207 at $Q^2=4$ and 9 GeV$^2$ in Fig. \[fig0\]a and \[fig0\]b, respectively. Fig. \[fig0\] shows that although the exact $x_B$-dependence and the $A$-dependence of the structure functions are non-trivial, the overall $A$-dependence of the structure functions is limited to $A^{\alpha}$ with a value of $\alpha\simeq \pm 0.02$ for $x_B$ values between two vertical lines in Fig. \[fig0\], which are relevant to pion production in this paper. Actually, as shown in Fig. \[fig0\], the absolute value of $\alpha$ is limited to 0.05 for any practical value of $x_B$ accessible at fixed target energies. Such $A$-dependence in the structure function as well as in the $\phi_{a/A}(x)$ is much weaker than the $A^{1/3}$-dependence caused by multiple scattering. Since the parton-to-pion fragmentation functions, $D_{c\rightarrow
\pi}$ and $d_{c\rightarrow \pi}$, should not have explicit $A^{1/3}$-dependence, the term $\bar{H}^{(2)}_A$ is of the order of $O(1/Q^2)$, not $O(A^{1/3}/Q^2)$. On the other hand, the term $H^{(2)}_A$ depends on the multi-parton correlation function in a nucleus $T_{a/A}(x)$, and therefore, it will have an $A^{1/3}$-type enhancement [@LQS2].

Substituting Eqs. (\[D0\]) and (\[Hexp\]) into Eq. (\[LTavg\]), and keeping terms up to $O(A^{1/3}/Q^2)$, we obtain $$\langle \ell_{T}^2\rangle^{eA} \approx
\frac{H^{(0)}_A+H^{(2)}_A}{D^{(0)}_A} +
O\left(\frac{A^0}{Q^2}\right)\ .
\label{expLTA}$$ Similarly, for a nucleon target, we have $$\langle \ell_{T}^2\rangle^{eN} \approx
