I'm trying to understand how fragmentation is put into a cross section calculation. I have learned that the full cross section can look something like \begin{equation} \sigma=\int_0^1d\xi\int_0^1dzf(\xi)D(z)\hat{\sigma} \end{equation} (it can look more complicated, this is just for the general idea). Here $\hat{\sigma}$ is the cross section without the PDFs and hadronization. $\xi$ is the momentum fraction of the parton in the initial state and $z$ is the ratio $E_h/E$, where $E_h$ is the energy of the hadron produced and $E$ is the energy of the particle which is being hadronized (I'm not sure about the definition of $z$, I have seen some conflicting information). My guestion is, does $\hat{\sigma}$ depend on $z$? I don't see how it would depend on it, but if it doesn't, then the fragmentation doesn't depend on the specific process at all.
Answer to this guestion and corrections on what I said are greatly appriciated.
