Heavy quarkonium spin transport in a hot medium

Abstract

We investigate the in-medium spin transport of heavy quarkonium using an open-quantum-system approach based on potential nonrelativistic QCD. We express the heavy quarkonium dilepton decay angular distribution in terms of late-time quarkonium spin-dependent distribution functions. Working in the quantum-optical regime, where the inverse quarkonium size is much larger than the binding energy and the binding energy is comparable to or larger than the medium temperature $T$, we derive a spin-dependent quantum master equation incorporating both dissociation and regeneration, followed by the corresponding projected semiclassical Boltzmann equations. At leading order in the coupling, we retain the recoil corrections of relative order $T/M$ that contribute to the leading spin-dependent collision kernel. Here $M$ denotes the heavy-quark mass. At zeroth order in fluid gradients, we show that the relative motion between quarkonium and the medium supplies the leading anisotropy, while spin-chromomagnetic and spin-orbit interactions both contribute to the leading nonzero spin-alignment kernel. As an exploratory phenomenological application, we also estimate the medium-induced polarization parameter $λ_θ$ of bottomonium $Υ(1\text{S})$ using a simplified rate equation with background density matrices obtained from the Lindblad equation using QTraj. Within this simplified treatment, the resulting medium-induced polarization is found to be very small while a naive rescaling for charmonium can qualitatively describe the polarization of charmonium.