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
 A: Yes, this can really happen. One example is a process called Drell-Yan production (at a hadron collider). A Drell-Yan event is the interaction of a quark and an anti-quark, which annihilate to form a photon or Z-boson (which then at some point decays to a pair of leptons).
At a proton-proton collider this can only happen if the anti-quark is a sea-quark (because the proton has only three quarks as valence quarks).
The Feynman graph for this process looks something like this:

A: Assume proton proton  scattering: something has to be exchanged in order to interact. Because they are strong interacting particles they exchange  at least a gluon  with the out going protons absorbing the energy and breaking out into jets. 

A gluon leaves from a quarq of one of the protons and  gives energy to one of the quarks of the other resulting into three jets.
For your diagram, a triple gluon vertex is allowed, as for example:

where your C and D are the two exchange gluons going into a third one. The event will have at least three jets, the two from the "spectator" protons and the third from the gluon process I (the diagram is written for hypothetical new particles  searched for). 
Your C and D cannot be a quark and antiquark unless you draw the corresponding anti to them and do something with them. There are quantum numbers that have to be kept track of, particularly baryon number . Two quarks cannot annihilate, they can interact.
