Exotic hadrons are subatomic particles composed of quarks and gluons, but which do not fit into the usual scheme of hadrons. While bound by the strong interaction they are not predicted by the simple quark model. That is, exotic hadrons do not have the same quark content as ordinary hadrons: exotic baryons have more than just the three quarks of ordinary baryons and exotic mesons do not have one quark and one antiquark like ordinary mesons. Exotic hadrons can be searched for by looking for S-matrix poles with quantum numbers forbidden to ordinary hadrons. Experimental signatures for such exotic hadrons have been seen recently but remain a topic of controversy in particle physics.
Jaffe and Low  suggested that the exotic hadrons manifest themselves as poles of the P matrix, and not of the S matrix. Experimental P-matrix poles are determined reliably in both the meson-meson channels and nucleon-nucleon channels.
When the quark model was first postulated by Murray Gell-Mann and others in the 1960s, it was to organize the states known then to be in existence in a meaningful way. As Quantum Chromodynamics (QCD) developed over the next decade, it became apparent that there was no reason why only 3-quark and quark-antiquark combinations could exist. In addition, it seemed that gluons, the mediator particles of the strong interaction, could also form bound states by themselves (glueballs) and with quarks (hybrid hadrons). Several decades have passed without conclusive evidence of an exotic hadron that could be associated with the S-matrix pole.
There are several exotic hadron candidates:
- X(3872) – Discovered by the Belle detector at KEK in Japan, this particle has been variously hypothesized to be diquark or a mesonic molecule.
- Y(3940) – This particle fails to fit into the Charmonium spectrum predicted by theorists.
- Y(4140) – Discovered at Fermilab in March 2009 .
- Y(4260) – Discovered by the BaBar detector at SLAC in Menlo Park, California this particle is hypothesized to be made up of a gluon bound to a quark and antiquark.
- Zc(3900) – Discovered by Belle and BES III
- Z(4430) – Discovered by Belle and later confirmed by LHCb with 13.9σ significance 
- See "note on non-q qbar mesons" in PDG 2006, Journal of Physics, G 33 (2006) 1.
- R. L. Jaffe and F. E. Low, Phys. Rev. D 19, 2105 (1979). doi:10.1103/PhysRevD.19.2105
- LHCb collaboration (7 April 2014). "Observation of the resonant character of the Z(4430)- state". arXiv:1404.1903.
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