Bottomonium sequential suppression and strong heavy-quark potential in heavy-ion collisions

TL;DR

This study models bottomonium suppression in heavy-ion collisions using complex potentials in the Schrödinger equation, revealing that the suppression pattern can probe the strength of the heavy-quark potential in quark-gluon plasma.

Contribution

It introduces a parametrization of the heavy-quark potential between free and internal energies to explain bottomonium suppression patterns in heavy-ion collisions.

Findings

Real potential close to internal energy explains sequential suppression.

Weak potential leads to wave expansion and non-sequential suppression.

Sequential suppression pattern can probe the heavy-quark potential strength.

Abstract

We employ the time-dependent Schr\"odinger equation with different complex potentials to study the bottomonium sequential suppression in Pb-Pb collisions at $\sqrt{s_{NN}}=2.76$ TeV and 5.02 TeV and Au-Au collisions at $\sqrt{s_{NN}}=200$ GeV. Both color screening effect and the random scatterings with thermal partons are considered in the real and imaginary parts of the heavy-quark potentials. As the real part of the heavy-quark potential is between the free energy $F(T,r)$ and the internal energy $U(T,r)$ of heavy quarkonium, we parametrize different potentials with a function of $F$ and $U$ to evolve the bottomonium wave packages in the medium. We find that when the real part of the potential is close to $U(T,r)$, it can explain well the pattern of bottomonium sequential suppression where their nuclear modification factors satisfy the relation $R_{AA}(1s)>R_{AA}(2s)>R_{AA}(3s)$ observed in experiments. In the other limit of $F(T,r)$, bottomonium wave packages tend to expand due to weak attracted force, which results in evident transitions from $\Upsilon(2s)$ to $\Upsilon(3s)$ components and does not satisfy the sequential suppression pattern. We suggest that the bottomonium sequential suppression can be a probe of strong heavy-quark potential in the medium.