Quarkonium in-medium transport equation derived from first principles

Yao, Xiaojun; Mehen, Thomas

doi:10.1103/physrevd.99.096028

Title: Quarkonium in-medium transport equation derived from first principles

Journal Article · 31 May 2019 · Physical Review. D.

DOI: https://doi.org/10.1103/physrevd.99.096028 · OSTI ID:1523685

Yao, Xiaojun ^[1]; Mehen, Thomas ^[1]

Duke Univ., Durham, NC (United States)

We use the open quantum system formalism to study the dynamical in-medium evolution of quarkonium. The system of quarkonium is described by potential nonrelativistic QCD while the environment is a weakly coupled quark-gluon plasma in local thermal equilibrium below the melting temperature of the quarkonium. Under the Markovian approximation, it is shown that the Lindblad equation leads to a Boltzmann transport equation if a Wigner transform is applied to the system density matrix. Our derivation illuminates how the microscopic time reversibility of QCD is consistent with the time-irreversible in-medium evolution of quarkonium states. Static screening, dissociation, and recombination of quarkonium are treated in the same theoretical framework. In addition, quarkonium annihilation is included in a similar way, although the effect is negligible for the phenomenology of the current heavy ion collision experiments. The methods used here can be extended to study quarkonium dynamical evolution inside a strongly coupled QGP, a hot medium out of equilibrium, or cold nuclear matter, which is important to studying quarkonium production in heavy ion, proton-ion, and electron-ion collisions.

View Journal Article

Cite

Export

Save

Research Organization:: Duke Univ., Durham, NC (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: FG02-05ER41367; FG02-05ER41368

OSTI ID:: 1523685

Alternate ID(s):: OSTI ID: 1609635

Journal Information:: Physical Review. D., Vol. 99, Issue 9; ISSN 2470-0010

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 66 works

Citation information provided by
Web of Science

References (75)

Modern Quantum Mechanics Sakurai, J. J.; Napolitano, Jim https://doi.org/10.1017/9781108499996	book	January 2017
High transverse momentum quarkonium production and dissociation in heavy ion collisions Sharma, Rishi; Vitev, Ivan Physical Review C, Vol. 87, Issue 4 https://doi.org/10.1103/PhysRevC.87.044905	journal	April 2013
Open effective field theories from deeply inelastic reactions Braaten, Eric; Hammer, H. -W.; Lepage, G. Peter Physical Review D, Vol. 94, Issue 5 https://doi.org/10.1103/PhysRevD.94.056006	journal	September 2016
Modern Quantum Mechanics Sakurai, J. J.; Liboff, Richard L. American Journal of Physics, Vol. 54, Issue 7 https://doi.org/10.1119/1.14491	journal	July 1986
Heavy quark master equations in the Lindblad form at high temperatures Akamatsu, Yukinao Physical Review D, Vol. 91, Issue 5 https://doi.org/10.1103/PhysRevD.91.056002	journal	March 2015
Heavy quark bound states in a quark–gluon plasma: Dissociation and recombination Blaizot, Jean-Paul; De Boni, Davide; Faccioli, Pietro Nuclear Physics A, Vol. 946 https://doi.org/10.1016/j.nuclphysa.2015.10.011	journal	February 2016
Quantum and classical dynamics of heavy quarks in a quark-gluon plasma Blaizot, Jean-Paul; Escobedo, Miguel Angel Journal of High Energy Physics, Vol. 2018, Issue 6 https://doi.org/10.1007/JHEP06(2018)034	journal	June 2018
Charmonium production from nonequilibrium charm and anticharm quarks in quark-gluon plasma Song, Taesoo; Han, Kyong Chol; Ko, Che Ming Physical Review C, Vol. 85, Issue 5 https://doi.org/10.1103/PhysRevC.85.054905	journal	May 2012
Erratum: Rigorous QCD analysis of inclusive annihilation and production of heavy quarkonium [Phys. Rev. D 51 , 1125 (1995)] Bodwin, Geoffrey T.; Braaten, Eric; Lepage, G. Peter Physical Review D, Vol. 55, Issue 9 https://doi.org/10.1103/PhysRevD.55.5853	journal	May 1997
Thermal width and gluo-dissociation of quarkonium in pNRQCD Brambilla, Nora; Escobedo, Miguel Ángel; Ghiglieri, Jacopo Journal of High Energy Physics, Vol. 2011, Issue 12 https://doi.org/10.1007/JHEP12(2011)116	journal	December 2011
Bottomonia suppression in 2.76 TeV Pb-Pb collisions Krouppa, Brandon; Ryblewski, Radoslaw; Strickland, Michael Physical Review C, Vol. 92, Issue 6 https://doi.org/10.1103/PhysRevC.92.061901	journal	December 2015
Charmonium production in relativistic heavy-ion collisions Song, Taesoo; Han, Kyong Chol; Ko, Che Ming Physical Review C, Vol. 84, Issue 3 https://doi.org/10.1103/PhysRevC.84.034907	journal	September 2011
Dynamical dissociation of quarkonia by wave function decoherence Kajimoto, Shiori; Akamatsu, Yukinao; Asakawa, Masayuki Physical Review D, Vol. 97, Issue 1 https://doi.org/10.1103/PhysRevD.97.014003	journal	January 2018
Quarkonium above deconfinement as an open quantum system Young, C.; Dusling, K. Physical Review C, Vol. 87, Issue 6 https://doi.org/10.1103/PhysRevC.87.065206	journal	June 2013
Collisional and thermal dissociation of J / ψ and ϒ states at the LHC Aronson, Samuel; Borras, Evan; Odegard, Brunel Physics Letters B, Vol. 778 https://doi.org/10.1016/j.physletb.2018.01.038	journal	March 2018
Heavy quarkonia in a medium as a quantum dissipative system: master-equation approach Borghini, Nicolas; Gombeaud, Clément The European Physical Journal C, Vol. 72, Issue 5 https://doi.org/10.1140/epjc/s10052-012-2000-7	journal	May 2012
Imaginary part of the static gluon propagator in an anisotropic (viscous) QCD plasma Dumitru, Adrian; Guo, Yun; Strickland, Michael Physical Review D, Vol. 79, Issue 11 https://doi.org/10.1103/PhysRevD.79.114003	journal	June 2009
Is bottomonium suppression in proton-nucleus and nucleus-nucleus collisions at LHC energies due to the same effects? Ferreiro, E. G.; Lansberg, J. P. Journal of High Energy Physics, Vol. 2018, Issue 10 https://doi.org/10.1007/JHEP10(2018)094	journal	October 2018
Fate of in-medium heavy quarks via a Lindblad equation De Boni, Davide Journal of High Energy Physics, Vol. 2017, Issue 8 https://doi.org/10.1007/JHEP08(2017)064	journal	August 2017
Complex Heavy-Quark Potential at Finite Temperature from Lattice QCD Rothkopf, Alexander; Hatsuda, Tetsuo; Sasaki, Shoichi Physical Review Letters, Vol. 108, Issue 16 https://doi.org/10.1103/PhysRevLett.108.162001	journal	April 2012
Color screening in ( 2 + 1 )-flavor QCD Bazavov, A.; Brambilla, N.; Petreczky, P. Physical Review D, Vol. 98, Issue 5 https://doi.org/10.1103/PhysRevD.98.054511	journal	September 2018
Statistical hadronization of charm in heavy-ion collisions at SPS, RHIC and LHC Andronic, A.; Braun-Munzinger, P.; Redlich, K. Physics Letters B, Vol. 571, Issue 1-2 https://doi.org/10.1016/j.physletb.2003.07.066	journal	October 2003
Open Quantum Systems Far from Equilibrium Schaller, Gernot Lecture Notes in Physics https://doi.org/10.1007/978-3-319-03877-3	book	January 2014
Bottomonia suppression in relativistic heavy-ion collisions Song, Taesoo; Han, Kyong Chol; Ko, Che Ming Physical Review C, Vol. 85, Issue 1 https://doi.org/10.1103/PhysRevC.85.014902	journal	January 2012
Doubly heavy baryons, heavy quark-diquark symmetry, and nonrelativistic QCD Fleming, Sean; Mehen, Thomas Physical Review D, Vol. 73, Issue 3 https://doi.org/10.1103/PhysRevD.73.034502	journal	February 2006
J/ψ suppression by quark-gluon plasma formation Matsui, T.; Satz, H. Physics Letters B, Vol. 178, Issue 4 https://doi.org/10.1016/0370-2693(86)91404-8	journal	October 1986
Toward an understanding of the single electron data measured at the BNL Relativistic Heavy Ion Collider (RHIC) Gossiaux, P. B.; Aichelin, J. Physical Review C, Vol. 78, Issue 1 https://doi.org/10.1103/PhysRevC.78.014904	journal	July 2008
Quantum and Classical Dynamics of Heavy Quarks in a Quark-Gluon Plasma Escobedo, Miguel Ángel; Blaizot, Jean-Paul Nuclear Physics A, Vol. 982 https://doi.org/10.1016/j.nuclphysa.2018.10.025	journal	February 2019
Static quark-antiquark pairs at finite temperature Brambilla, Nora; Ghiglieri, Jacopo; Vairo, Antonio Physical Review D, Vol. 78, Issue 1 https://doi.org/10.1103/PhysRevD.78.014017	journal	July 2008
Bottomonium production at s NN = 200 GeV and s NN = 5.5 TeV Grandchamp, L.; Lumpkins, S.; Sun, D. Physical Review C, Vol. 73, Issue 6 https://doi.org/10.1103/PhysRevC.73.064906	journal	June 2006
How much do heavy quarks thermalize in a heavy ion collision? Moore, Guy D.; Teaney, Derek Physical Review C, Vol. 71, Issue 6 https://doi.org/10.1103/PhysRevC.71.064904	journal	June 2005
Heavy quarkonium suppression in a fireball Brambilla, Nora; Escobedo, Miguel A.; Soto, Joan Physical Review D, Vol. 97, Issue 7 https://doi.org/10.1103/PhysRevD.97.074009	journal	April 2018
Bottomium suppression in PbPb collisions at LHC energies Nendzig, Felix; Wolschin, Georg Journal of Physics G: Nuclear and Particle Physics, Vol. 41, Issue 9 https://doi.org/10.1088/0954-3899/41/9/095003	journal	July 2014
Bulk viscous corrections to screening and damping in QCD at high temperatures Du, Qianqian; Dumitru, Adrian; Guo, Yun Journal of High Energy Physics, Vol. 2017, Issue 1 https://doi.org/10.1007/JHEP01(2017)123	journal	January 2017
Thermal width and quarkonium dissociation by inelastic parton scattering Brambilla, Nora; Escobedo, Miguel Ángel; Ghiglieri, Jacopo Journal of High Energy Physics, Vol. 2013, Issue 5 https://doi.org/10.1007/JHEP05(2013)130	journal	May 2013
Quantum dissipation of a heavy quark from a nonlinear stochastic Schrödinger equation Akamatsu, Yukinao; Asakawa, Masayuki; Kajimoto, Shiori Journal of High Energy Physics, Vol. 2018, Issue 7 https://doi.org/10.1007/JHEP07(2018)029	journal	July 2018
From reversible quantum microdynamics to irreversible quantum transport Rau, J.; Müller, B. Physics Reports, Vol. 272, Issue 1 https://doi.org/10.1016/0370-1573(95)00077-1	journal	July 1996
Diffusion of charmed quarks in the quark-gluon plasma Svetitsky, Benjamin Physical Review D, Vol. 37, Issue 9 https://doi.org/10.1103/PhysRevD.37.2484	journal	May 1988
Effective field theory of dissipative fluids Crossley, Michael; Glorioso, Paolo; Liu, Hong Journal of High Energy Physics, Vol. 2017, Issue 9 https://doi.org/10.1007/JHEP09(2017)095	journal	September 2017
Modern Quantum Mechanics Sakurai, J. J.; Napolitano, Jim Cambridge University Press https://doi.org/10.1017/9781108587280	book	January 2020
Stochastic potential and quantum decoherence of heavy quarkonium in the quark-gluon plasma Akamatsu, Yukinao; Rothkopf, Alexander Physical Review D, Vol. 85, Issue 10 https://doi.org/10.1103/PhysRevD.85.105011	journal	May 2012
Erratum to: Is bottomonium suppression in proton-nucleus and nucleus-nucleus collisions at LHC energies due to the same effects? Ferreiro, E. G.; Lansberg, J. P. Journal of High Energy Physics, Vol. 2019, Issue 3 https://doi.org/10.1007/JHEP03(2019)063	journal	March 2019
Heavy quarks in turbulent QCD plasmas Mrówczyński, Stanisław The European Physical Journal A, Vol. 54, Issue 3 https://doi.org/10.1140/epja/i2018-12478-5	journal	March 2018
The renormalization group improvement of the QCD static potentials Pineda, Antonio; Soto, Joan Physics Letters B, Vol. 495, Issue 3-4 https://doi.org/10.1016/S0370-2693(00)01261-2	journal	December 2000
J / ψ Production in Quark-Gluon Plasma Yan, Li; Zhuang, Pengfei; Xu, Nu Physical Review Letters, Vol. 97, Issue 23 https://doi.org/10.1103/PhysRevLett.97.232301	journal	December 2006
Potential NRQCD: an effective theory for heavy quarkonium Brambilla, Nora; Pineda, Antonio; Soto, Joan Nuclear Physics B, Vol. 566, Issue 1-2 https://doi.org/10.1016/S0550-3213(99)00693-8	journal	January 2000
J/ψ transverse momentum distribution in high energy nuclear collisions Liu, Yunpeng; Qu, Zhen; Xu, Nu Physics Letters B, Vol. 678, Issue 1 https://doi.org/10.1016/j.physletb.2009.06.006	journal	July 2009
Rigorous QCD analysis of inclusive annihilation and production of heavy quarkonium Bodwin, Geoffrey T.; Braaten, Eric; Lepage, G. Peter Physical Review D, Vol. 51, Issue 3 https://doi.org/10.1103/PhysRevD.51.1125	journal	February 1995
Strong diffusion effect of charm quarks on J / ψ production in Pb–Pb collisions at the LHC Zhao, Jiaxing; Chen, Baoyi Physics Letters B, Vol. 776 https://doi.org/10.1016/j.physletb.2017.11.014	journal	January 2018
Quarkonium production in heavy ion collisions: coupled Boltzmann transport equations Yao, Xiaojun; Ke, Weiyao; Xu, Yingru Nuclear Physics A, Vol. 982 https://doi.org/10.1016/j.nuclphysa.2018.10.005	journal	February 2019
Erratum: Approach to equilibrium of quarkonium in quark-gluon plasma [Phys. Rev. C 97 , 014908 (2018)] Yao, Xiaojun; Müller, Berndt Physical Review C, Vol. 97, Issue 4 https://doi.org/10.1103/PhysRevC.97.049903	journal	April 2018
Evidence for charmonium generation at the phase boundary in ultra-relativistic nuclear collisions Andronic, A.; Braun-Munzinger, P.; Redlich, K. Physics Letters B, Vol. 652, Issue 5-6 https://doi.org/10.1016/j.physletb.2007.07.036	journal	September 2007
The heavy-quark potential in an anisotropic plasma Dumitru, Adrian; Guo, Yun; Strickland, Michael Physics Letters B, Vol. 662, Issue 1 https://doi.org/10.1016/j.physletb.2008.02.048	journal	April 2008
Color screening and regeneration of bottomonia in high-energy heavy-ion collisions Du, X.; He, M.; Rapp, R. Physical Review C, Vol. 96, Issue 5 https://doi.org/10.1103/PhysRevC.96.054901	journal	November 2017
Bottomonium continuous production from unequilibrium bottom quarks in ultrarelativistic heavy ion collisions Chen, Baoyi; Zhao, Jiaxing Physics Letters B, Vol. 772 https://doi.org/10.1016/j.physletb.2017.07.054	journal	September 2017
In-Medium Effects on Charmonium Production in Heavy-Ion Collisions Grandchamp, Loïc; Rapp, Ralf; Brown, Gerald E. Physical Review Letters, Vol. 92, Issue 21 https://doi.org/10.1103/PhysRevLett.92.212301	journal	May 2004
Heavy quarkonium in a weakly-coupled quark-gluon plasma below the melting temperature Brambilla, Nora; Escobedo, Miguel Ángel; Ghiglieri, Jacopo Journal of High Energy Physics, Vol. 2010, Issue 9 https://doi.org/10.1007/JHEP09(2010)038	journal	September 2010
Linearized Boltzmann-Langevin model for heavy quark transport in hot and dense QCD matter Ke, Weiyao; Xu, Yingru; Bass, Steffen A. Physical Review C, Vol. 98, Issue 6 https://doi.org/10.1103/PhysRevC.98.064901	journal	December 2018
Approach to equilibrium of quarkonium in quark-gluon plasma Yao, Xiaojun; Müller, Berndt Physical Review C, Vol. 97, Issue 1 https://doi.org/10.1103/PhysRevC.97.014908	journal	January 2018
A linearized Boltzmann-Langevin model for heavy quark transport in hot and dense QCD matter Ke, Weiyao; Xu, Yingru; Bass, Steffen A. Unpublished https://doi.org/10.13140/rg.2.2.10853.50400	text	January 2018
Quarkonium production in heavy ion collisions: coupled Boltzmann transport equations Yao, Xiaojun; Ke, Weiyao; Xu, Yingru Proceedings of International Conference on Hard and Electromagnetic Probes of High-Energy Nuclear Collisions — PoS(HardProbes2018) https://doi.org/10.22323/1.345.0157	conference	April 2019
Static quark-antiquark pairs at finite temperature Brambilla, Nora; Ghiglieri, Jacopo; Petreczky, Peter arXiv https://doi.org/10.48550/arxiv.0804.0993	text	January 2008
J/psi Transverse Momentum Distribution in High Energy Nuclear Collisions Liu, Yunpeng; Qu, Zhen; Xu, Nu arXiv https://doi.org/10.48550/arxiv.0901.2757	text	January 2009
Quarkonium above deconfinement as an open quantum system Young, Clint; Dusling, Kevin arXiv https://doi.org/10.48550/arxiv.1001.0935	text	January 2010
Heavy quark master equations in the Lindblad form at high temperatures Akamatsu, Yukinao arXiv https://doi.org/10.48550/arxiv.1403.5783	text	January 2014
Heavy quark bound states in a quark-gluon plasma: dissociation and recombination Blaizot, Jean-Paul; De Boni, Davide; Faccioli, Pietro arXiv https://doi.org/10.48550/arxiv.1503.03857	text	January 2015
Effective field theory of dissipative fluids Crossley, Michael; Glorioso, Paolo; Liu, Hong arXiv https://doi.org/10.48550/arxiv.1511.03646	preprint	January 2015
Fate of in-medium heavy quarks via a Lindblad equation De Boni, Davide arXiv https://doi.org/10.48550/arxiv.1705.03567	text	January 2017
Quantum and Classical Dynamics of Heavy Quarks in a Quark-Gluon Plasma Blaizot, Jean-Paul; Escobedo, Miguel Angel arXiv https://doi.org/10.48550/arxiv.1711.10812	text	January 2017
The Renormalization Group Improvement of the QCD Static Potentials Pineda, Antonio; Soto, Joan arXiv https://doi.org/10.48550/arxiv.hep-ph/0007197	text	January 2000
How Much do Heavy Quarks Thermalize in a Heavy Ion Collision? Moore, Guy D.; Teaney, Derek arXiv https://doi.org/10.48550/arxiv.hep-ph/0412346	text	January 2004
Statistical hadronization of charm in heavy-ion collisions at SPS, RHIC and LHC Andronic, A.; Braun-Munzinger, P.; Redlich, K. arXiv https://doi.org/10.48550/arxiv.nucl-th/0303036	text	January 2003
From Reversible Quantum Microdynamics to Irreversible Quantum Transport Rau, J.; Müller, B. arXiv https://doi.org/10.48550/arxiv.nucl-th/9505009	text	January 1995
Heavy quarkonium spectrum and width in a weakly-coupled quark-gluon plasma Ghiglieri, Jacopo arXiv https://doi.org/10.48550/arxiv.1108.5875	preprint	January 2011
Relations between Heavy-light Meson and Quark Masses Brambilla, N.; Komijani, J.; Kronfeld, A. S. arXiv https://doi.org/10.48550/arxiv.1712.04983	text	January 2017

Cited By (12)

Finite volume effects on the quarkonium dissociation temperature in an impenetrable QGP sphere Cheng, Peng; Luo, Xiaofeng; Ping, Jialun Physical Review D, Vol. 100, Issue 1 https://doi.org/10.1103/physrevd.100.014027	journal	July 2019
Quantum Brownian motion of a heavy quark pair in the quark-gluon plasma Miura, Takahiro; Akamatsu, Yukinao; Asakawa, Masayuki Physical Review D, Vol. 101, Issue 3 https://doi.org/10.1103/physrevd.101.034011	journal	February 2020
Quarkonium inside the quark-gluon plasma: Diffusion, dissociation, recombination, and energy loss Yao, Xiaojun; Müller, Berndt Physical Review D, Vol. 100, Issue 1 https://doi.org/10.1103/physrevd.100.014008	journal	July 2019
An Effective Theory of Quarkonia in QCD Matter Makris, Yiannis; Vitev, Ivan Nuclear Physics A, Vol. 1005 https://doi.org/10.1016/j.nuclphysa.2020.121848	journal	January 2021
An effective theory of quarkonia in QCD matter Makris, Yiannis; Vitev, Ivan Journal of High Energy Physics, Vol. 2019, Issue 10 https://doi.org/10.1007/jhep10(2019)111	journal	October 2019
Quarkonium inside Quark-Gluon Plasma: Diffusion, Dissociation, Recombination and Energy Loss Yao, Xiaojun; Müller, Berndt arXiv https://doi.org/10.48550/arxiv.1811.09644	text	January 2018
Quantum Brownian motion of a heavy quark pair in the quark-gluon plasma Miura, Takahiro; Akamatsu, Yukinao; Asakawa, Masayuki arXiv https://doi.org/10.48550/arxiv.1908.06293	text	January 2019
Second law of thermodynamics for relativistic fluids formulated with relative entropy Dowling, Neil; Floerchinger, Stefan; Haas, Tobias Physical Review D, Vol. 102, Issue 10 https://doi.org/10.1103/physrevd.102.105002	journal	November 2020
Quarkonium Production in the QGP Rothkopf, Alexander Universe, Vol. 5, Issue 5 https://doi.org/10.3390/universe5050117	journal	May 2019
Improved Gauss law model and in-medium heavy quarkonium at finite density and velocity Lafferty, David; Rothkopf, Alexander arXiv https://doi.org/10.48550/arxiv.1906.00035	text	January 2019
Dark Matter bound-state formation at higher order: a non-equilibrium quantum field theory approach Binder, Tobias; Blobel, Burkhard; Harz, Julia arXiv https://doi.org/10.48550/arxiv.2002.07145	text	January 2020
Bottomonium suppression and elliptic flow from real-time quantum evolution Islam, Ajaharul; Strickland, Michael arXiv https://doi.org/10.48550/arxiv.2007.10211	text	January 2020

Figures / Tables (1)

FIG. 1(p. 6)

Similar Records

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

Journal Article · 2021 · Journal of High Energy Physics (Online) · OSTI ID:1849607

Yao, Xiaojun; Mehen, Thomas

Approach to equilibrium of quarkonium in quark-gluon plasma

Journal Article · 2018 · Physical Review. C · OSTI ID:1418073

Yao, Xiaojun; Müller, Berndt

Traces of nonequilibrium effects, initial condition, bulk dynamics, and elementary collisions in the charm observables

Journal Article · 2020 · Physical Review C · OSTI ID:1800265

Song, Taesoo; Moreau, Pierre; Xu, Yingru; +6 more

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
astronomy & astrophysics
physics
nonrelativistic QCD
open quantum systems
quark-gluon plasma
relativistic heavy-ion collisions
transport phenomena
quarkonia
Markovian processes
perturbative methods