Approach to equilibrium of quarkonium in quark-gluon plasma

We calculate the dissociation and recombination rates of $\mathrm{{\rm Y}}\left(1S\right)$ in quark-gluon plasma by using potential nonrelativistic QCD. We then study the dynamical in-medium evolution of the $b\overline{b}-\mathrm{{\rm Y}}$ system in a periodic box via the Boltzmann equation and explore how the system reaches equilibrium. We find that interactions between the free heavy quarks and the medium are necessary for the system to reach equilibrium. We find that the angular distribution of $\mathrm{{\rm Y}}\left(1S\right)$ probes the stages at which recombination occurs. Finally, we study the system under a longitudinal expansion and show that different initial conditions evolve to distinct final ratios of hidden and open $b$ flavors. We argue that experimental measurements of the ratio could address open questions in the quarkonium production in heavy ion collisions.

Figure 1

Transition between $\mathrm{{\rm Y}}\left(1S\right)$ and $b\overline{b}$ octet by absorbing or emitting an on-shell gluon. Single line indicates quarkonium while double lines represent unbound octet.

Figure 2

Simulations at $T=350$ MeV. $N_b=N_{\overline{b}}=40$ and $N_{\mathrm{{\rm Y}}}=10$ (case 1) with thermal momenta (upper) and $N_b=N_{\overline{b}}=50$ and $N_{\mathrm{{\rm Y}}}=0$ (cases 2, 3) with uniform momenta (lower). The dashed lines indicate the abundance ratio at equilibrium.

Figure 3

Angular anisotropy $v_2$ of $\mathrm{{\rm Y}}$ from recombinations of $b,\overline{b}$ with anisotropic momentum distributions for different values of $v_2^{\left(b\right)}$.

Figure 4

Thermal rates of expansion, dissociation, HQ thermalization and recombination.

Figure 5

Evolution of the $\mathrm{{\rm Y}}\left(1S\right)$ fraction in QGP undergoing a boost invariant expansion. The upper (yellow) and lower (purple) solid curves correspond to the cases where all $b,\overline{b}$ quarks are assumed to be initially bound and free, respectively. The horizontal dotted line indicates the $\mathrm{{\rm Y}}\left(1S\right)$ fraction measured in pp collisions. The middle (red) solid curve represents the average of the upper and lower ones weighted in such a way that it starts at the measured $pp$ $\mathrm{{\rm Y}}\left(1S\right)$ fraction.