Fluctuations and correlations of conserved charges in an excluded-volume hadron resonance gas model

We present temperature and baryonic chemical potential dependence of higher-order fluctuations and the correlation between conserved charges in an excluded-volume hadron resonance gas model. Products of moments, such as the ratio of variance to mean, product of skewness and standard deviation, product of kurtosis and variance, for the net proton, net kaon, and net charge have been evaluated on the phenomenologically determined freeze-out curve. Further, products of moments for net proton and net charge have been compared with the experimental data measured by the STAR experiment. The dependence of the model result on the hadronic radius parameter has also been discussed.

Figure 1

Equations of state as a function of ${\mu }_B$ at constant $T$ keeping ${\mu }_S={\mu }_Q=0$. Noninteracting means noninteracting HRG model, i.e., without excluded-volume correction, and interacting refers to EVHRG. $R_m$ refers to radius of mesons and $R_b$ refers to radius of baryons.

Figure 2

Variation of pressure and second-order susceptibilities ${\chi }_B^2,{\chi }_S^2$, and ${\chi }_Q^2$ with temperature at $\mu =0$. Lattice data for pressure are taken from Bazavov et al. [71] and Borsányi et al. [25] whereas those for ${\chi }^2$ are taken from Bazavov et al. [24] and Borsányi et al. [27].

Figure 3

Variation of fourth-order susceptibilities ${\chi }_B^4,{\chi }_S^4,{\chi }_Q^4$ with temperature $\left(\mu =0\right)$. Lattice data is taken from Ref. [72].

Figure 4

Variation of ${\chi }_{BS}^{11},{\chi }_{BQ}^{11}$, and ${\chi }_{QS}^{11}$ with temperature at $\mu =0$. Lattice data for continuum extrapolation is taken from Ref. [24].

Figure 5

Variation of $C_{BS},C_{QS}$, and $C_{BQ}$ with temperature at $\mu =0$. Lattice data for continuum extrapolation is taken from Ref. [24].

Figure 6

Susceptibilities ${\chi }_B^1,{\chi }_B^2,{\chi }_B^3,{\chi }_B^4$ as a function of ${\mu }_B$ keeping $T$ fixed and ${\mu }_S={\mu }_Q=0$.

Figure 7

Susceptibilities ${\chi }_S^1,{\chi }_S^2,{\chi }_S^3,{\chi }_S^4$ as a function of ${\mu }_B$ keeping $T$ fixed and ${\mu }_S={\mu }_Q=0$.

Figure 8

Susceptibilities ${\chi }_Q^1,{\chi }_Q^2,{\chi }_Q^3,{\chi }_Q^4$ as a function of ${\mu }_B$ keeping $T$ fixed and ${\mu }_S={\mu }_Q=0$.

Figure 9

${\chi }_{BS}^{11},{\chi }_{BQ}^{11},{\chi }_{QS}^{11}$ as a function of ${\mu }_B$ keeping ${\mu }_S={\mu }_Q=0$.

Figure 10

Variation of $C_{BS},C_{QS}$, and $C_{BQ}$ with ${\mu }_B$ keeping ${\mu }_S={\mu }_Q=0$.

Figure 11

Energy dependence of ${\sigma }^2/M,S\sigma$, and $\kappa {\sigma }^2$ for net proton. Experimental data is taken from Ref. [79].

Figure 12

Energy dependence of ${\sigma }^2/M,S\sigma$, and $\kappa {\sigma }^2$ for net kaon.

Figure 13

Energy dependence of ${\sigma }^2/M,S\sigma$, and $\kappa {\sigma }^2$ for net charge. Experimental data is taken from Ref. [82].