these results to lattice findings.

Figure 1

Temperature dependence of the thermal averaged Polyakov loop for quark masses $m=0.5$, 1.48, and 3.5 GeV at $N_f=3$.

Figure 2

The temperature dependence of the longitudinal ${\chi }_{\mathrm{L}}$ and the transverse ${\chi }_{\mathrm{T}}$ Polyakov loop susceptibility for $N_f=3$ and quark masses, $m=0.5$, 1.48, and 3.5 GeV.

Figure 3

Quark mass dependence of the deconfinement temperature, defined by a peak of ${\chi }_{\mathrm{L}}$, for different $N_f$’s. Full lines correspond to the first-order phase transitions, while dashed lines represent the pseudocritical temperature of the crossover transition. The points indicate the locations of the CEP.

Figure 4

The expectation values of the Polyakov loop $\ell$ (full lines) and its conjugate $\overline{\ell }$ (dashed lines) at $\mu =0.5\mathrm{GeV}$ and for different values of the quark mass, $m=3.5,1.88,0.5\mathrm{GeV}$. (from right to left).

Figure 5

The longitudinal ${\chi }_{\mathrm{L}}$ and transverse ${\chi }_{\mathrm{T}}$ susceptibility (15) vs $T$ at $\mu =0.5\mathrm{GeV}$ and for different quark mass values.

Figure 6

The $\mu$ dependence of the deconfinement temperature, defined by the peak of ${\chi }_{\mathrm{L}}$, for $m=1.6\mathrm{GeV}$ and $N_f=3$. The full line corresponds to a first-order phase transition, while the dashed line represents the pseudocritical temperature of the crossover transition. The point indicates the location of the CEP.

Figure 7

The critical quark mass as a function of the quark chemical potential for $N_f=3$. Solid points represent results obtained from the global maximum of ${\chi }_{\mathrm{L}}$. The line represents the result obtained by keeping only the linear symmetry breaking term in the quark potential, as shown in Eq. (20). It corresponds to the solution of Eq. (23) with $h_c=0.17$ and $T_{\mathrm{CEP}}=0.261\mathrm{GeV}$.