transverse momentum broadening defined in this paper is an inclusive and infrared safe calculable quantity, the scale $\mu^2$ should be chosen to be the order of the physically measured momentum scales. As shown in Eq. (\[pilt\]), the only physically measured momentum scales for the transverse momentum broadening are $Q$ and $\ell_{\rm min}$. Since $|\vec{\ell}_{\rm min}|$ are of the same order as $\sqrt{Q^2}$, we choose $\mu^2=Q^2$ for the numerical calculations below, and we believe that such a choice will not result into the large logarithmic high order corrections.

Since the quark-to-pion fragmentation functions have been measured [@newDD], Eq. (\[pilt\]) shows that the transverse momentum broadening of pions provides direct information on the quark-gluon correlation functions inside a nucleus. The measured size of the transverse momentum broadening, $\Delta\langle \ell_{T}^2\rangle_{1/3}$, depends on the choice of the momentum cut $\ell_{\rm min}$ (or equivalently $z_{\rm min}$). Our predictions should be more reliable for the leading pions, or pions with relatively large momenta. By measuring the transverse momentum broadening for $\pi^{\pm}$ and $\pi^0$, and keeping a reasonable large value of $z_{\rm min}$, we can extract the quark flavor dependence of the correlation functions.

Numerical Results and Discussions
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The numerical values of the pion transverse momentum 