Abstract
We perform a comprehensive study of the time evolution of heavy-quarkonium states in an expanding hot QCD medium by implementing effective field theory techniques in the framework of open quantum systems. The formalism incorporates quarkonium production and its subsequent evolution in the fireball including quarkonium dissociation and recombination. We consider a fireball with a local temperature that is much smaller than the inverse size of the quarkonium and much larger than its binding energy. The calculation is performed at an accuracy that is leading-order in the heavy-quark density expansion and next-to-leading order in the multipole expansion. Within this accuracy, for a smooth variation of the temperature and large times, the evolution equation can be written as a Lindblad equation. We solve the Lindblad equation numerically both for a weakly-coupled quark-gluon plasma and a strongly-coupled medium. As an application, we compute the nuclear modification factor for the $\Upsilon(1S)$ and $\Upsilon(2S)$ states. We also consider the case of static quarks, which can be solved analytically. Our study fulfils three essential conditions: it conserves the total number of heavy quarks, it accounts for the non-Abelian nature of QCD and it avoids classical approximations.
Highlights
The main way in which heavy quarkonium is detected in heavy-ion collisions is through its decay into a lepton pair
From a mathematical point of view, the Lindblad equation follows from requiring the time evolution of the density matrix of the open quantum system to be Markovian, to preserve the trace, the equation to be linear in the density, and the corresponding linear operator to be a completely positive map
In the paper we present a systematic description in an effective field theory framework of heavyquark-antiquark systems as open quantum systems interacting with an environment made of light quarks and gluons, the fireball formed in heavy-ion collisions
Summary
The main way in which heavy quarkonium is detected in heavy-ion collisions is through its decay into a lepton pair. Under the condition (10), we can use potential NRQCD (pNRQCD), which provides a valid description of the quarkonium at energy scales below 1=a0 [5,6,7,8,9] In this effective field theory (EFT), the heavy-quark-antiquark system can be described in terms of a color-singlet field S and a color-octet field O instead of the fields ψ and χ of NRQCD. The above equation tells us that the emission rate of dileptons with the energy of a given quarkonium state n [q0 1⁄4 2M þ ReðEnÞ þ q2=4M] will be proportional to the projection of ρsðtF; tFÞ into that state at freeze-out time. A concise version of the evolution equations and their solution in the case of a strongly coupled plasma has been presented in [10]
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