Review of Charmonium and Bottomonium Quark State Production via Relativistic Heavy Ion Collisions

This is a review of the production of heavy quark states via relativistic heavy ion collisions in RHIC. The heavy quarks here are html-italic^>c, charm quark, and html-italic^>b, bottom quark. The states are charmonium meson states $\Psi \left(nS\right)$, with n = 1,2 and upsilon meson states ${\rm Y}\left(mS\right)$, with m = 1,2,3. Quantum Chromodynamics (QCD) sum rules were used to derive the result that the $\Psi \left(2S\right)$ and ${\rm Y}\left(3S\right)$ are mixed hybrid states, which increase their production cross sections. We also review the $\Psi \left(nS\right)$ and ${\rm Y}\left(mS\right)$ production cross sections via Cu-Cu and Au-Au collisions, which are very important for this review of the production of heavy quark states in RHIC. The possible detection of the Quark Gluon Plasma (QGP) is also reviewed.