Quarkonium semiclassical transport in quark-gluon plasma: factorization and quantum correction

Yao, Xiaojun; Mehen, Thomas

doi:10.1007/jhep02(2021)062

Title: Quarkonium semiclassical transport in quark-gluon plasma: factorization and quantum correction

Journal Article · Mon Feb 08 00:00:00 EST 2021 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/jhep02(2021)062· OSTI ID:1849607

^[1]; Mehen, Thomas ^[2]

Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Center for Theoretical Physics
Duke Univ., Durham, NC (United States). Dept. of Physics

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.

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Research Organization:: Duke Univ., Durham, NC (United States); Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Nuclear Physics (NP)

Grant/Contract Number:: FG02-05ER41368; SC0011090

OSTI ID:: 1849607

Journal Information:: Journal of High Energy Physics (Online), Vol. 2021, Issue 2; ISSN 1029-8479

Publisher:: Springer NatureCopyright Statement

Country of Publication:: United States

Language:: English

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Title: Quarkonium semiclassical transport in quark-gluon plasma: factorization and quantum correction

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