Study the origin of the $\log Q^2$ term. Recall that the $\gamma^* \mathrm{q} \rightarrow \mathrm{qg}$ cross section, $d \hat{\sigma} / d p_T^2$, is dominated by the forward peak. The $t$-channel quark propagator leads to a factor $1 / p_T^4$. Show that helicity conservation at the gluon vertex weakens this singularity by introducing a factor $p_T^2$ in the numerator.