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 $μB = 0$ MeV, the calculation covers the diagonal $χ_n^{B,Q,S}$ through eighth order and all twelve independent fourth-order off-diagonal correlators. Extending to finite $μ_B$ at $μ_Q = μ_S = 0$, we compute $χ_n^B$ through eighth order, $χ_n^{Q,S}$ through fourth order, the second-order off-diagonals, all twelve fourth-order off-diagonal correlators, and the odd-order baryon susceptibilities $χ_1^B$, $χ_3^B$, $χ_5^B$. The calculation includes the vacuum term (vac=1) and is repeated for an independently refitted no-sea variant (vac=0). At $μ_B = 0$ 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 $-dΔ{l,s}/dT$ of the subtracted chiral condensate develops an inflection near $T{\mathrm{dec}}$. Higher derivative orders resolve the chiral-deconfinement splitting as twin maxima in $χ4^B$ and $χ_6^Q$, twin minima in $χ_8^B$ and $χ_8^Q$, and multiple zero crossings in $χ_6^B$. 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 $T{\mathrm{pc}}(μB)$, the kurtosis ratio $R{42}^B \equiv χ4^B/χ_2^B$ of vac=1 crosses zero at $μ_B/T{\mathrm{pc}} \approx 2.15$, while vac=0 stays positive across the full range. The higher-order ratios $R_{51}^B \equiv χ5^B/χ_1^B$ and $R{62}^B \equiv χ_6^B/χ_2^B$ start negative in vac=1 and grow more negative as $μ_B$ increases.