Quarkonium formation time in relativistic heavy-ion collisions

TL;DR

This paper calculates the formation times of various quarkonia in relativistic heavy-ion collisions using a hydrodynamics model and lattice QCD data, showing how formation time impacts quarkonium survival in hot dense matter.

Contribution

It provides a novel calculation of quarkonium formation times incorporating in-medium properties and hydrodynamics, highlighting their dependence on collision centrality and impact on quarkonium survival.

Findings

$$(1S), $$(2S), $$(3S), $J/\u03a9$, and $\u03a8^\u2032$ form at 1.2, 6.6, 8.8, 5.8, and 11.0 fm/c respectively.

Formation times are shorter in semi-central collisions.

Including formation time effects increases the survivability of $$(1S) in hot dense matter.

Abstract

We calculate the quarkonium formation time in relativistic heavy-ion collisions from the space-time correlator of heavy quark vector currents in a hydrodynamics background with the initial nonequilibrium stage expanding only in the longitudinal direction. Using in-medium quarkonia properties determined with the heavy quark potential taken to be the free energy from lattice calculations and the fact that quarkonia can only be formed below their dissociation temperatures due to color screening, we find that $\Upsilon$(1S), $\Upsilon$(2S), $\Upsilon$(3S), $J/\psi$ and $\psi^\prime$ are formed, respectively, at 1.2, 6.6, 8.8, 5.8, and 11.0 fm/c after the quark pair are produced in central Au+Au collisions at the top energy of Relativistic Heavy Ion Collider (RHIC), and these times become shorter in semi-central collisions. We further show, as an example, that including the effect of formation time enhances appreciably the survivability of $\Upsilon$(1S) in the produced hot dense matter.