Relation between the continuum threshold and the Polyakov loop with the QCD deconfinement transition

Using vector and axial-vector correlators within finite-energy sum rules with inputs from a chiral quark model, coupled to the Polyakov loop, with nonlocal vector interactions, we extend our previous work to confirm the equivalence between the continuum threshold $s_0$ and the trace of the Polyakov loop $\mathrm{\Phi }$ as order parameters for the deconfinement transition at finite temperature $T$ and quark chemical potential $\mu$. The obtained results are in agreement with our initial conclusion, where we showed that $s_0(T,\mu )$ and $\mathrm{\Phi }(T,\mu )$ provide the same information for the QCD deconfinement transition.

Figure 1

Fit to ALEPH data in the axial-vector channel [36] up to $s\simeq 2{\mathrm{GeV}}^2$. Errors are represented by the size of the data points.

Figure 2

Diagrammatic representation of the contributions to the weak decay constants. The cross represents the axial current vertex. (a) Two-vertex diagram. (b) Tadpole-like contribution.

Figure 3

Diagrams contributing to $\rho$ and $a_1$ decays due to the $\pi -a_1$ mixing.

Figure 4

Polyakov loop and normalized quark condensate (dotted and dash-dotted lines, respectively), together with the continuum threshold $s_0$ for the vector (solid line) and axial (dashed line) channels as a function of $T/T_c$, with $T_c=202\mathrm{MeV}$.

Figure 5

Normalized $C_4⟨{\widehat{\mathcal{O}}}_4⟩$, Eq. (37), for the axial and vector channels (solid and dashed lines, respectively) as a function of $T/T_c$.

Figure 6

QCD phase diagrams for $\eta =0$ and $\eta =0.3$ in the upper and lower panel, respectively [23], together with the $(\mu ,T)$ coordinates and position of the CEP. The $s_0^{A,V}$ associated deconfinement temperatures are represented by the patterned areas.

Figure 7

Polyakov loop and normalized quark condensate (dotted and dash-dotted lines, respectively) together with the continuum threshold $s_0$ for the vector and axial channels (solid and dashed lines, respectively) for $\eta =0$ and $\eta =0.3$, in the upper and lower panels, respectively.