Thermal bottomonium suppression at RHIC and LHC

Abstract

In this paper we consider the suppression of bottomonium states in ultrarelativistic heavy ion collisions. We compute the suppression as a function of centrality, rapidity, and transverse momentum for the states Υ(1s), Υ(2s), Υ(3s), χ b1 , and χ b2 . Using this information, we then compute the inclusive Υ(1s) suppression as a function of centrality, rapidity, and transverse momentum including feed down effects. Calculations are performed for both RHIC √ s N N = 200 GeV Au-Au collisions and LHC √ s N N = 2.76 TeV Pb-Pb collisions. From the comparison of our theoretical results with data available from the STAR and CMS Collaborations we are able to constrain the shear viscosity to entropy ratio to be in the range 0.08 < η/S < 0.24. Our results are consistent with the creation of a high temperature quark-gluon plasma at both RHIC and LHC collision energies.

High transverse momentum quarkonium production and dissociation in heavy ion collisions

“…In our formalism, we have approximated the quarkonium wavefunction by the vacuum wavefunction, which is valid if the thermal effects on the quarkonium wavefunctions are small. The thermal wavefunctions (for example, those obtained by solving the Schrödinger equation with thermal potentials [2,[8][9][10]) will be wider in position space at higher temperature and therefore will dissociate more easily. Therefore a stronger suppression at LHC could be the evidence for thermalization effects at the level of the quarkonium wavefunction.…”

“…This picture suggests that it may be possible to observe sequential melting of narrower quarkonia as we explore thermal media of increasing temperatures [3,4]. Several studies (see [5] for a recent review) have calculated the modification of quarkonium yields in collisions at SPS, RHIC, and the LHC [6][7][8][9][10][11].…”

“…The microscopic input for the equations are the time scales for the formation and the dissociation of the quarkonia. Since the size of proto-quarkonium is small, it is typically assumed that the formation time t form for the "proto-quarkonium" to "expand" into the quarkonium wavefunction, is not significantly modified by the presence of the QGP [9]. Hence, t form in the rest frame of the meson is ∼ 1/(m Q v 2 ).…”

“…(Some equilibrium approaches [6] include effects of a finite time of formation by suppressing the decay rate.) For dissociation times, most studies use results for thermally equilibrated quarkonia [6,8,9]. For a quarkonium which is stationary or slowly moving through the thermal medium it might be safe to assume that it reaches thermal equilibrium with the medium.…”

“…For a quarkonium which is stationary or slowly moving through the thermal medium it might be safe to assume that it reaches thermal equilibrium with the medium. In this picture, the wavefunction of the quarkonium (the lowest Fock component) is better described by the solution of the Schrödinger equation with a modified potential that depends on the temperature [2,[8][9][10]. The potentials used are based on finite temperature lattice calculations of the potential between two static charges [33].…”