>
    0 } \frac{x_j~ x_k \left( 2~ +~
      v~\sum_i x_i \right)}{\left(1~+~
       v \sum_i x_i \right)^2 }\right]    ~\times ~
      \left(\sum_{j,q_j>0}~ x_j\right)^{-1}~.\end{aligned}$$ and similar expressions for $\omega_-$ and $\omega_{ch}$ with the summation over $q_j<0,~q_k<0$ and $q_j\neq
0,~q_k\neq 0$, respectively.

Final State Fluctuations
------------------------

To take into account resonance decay we follow the procedure from Refs. [@res_CE; @res_MCE]. The correlators for the final hadrons are expressed as, $$\begin{aligned}
  \langle \Delta N_j\,\Delta N_k\rangle
  ~&=\; \langle\Delta N_j^* \Delta N_k^*\rangle
  \;+\; \sum_R \langle N_R\rangle\; \langle n_{j} n_{k}\rangle_R
  \;+\; \sum_R \langle\Delta N_j^*\; \Delta N_R\rangle\; \langle n_{k}\rangle_R
  \; \nonumber
  \\
  &+\; \sum_R  \langle\Delta N_k^*\;\Delta N_R\rangle\; \langle n_{j}\rangle_R
  \;+\; \sum_{R\neq R'} \langle\Delta N_R\;\Delta N_{R'}\rangle
  \; \langle n_{j}\rangle_R\;
       \langle n_{k}\rangle_{R^{'}}\;.\label{corr-VDW}\end{aligned}$$ where all particle-particle, $\langle\Delta N_j^* \Delta
N_k^*\rangle$, particle-resonance, $\langle\Delta N_j^* \Delta
N_R\rangle$, and resonance-resonance, $ \langle\Delta N_R\Delta
N_{R'}\rangle$, correlators in Eq. (\[corr-VDW\]) are calculated according to Eq. (\[VDW-corr\]). Note the essential difference between the correlators in the ideal gas (\[corr-id-B\]) and those in the VDW gas (\[corr-VDW\]). The new terms in Eq. (\[corr-VDW\]) come from the anticorrelations of different stable hadron and resonance species in the VDW gas according to Eq. (\[VDW-corr\]).

Scaled Variance along Chemical Freeze-out Line
==============================================

In this section we present the results of the VDW HG 