$\phi_{a/A}$ are nuclear parton distributions, and the $T_{a/A}$ in Eq. (\[Hexp\]) represents the twist-4 quark-gluon correlation functions (e.g., the one defined in Eq. (\[T4qA\])). Both $\phi_{a/A}$ and $T_{a/A}$ are normalized by the atomic weight $A$.

Effective nuclear parton distributions $\phi_{a/A}(x)$ have been measured [@EMC; @SLAC; @NMC; @E665] and are known to have the nuclear shadowing for small $x$ ($x\simeq 0.1$), the EMC effect for intermediate $x$ values ($0.3\simeq x \simeq 0.7$), and Fermi motion effect for the large $x$ region. By fitting recent high precision DIS and Drell-Yan data on various nuclear targets, Eskola [*et al.*]{} [@Eskola] extracted a set of effective scale dependent nuclear parton distributions. In order to estimate the $A$-dependence of the nuclear parton distributions, we introduce a parameter $\alpha(A,x_B)$ as $$F_2^A(x_B,Q^2) \equiv A^{\alpha(A,x_B)}\, F_2^N(x_B,Q^2)\ ,
\quad\quad
\mbox{or}
\quad\quad
\alpha(A,x_B) =
\frac{\ln\left[F_2^A(x_B,Q^2)\left/F_2^N(x_B,Q^2)\right.\right]}
     {\ln\left[A\right]}\, ,
\label{F2}$$ where $F_2^A(x_B,Q^2)$ is a nuclear structure function normalized by $A$ and $F_2^N(x_B,Q^2)$ is an isoscalar nucleon structure function. Using the lowest order expression for the structure function: $F_2(x_B,Q^2)=\sum_q\, e_q^2\, x_B\, \phi_{q}(x_B,Q^2)$ with $e_q$ being a quark’s fractional charge and $\phi_{q}$ the effective nuclear parton distributions of Ref. [@Eskola], we plot the parameter $\alpha(A,x_B)$ as a function of $x_B$ for $A$=12, 64, and 