$$T_{qF}^A(x,Q^2)=\lambda^2 A^{1/3} q^A(x,Q^2) \ ,
\label{TiM}$$ where $q^A(x)$ is the effective twist-2 quark distribution of a nucleus normalized by the atomic weight $A$, and $\lambda$ is a free parameter to be fixed by experimental data. This model was proposed after comparing the operator definitions of the four-parton correlation functions and the definitions of the normal twist-2 parton distributions. Substituting Eq. (\[TiM\]) into Eq. (\[pilt\]), we have $$\Delta\langle \ell_{T}^2\rangle_{1/3} = 
\frac{4\pi^2\alpha_s(Q^2)}{3}\, A^{1/3}\, \lambda^2\,
\frac{\sum_q e_q^2\,q^{A}(x_B,Q^2)\, 
      D_{q \rightarrow \pi}(2,z_{\rm min})}
     {\sum_q e_q^2\,q^{A}(x_B,Q^2)}\, .
\label{pilt2}$$

From Eq. (\[pilt2\]), we can deduce a very simple formula for the transverse momentum broadening of $\pi^0$ by using the fragmentation functions given in Eq. (\[D01\]): $$\Delta \langle \ell_{T}^2\rangle_{1/3}^{\pi^0} 
\approx \frac{4\pi^2\alpha_s(Q^2)}{3}\, A^{1/3}\, \lambda^2\,
D^0(2,z_{\rm min})\ .
\label{ltpi0}$$ In deriving Eq. (\[ltpi0\]), we neglected the strange quark contribution which is much smaller. This simple expression shows that $\Delta \langle \ell_{T}^2\rangle_{1/3}^{\pi^0}$ has a scaling behavior as $x_B$ varies. The approximate $x_B$-scaling behavior of $\Delta \langle \ell_{T}^2\rangle_{1/3}^{\pi^0}$ is a direct consequence of the model for $T_{qF}^A(x)$, given in Eq. (\[TiM\]). If the future experimental data on the transverse momentum broadening of $\pi^0$ shows a strong violation of the $x_B$-scaling, the model for the quark-gluon correlation function $T_{qF}^A(x_B)$, given in Eq. (\[TiM\]), 