Quarkonium semiclassical transport in quark-gluon plasma: factorization and quantum correction
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 usin...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
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Springer Berlin Heidelberg
2021
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| Online Access: | https://hdl.handle.net/1721.1/132035 |
| _version_ | 1811085512773992448 |
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| author | Yao, Xiaojun Mehen, Thomas |
| author2 | Massachusetts Institute of Technology. Center for Theoretical Physics |
| author_facet | Massachusetts Institute of Technology. Center for Theoretical Physics Yao, Xiaojun Mehen, Thomas |
| author_sort | Yao, Xiaojun |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T13:10:46Z |
| format | Article |
| id | mit-1721.1/132035 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T13:10:46Z |
| publishDate | 2021 |
| publisher | Springer Berlin Heidelberg |
| record_format | dspace |
| spelling | mit-1721.1/1320352023-12-19T21:12:19Z Quarkonium semiclassical transport in quark-gluon plasma: factorization and quantum correction Yao, Xiaojun Mehen, Thomas Massachusetts Institute of Technology. Center for Theoretical Physics 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. 2021-09-20T17:41:34Z 2021-09-20T17:41:34Z 2021-02-08 2021-02-11T16:29:02Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/132035 Journal of High Energy Physics. 2021 Feb 08;2021(2):62 PUBLISHER_CC en https://doi.org/10.1007/JHEP02(2021)062 Creative Commons Attribution https://creativecommons.org/licenses/by/4.0/ The Author(s) application/pdf Springer Berlin Heidelberg Springer Berlin Heidelberg |
| spellingShingle | Yao, Xiaojun Mehen, Thomas Quarkonium semiclassical transport in quark-gluon plasma: factorization and quantum correction |
| title | Quarkonium semiclassical transport in quark-gluon plasma: factorization and quantum correction |
| title_full | Quarkonium semiclassical transport in quark-gluon plasma: factorization and quantum correction |
| title_fullStr | Quarkonium semiclassical transport in quark-gluon plasma: factorization and quantum correction |
| title_full_unstemmed | Quarkonium semiclassical transport in quark-gluon plasma: factorization and quantum correction |
| title_short | Quarkonium semiclassical transport in quark-gluon plasma: factorization and quantum correction |
| title_sort | quarkonium semiclassical transport in quark gluon plasma factorization and quantum correction |
| url | https://hdl.handle.net/1721.1/132035 |
| work_keys_str_mv | AT yaoxiaojun quarkoniumsemiclassicaltransportinquarkgluonplasmafactorizationandquantumcorrection AT mehenthomas quarkoniumsemiclassicaltransportinquarkgluonplasmafactorizationandquantumcorrection |