particle physics - Sea quark parton annihilation?

Consider the figure below¹:

This can be read as follows (please correct me if I am wrong): two particles come in and 'fragment', a parton from each particle $C$ and $D$ annihilate to form the particle $X$. An intuitive guess is that the partons $C$ and $D$ must correspond to valence quarks whist the 'jets' of $A$ and $B$ must contain the remaining valence quarks and the usual gluon and sea quarks. My question is this: Is such a reaction possible but in which $C$ and $D$ represent sea quarks (or even gluons)? Please can you explain either way.

_{¹Image adapted from that given on page 20 of http://www.hep.man.ac.uk/u/hanl/lecture/Lecture1_LHC+TeVatron.PDF}