Heavy quarkonium dynamics beyond the binding energy over temperature expansion

Abstract

We revisit the pNRQCD open-quantum-system description of bottomonium in a quark-gluon plasma, writing the full master equation in a spherical basis and establishing a framework for its numerical treatment. The equation does not rely on an expansion in the ratio of the binding energy over the temperature, while retaining the Born, Markov, and dilute approximations. It depends on suitable convolutions of Coulombic Green's functions with real-time chromoelectric correlators, rather than a finite set of transport coefficients. It contains jump-operator contributions that enter with both positive and negative signs, so it is not of a Lindblad type. We utilize optimal operator rotations to minimize the negative sector and define a positive-sector approximation that retains only the optimized positive terms, obtaining in this way a Lindblad equation that can be simulated efficiently with the open-source code QTraj for arbitrary chromoelectric spectral functions. We treat the discarded sector as a systematic uncertainty associated with positivity-breaking effects of the pseudo-Lindblad generator. Positivity breaking effects can be attributed to the approximations made in the derivation of the quarkonium master equation, such as the Born--Markov approximations. Using a spectral model constrained by known infrared and ultraviolet limits, we compute the in-medium width and Bjorken-evolved survival probabilities of the $Υ(1\mathrm{S},2\mathrm{S},3\mathrm{S})$. The computations show the convergence of the binding-energy-over-temperature expansion at high temperatures and provide the first large-scale quantum-trajectory simulation results for bottomonium in the low temperature regime. We can thus follow the bottomonium evolution over the full temperature range relevant in heavy-ion collisions.