Abstract
We study quarkonium transport in the quark-gluon plasma by using the potential nonrelativistic QCD (pNRQCD) effective field theory and the framework of open quantum systems. We argue that the coupling between quarkonium and the thermal bath is weak using separation of scales, so the initial density matrix of the total system factorizes and the time evolution of the subsystem is Markovian. We derive the semiclassical Boltzmann equation for quarkonium by applying a Wigner transform to the Lindblad equation and carrying out a semiclassical expansion. We resum relevant interactions to all orders in the coupling constant at leading power of the nonrelativistic and multipole expansions. The derivation is valid for both weakly coupled and strongly coupled quark-gluon plasmas. We find reaction rates in the transport equation factorize into a quarkonium dipole transition function and a chromoelectric gluon distribution function. For the differential reaction rate, the definition of the momentum dependent chromoelectric gluon distribution function involves staple-shaped Wilson lines. For the inclusive reaction rate, the Wilson lines collapse into a straight line along the real time axis and the distribution becomes momentum independent. The relation between the two Wilson lines is analogous to the relation between the Wilson lines appearing in the gluon parton distribution function (PDF) and the gluon transverse momentum dependent parton distribution function (TMDPDF). The centrality dependence of the quarkonium nuclear modification factor measured by experiments probes the momentum independent distribution while the transverse momentum dependence and measurements of the azimuthal angular anisotropy may be able to probe the momentum dependent one. We discuss one way to indirectly constrain the quarkonium in-medium real potential by using the factorization formula and lattice calculations. The leading quantum correction to the semiclassical transport equation of quarkonium is also worked out. The study can be easily generalized to quarkonium transport in cold nuclear matter, which is relevant for quarkonium production in eA collisions in the future Electron-Ion Collider.
Highlights
Bound state above Tc ∼ 150 MeV, which is a rough estimate of the transition temperature from the QGP phase to the hadronic phase,1generation of this quarkonium state inside the QGP should be possible [5]
We study quarkonium transport in the quark-gluon plasma by using the potential nonrelativistic QCD effective field theory and the framework of open quantum systems
Quarkonium suppression has been intensively investigated in experiments at both the Relativistic Heavy Ion Collider (RHIC) and Large Hadron Collider (LHC)
Summary
We consider the following hierarchy of scales: M M v M v2, T, ΛQCD, where M is the heavy quark mass, v is the typical relative velocity between the heavy quark pair inside quarkonium, T is the temperature of the medium and ΛQCD is the nonperturbative scale of QCD. At leading order in the v expansion, which is the order we are working, quarkonium can only be a color singlet QQpair. The operators a(n†l)(pcm), b(p†r)el(pcm) and cApr(e†l)(pcm) act on the Fock space to annihilate (create) composite particles with the c.m. momentum pcm and the corresponding quantum numbers in the relative motion These quantum numbers can be nl for bound singlet states, prel for unbound singlet states and color A and prel for unbound octet states. The dissociation and recombination of quarkonium occur via the dipole interaction between the color singlet and octet states. Quarkonium is treated as a color singlet QQpair in this work, consistent with the leading power (in v) calculation
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