As you probably know, when proton and antiprotons -bags of quarks and gluons- are brought one against the other at light speed, most of the energy produced in the collision that sometimes takes place is not exchanged between the two bags, but between a quark or gluon and another quark or gluon. When this happens, the bags break apart, producing two streams of hadrons in opposite directions, close to the beam direction.
In addition, the two "hard" objects that hit each other head-on spend the collision energy to produce jets, or more fancy subatomic particles like W and Z bosons, heavy quarks, etcetera. These constitute the "central" part of the observed collision: stuff that flies off in all directions, and not along the beam. It is this latter debris what we intercept with our detectors -we usually only care about the "transverse" component of the produced collision, and leave holes in our otherwise hermetic detectors not just to let in and out the proton and antiproton beams, but also to give an escape route to the proton and antiproton remnants. These carry almost the total energy of the incoming projectiles, but this energy is not the result of an acceleration due to the collision, and we do not care to study it in detail. What we care for is to study stuff that is the result of large accelerations -large exchanged forces!
So the Tevatron might be thought of as a quark/gluon collider. But this is not always the case. In rare instances, the proton and antiproton do NOT break apart. Crucially, the difference involves the fact that the two projectiles do not exchange a net amount of colour charge.
Colour charge is possessed by quarks and gluons and it is the source of the interaction which binds them inside the protons. Protons have a null total colour charge, and this is a requisite to be stable: coloured objects cannot exist as stable entities. So, if you take a quark or a gluon off a proton, you create an imbalance in its net colour charge, and the proton breaks apart. This is what normally happens in a hard collision at the Tevatron.
But sometimes, you can create a hard collision without breaking the protons! If you take a photon off a proton the colour of the latter remains neutral, and it may survive unbroken. And the same result may occur because of the simultaneous exchange of two gluons!
If you are wondering what I am talking about, have a look at the diagrams below. They represent so-called "exclusive" production diagrams, because what happens is exclusively the creation of matter by the hard interaction, while the proton and antiproton remain themselves, only decelerating slightly.
Processes that have been observed involve the exclusive creation of Z bosons, pairs of jets, J/Psi mesons, and also other particles. All these final states must have quantum numbers that can be taken off the initial state - the proton-antiproton pair - without changing their basic fundamental properties. So, for instance, we could not produce an exclusive production of W bosons, because W bosons have one unit of electric charge: this charge could not be taken off the proton without changing it into a neutron, for instance. And so the W production would not be "exclusive", as the net effect of the collision would not be just the W production, but also a change in the identity of the projectiles.
So, the diagrams below show the proton and antiproton coming in from the left, exchanging photons or gluons, and creating interesting final states, without being affected other than in their total energy. All of the diagrams below, but one, have been observed at the Tevatron so far. Guess which one we are still searching for!