Physics of Experiment 852
The above quote is the motivation behind E852. Quantum ChromoDynamics (or any other part of the Standard Model) does not forbid exotic mesons, therefore they must exist. If they exist, it is the responsibility of science to find them. If they don't exist, then our understanding of the world is flawed.
Exotic mesons (also refered to as exotics) are bound states which are not composed of a quark/anti-quark pair (as a meson is) or of three quarks (as a baryon is). They are states composed of various combinations of quarks, anti-quarks and gluons. There are 3 main types of exotics mesons. They are glueballs, hybrids, and diquarkonium.
A glueball is a resonance which is composed of 2 or 3 gluons. Gluons are the mediators of the strong force and are exchanged by quarks within hadrons. The gluon also carries color and can interact with another gluon. This allows gluons to form bound states which are called glueballs.
A hybrid is a particle made up of a quark, an anti-quark, and a gluon. The gluon in this case is not a virtual exchange particle. This is a variation on the meson structure of a quark and an anti-quark.
Diquarkonium is a resonance composed of two quarks and two anti-quarks.