In this chapter, I treat inclusive hard processes in hadron-hadron collisions. These give some of the most important practical applications of factorization. But the actual derivation has substantial extra difficulties, compared with other processes we have examined.

Technically the extra difficulties concern the Glauber region. In e+e- annihilation or SIDIS, we deformed loop momenta out of the Glauber region in individual (cut) graphs. But this is no longer possible in hadron-hadron collisions. This situation results from interactions between the spectator parts of the beam hadrons, as I will illustrate by an example in Sec. 14.3. To get factorization, we will need a sum over cuts of the graphs, which in turn entails a sum over different unobserved final states in an inclusive cross section. The technical details will be explained in Sec. 14.4 for the case of the Drell-Yan process.

After that we will obtain factorization, including the version using TMD parton densities. I will summarize the situation for more general reactions with detected hadrons of high transverse momentum. There is a surprising lack of detailed published proofs. Although the statements of factorization are essentially trivial generalizations of those for Drell-Yan, there are underlying complications in the physics which makes the justification of the generalizations quite non-trivial.

This work also leads us to the frontiers of the factorization approach, beyond which more general methods are needed, e.g., in diffractive hadron-hadron scattering.