Generalized quark number susceptibilities from fugacity expansion at finite chemical potential for $N_f=2$ Wilson fermions

Generalized susceptibilities of the net quark number have been proposed to be good probes for the transitions in the QCD phase diagram and for the search of a possible critical end point. In this article we explore a new strategy for computing quark number susceptibilities from lattice QCD via an expansion in the fugacity parameter $e^{\mu \beta }$. All quark number related bulk observables are particularly easy to access in this approach, and we present results for generalized quark number susceptibilities up to fourth order. Ratios of these quantities are studied and compared with model calculations for the high- and low-temperature regions up to a chemical potential of $\mu \beta \approx 1.0$.

Figure 1

Distribution of the absolute values of the canonical determinants normalized by $|D^{(0)}|$ and weighted with the fugacity factors as a function of the net quark number $q$. The results are from our $12^3\times 6$, $\kappa =0.162$, $6/g^2=5.40$ ensemble. In the top plot, we use a linear scale and values of $\mu \beta$ up to 0.4, while in the bottom plot a log scale is used for values of $\mu \beta$ up to 1.0.

Figure 2

Comparison of the quark number density as a function of the chemical potential for three spatial volumes with $N_s=8$, $N_s=10$ and $N_s=12$. The results are for $N_t=4$, $\kappa =0.158$ and $6/g^2=5.30$.

Figure 3

Logarithm of the normalized canonical determinants and a fit of the data to a Skellam distribution [Eq. (11)] are shown. The data is for the $8^3\times 4$, $\kappa =0.158$ ensemble at temperatures $T=144\mathrm{MeV}$ (upper plot) and $T=211\mathrm{MeV}$ (lower plot).

Figure 4

Quark number density $n_q/T^3$ and susceptibility ${\chi }_2^q/T^2$ as a function of the inverse coupling (corresponding temperature values on the top scale) for the $8^3\times 4$, $\kappa =0.158$ (lhs) and $12^3\times 6$, $\kappa =0.162$ (rhs) ensembles. The arrows on the rhs of the plots mark the Stefan-Boltzmann high-temperature limits.

Figure 5

The generalized quark number susceptibilities ${\chi }_3^q/T$ (top) and ${\chi }_4$ (bottom) as a function of the inverse coupling (corresponding temperature values on the top scale) for the $8^3\times 4$, $\kappa =0.158$ (lhs) and $12^3\times 6$, $\kappa =0.162$ (rhs) ensembles. The arrows on the rhs of the plots mark the Stefan-Boltzmann high-temperature limits.

Figure 6

Ratios of the generalized quark number susceptibilities $({\chi }_2^q/T^2)/(n_q/T^3)$, $({\chi }_3^q/T)/({\chi }_2^q/T^2)$, and $({\chi }_4^q)/({\chi }_2^q/T^2)$ (top to bottom) as a function of the inverse coupling (corresponding temperature values on the top scale) for the $8^3\times 4$, $\kappa =0.158$ (lhs) and $12^3\times 6$, $\kappa =0.162$ (rhs) ensembles. The dashed lines in the confined region are the HRG results and the arrows on the rhs of the plots mark the Stefan-Boltzmann high-temperature limits.

Figure 7

The critical line in the $\mu \beta \text{−}T$ plane, as determined from the inflection points of ${\chi }_2^q/T^2$.