Fluctuations and correlations of conserved charges in the Polyakov chiral SU(3) quark mean field model

Abstract

We compute generalized susceptibilities of conserved charges in the Polyakov chiral SU(3) quark mean field (PCQMF) model with the fermion vacuum term. At $\mu_B = 0$ MeV, the calculation covers the diagonal $\chi_n^{B,Q,S}$ through eighth order and all twelve independent fourth-order off-diagonal correlators. Extending to finite $\mu_B$ at $\mu_Q = \mu_S = 0$, we compute $\chi_n^B$ through eighth order, $\chi_n^{Q,S}$ through fourth order, the second-order off-diagonals, all twelve fourth-order off-diagonal correlators, and the odd-order baryon susceptibilities $\chi_1^B$, $\chi_3^B$, $\chi_5^B$. The calculation includes the vacuum term (vac=1) and is repeated for an independently refitted no-sea variant (vac=0). At $\mu_B = 0$ MeV, the chiral pseudocritical temperature is $T_{\mathrm{pc}} = 170.5$ MeV (vac=1) and $166.4$ MeV (vac=0), while the Polyakov-loop deconfinement temperature is $T_{\mathrm{dec}} = 144.4$ MeV (vac=1) and $146.6$ MeV (vac=0). In vac=1, the derivative $-d\Delta_{l,s}/dT$ of the subtracted chiral condensate develops an inflection near $T_{\mathrm{dec}}$. Higher derivative orders resolve the chiral-deconfinement splitting as twin maxima in $\chi_4^B$ and $\chi_6^Q$, twin minima in $\chi_8^B$ and $\chi_8^Q$, and multiple zero crossings in $\chi_6^B$. Among the fourth-order off-diagonal correlators, vac=1 amplitudes exceed vac=0 in the BQ channel across the chiral crossover. The BS, QS, and mixed BQS components peak near the strange-melting temperature, where vac=0 dominates. Along $T_{\mathrm{pc}}(\mu_B)$, the kurtosis ratio $R_{42}^B \equiv \chi_4^B/\chi_2^B$ of vac=1 crosses zero at $\mu_B/T_{\mathrm{pc}} \approx 2.15$, while vac=0 stays positive across the full range. The higher-order ratios $R_{51}^B \equiv \chi_5^B/\chi_1^B$ and $R_{62}^B \equiv \chi_6^B/\chi_2^B$ start negative in vac=1 and grow more negative as $\mu_B$ increases.