Width of the QCD transition in a Polyakov-loop Dyson-Schwinger equation model

We consider the pseudocritical temperatures for the chiral and deconfinement transitions within a Polyakov-loop Dyson-Schwinger equation approach which employs a nonlocal rank-2 separable model for the effective gluon propagator. These pseudocritical temperatures differ by a factor of 2 when the quark and gluon sectors are considered separately, but get synchronized and become coincident when their coupling is switched on. The coupling of the Polyakov loop to the chiral quark dynamics narrows the temperature region of the QCD transition in which chiral symmetry and deconfinement is established. We investigate the effect of rescaling the parameter $T_0$ in the Polyakov-loop potential on the QCD transition for both the logarithmic and polynomial forms of the potential. While the critical temperatures vary in a similar way, the width of the transition is more strongly affected for the logarithmic potential. For this potential, the character of the transition changes from crossover to a first-order one when $T_0<210\mathrm{MeV}$, but it remains crossover in the whole range of relevant $T_0$ values for the polynomial form.

Figure 1

(Color online) Quark-mass susceptibilities (blue dashed line: light flavors; red dash-dotted line: strange flavor) with coupling to the Polyakov loop (left panel) and without it (right panel) as a function of the temperature. Note that without coupling to the Polyakov loop the chiral transition temperature is unrealistically low and the peak value for the light flavors is different from that for the strange one.

Figure 2

(Color online) Same as Fig. 1, but as a function of the scaled temperature $T/T_c$ with $T_c=195\mathrm{MeV}$ (left panel) and $T_c=T_{\chi }=128\mathrm{MeV}$ (right panel). Without coupling to the Polyakov loop, $T_d=2.11T_c$ is outside the range shown.

Figure 3

(Color online) Temperature dependence of the order parameters for chiral symmetry breaking ($m(T)/m(0)$, blue lines) and for deconfinement ($\Phi (T)$, black lines) for different choices for the parameter $T_0$ in the Polyakov-loop potential.

Figure 4

(Color online) Pseudocritical temperature for the chiral restoration transition vs parameter $T_0$ of the Polyakov-loop potential in the logarithmic form (3) (black circles) and in the polynomial form (5) (blue squares). For further details, see text.

Figure 5

Temperature dependence of pseudoscalar $(\pi ,K)$ and scalar ($\sigma$) meson masses in the present model without (upper panel) and with (lower panel) coupling to the Polyakov-loop potential. The temperature $T_{\sigma -2\pi }$ ($T_{\sigma }-2q$) where the $\sigma$ meson mass equals the double pion mass (double quark mass) determines the threshold for closing (opening) the $\sigma \to 2\pi$ ($\sigma \to 2q$) decay channel.

Figure 6

Squared pseudoscalar mass vs current quark mass for different temperatures (data symbols, connected by lines to guide the eye), show a GMOR-like behavior which holds in a wide range of quark masses, and up to temperatures very close to the critical one.