Sequential bottomonium production at high temperatures

Bottomonium production in heavy ion collisions is modified compared with any simple extrapolation from elementary collisions. This modification is most likely caused by the presence of a deconfined system of quarks and gluons for times of several fm/c. In such a medium, bottomonium can be destroyed, but the constituent bottom quarks will likely stay spatially correlated due to small mean free paths in this system. With these facts in mind, we describe bottomonium formation with a coupled set of equations. A rate equation describes the destruction of $\Upsilon(1S)$ particles, while a Langevin equation describes how the bottom quarks stay correlated for a sufficiently long time so that recombination into bottomonia is possible. We show that within this approach it is possible to understand the magnitude of $\Upsilon(1S)$ suppression in heavy ion collisions and the larger suppression of the $\Upsilon(2S)$ state, implying that the reduction in the ratio of $\Upsilon(1S)/\Upsilon(2S)$ yield in heavy ion collision does not necessarily correspond to sequential melting picture.