Dynamical dissociation of quarkonia by wave function decoherence

We investigate the real-time evolution of quarkonium bound states in a quark-gluon plasma in one dimension using an improved QCD-based stochastic potential model. This model describes the quarkonium dynamics in terms of a Schrödinger equation with an in-medium potential and two noise terms encoding the residual interactions between the heavy quarks and the medium. The probabilities of bound states in a static medium and in a boost-invariantly expanding quark-gluon plasma are discussed. We draw two conclusions from our results: One is that the outcome of the stochastic potential model is qualitatively consistent with the experimental data in relativistic heavy-ion collisions. The other is that the noise plays an important role in order to describe quarkonium dynamics in medium; in particular, it causes decoherence of the quarkonium wave function. The effectiveness of decoherence is controlled by a new length scale $l_{\mathrm{corr}}$. It represents the noise correlation length and its effect has not been included in existing phenomenological studies.

Figure 1

Time evolution of the ground state occupation probability in the stochastic potential model in a static QGP. Both the initial state and the projected state are the ground state in the Debye screened potential. The noise correlation length ranges from $l_{\mathrm{corr}}=0.04$ to 0.96 fm.

Figure 2

Time evolution of the ground state occupation probability computed with the stochastic potential and complex potential in a static QGP. Both the initial state and the projected state are the ground state in the Debye screened potential. The noise correlation length in the stochastic potential is $l_{\mathrm{corr}}=0.48$, 0.16 fm.

Figure 3

Time evolution of the occupation probability of quarkonium bound states (the ground, the first excited, and the second excited states) in the stochastic potential model in a Bjorken-expanding QGP. Both the initial states and the projected states are the bound states in the vacuum Cornell potential. The left figure shows the calculation for bottomonium and the right for charmonium. For comparison purposes, we also plot the probability of the ground state from an evolution only with the Debye screened potential, i.e., without noise (dashed lines).